Forex market directional trends forecasting with Bidirectional-LSTM and enhanced DeepSense network using all member-based optimizer

Abstract

This study focuses on successful Forex trading by emphasizing the importance of identifying market trends and utilizing trend analysis for informed decision-making. The authors collected low-correlated currency pair datasets to mitigate multicollinearity risk. Authors developed a two-stage predictive model that combines regression and classification tasks, using the predicted closing price to determine entry and exit points. The model incorporates Bi-directional long short-term memory (Bi-LSTM) for improved price forecasting and higher highs and lower lows (HHs-HLs and LHs-LLs) to identify trend changes. They proposed an enhanced DeepSense network (DSN) with all member-based optimization (AMBO-DSN) to optimize decision variables of DSN. The performance of the models was compared to various machine learning, deep learning, and statistical approaches including support vector regressor (SVR), artificial neural network (ANN), auto-regressive integrated moving average (ARIMA), vanilla-LSTM (V-LSTM), and recurrent neural network (RNN). The optimized form of DSN using genetic algorithm (GA), particle swarm optimization (PSO), and differential evolution (DE) was compared with AMBO-DSN, yielding satisfactory results that demonstrated comparable quality to the observed trends on the original currency pairs. The effectiveness and reliability of the AMBO-DSN approach in forecasting trends for USD/EUR, AUD/JPY, and CHF/INR currency pairs were validated through statistical analysis while considering computational cost.

Keywords

Forex market forecasting forex trend forecasting long short-term memory (LSTM)bi-directional LSTM deepSense network (DSN)all member-based optimizer (AMBO)

1. Introduction

Forecasting of currency exchange in Forex market provides a platform to predict the current and future exchange price of currencies under consideration and perceiving the market trends such as; up-trends (higher lows), down-trends (lower highs) or side-ways (ranging) utilizing the historical data and various facts affecting this market [1, 2, 3, 4, 5]. The volatility of this market makes the forecasting more difficult than the economic fundamentals that are supposed to determine the market movements. The literature suggests the basic approach of determining the supply and demand is to understand the investors’ plan of purchase to acquire or sell currencies in near future. Also, the investors and traders must have thorough understanding of market drivers, current status of relationship between markets, their reason of relationship, various charts, cause of patterns and signals, previous price movements, consensus in other markets, the suitable time to trade etc. [2, 6, 7]. The analysts are mainly focussing on those fundamental facts and various statistical and forecasting tools to identify the correct market signal where the current exchange rate is heading next [8, 9]. Identifying market trends and understanding profitable entry and exit points are key to success in the Forex market [4, 5]. Trend analysis plays a crucial role in market analysis, providing insights into market direction, helping traders make informed decisions on trade timing and position size. It also aids in identifying support and resistance levels for setting stop-loss and take-profit levels. By focusing on trends, traders can avoid impulsive decisions based on short and long term fluctuations, improving their chances of success [6, 7, 8, 9, 10].

Researchers and professionals are increasingly utilizing machine learning (ML) and deep learning (DL) techniques for trend analysis in the financial market [11, 12, 13]. DL strategies, including artificial neural networks (ANNs) and their variants, combined with macroeconomics and technical indicators, have demonstrated the ability to predict future prices and trends in Forex data. DL strategies offer several advantages for Forex market analysis. They can handle large volumes of complex and unstructured data, enabling a comprehensive market analysis. DL algorithms can learn from data patterns and trends, making accurate predictions and identifying profitable trading opportunities. This is beneficial for traders employing quantitative trading strategies. DL algorithms continuously adapt and improve, allowing traders to stay ahead of the market and adjust their strategies accordingly and empower traders to make informed decisions and achieve greater success [12, 13, 14, 15]. LSTM and its variants are popular DL strategies for Forex market prediction with several advantages [15, 16]. LSTMs excel at processing sequential data, such as time-series data, capturing temporal dependencies and patterns for accurate market predictions. Their ability to retain relevant information over a long period enables better predictions for medium to long-term trades [17, 18, 19]. Moreover, LSTMs can be trained with smaller datasets, reducing the need for extensive data collection. Another promising approach gaining popularity is the DeepSense network (DSN), which combines CNN and RNN to extract spatial and temporal features from time series data [20, 21, 22, 23]. CNNs capture patterns and trends, while RNNs model temporal dependencies, making them suitable for time series analysis [22, 23, 24, 25]. The DSN network, trained with labelled time series data, learns to predict output based on input data, and can be used for predictions on new data [24, 25, 26, 27, 28].

This paper investigates various DL strategies, including Vanilla-LSTM (V-LSTM), Bidirectional-LSTM (Bi-LSTM) [1, 3, 29, 30, 31, 32] along with RNN, support vector regressor (SVR) [33], ANN, autoregressive integrated moving average (ARIMA) [34] and DSN [20, 21, 22, 23, 24, 25, 26, 27, 28]. It also integrates the all member-based optimizer (AMBO) [35] meta-heuristic optimizer with the DSN network to enhance classification accuracy and improve understanding of Forex market trends. The study aims to forecast the closing price and directional movements of currency pairs using trend analysis over short-term predictive horizons. This study achieved several objectives such as;

(a)
To address multicollinearity, low-correlation datasets of three currency pairs are collected, enabling the model to capture distinct factors for each pair and enhance prediction accuracy.
(b)
Augmenting the currency pairs with trend-based indicators namely moving average (MA), moving average convergence divergence (MACD), relative strength index (RSI), and on balance volume (OBV) [36, 37], a two-stage predictive model is developed, incorporating regression and classification tasks. This feature augmentation helps identify hidden relationships, generate new features, and provide trading insights.
(c)
Bi-LSTM is explored for closing price forecasting with augmented attributes (AAs). Its ability to process time series data in both directions, retain information for longer periods, and handle nonlinear relationships makes it a promising tool for Forex market forecasting. The Bi-LSTM has been shown to outperform other traditional time series models such as; ARIMA, ANN, SVR, V-LSTMs [16, 17, 18, 19, 29, 30, 31] and RNNs [13, 14, 15, 38, 39, 40, 41], making it a promising tool for Forex market forecasting;
(d)
Trend directions of currency pairs are obtained using higher highs and lower lows (HHs-HLs and LHs-LLs) [42, 43, 44, 45] from predicted closing prices. These trend indicators help traders make better decisions, avoid false signals, and reduce prediction risk.
(e)
An enhanced DSN network using AMBO is proposed for trend analysis. DSN extracts high-level representations from heterogeneous time-series data, while AMBO optimizes the model’s decision variables for improved performance and adaptability to market conditions.
(f)
Performance of the proposed regression and classification models is recorded and validated using various ML, DL, and optimization strategies [11, 12, 13, 14, 15].

The rest of work is organized as follows; the Section 2 reviews few recent literatures on Forex market trading and trend strategies, followed by a strong background detail of this proposed work in Section 3. The Section 4 discusses the experimentation, result analysis and validation of the proposed forecasting model. The discussions on key observations of this study are given in Section 5 and finally, the Section 6 concludes the work with some future scopes of this work.
2. Literature survey

DL strategies have emerged as promising tools for accurate and reliable predictions in Forex market. Researchers have explored CNNs, RNNs, LSTMs, and deep belief networks for financial market forecasting and trend analysis. CNNs extract features and capture non-linear relationships, achieving accuracies above 90%. RNNs model dynamic relationships with accuracies above 95%. LSTMs and their variants handle long-term dependencies and achieve accuracies above 97%. This section reviews the current research on these DL methods and their hybrid forms for financial market predictions.

Lu et al. [46] proposed a combined CNN-LSTM model to analyze relationships among time series data for predicting stock prices. Zhang et al. [47] utilized temporal convolutional networks (TCNs) to accurately estimate volatility and VaR for financial applications, and outperformed other models in terms of root mean square error (RMSE) and mean absolute error (MAE). Similarly, Zou et al. [48] proposed a new multiscale approach for estimating value at risk (VaR) in crude oil markets using ARMA-GARCH models and a CNN-based nonlinear ensemble model, which produced improved forecasting accuracy. Durairaj and Mohan [49] proposed a hybrid model combining Chaos theory, CNN, and polynomial regression for financial time series prediction, which outperformed several used models in various performance metrics. André et al. [50] proposed a new approach, DESCINet, using CNNs in a binary tree structure with skip connections to capture temporal relationships within a sequence, and significantly improved forecast accuracy on five real-life datasets.

A novel ANN architecture was suggested, integrating multi-layer perceptron (MLP) and ERNNs with a stochastic time effective function by Wang and Wang in [51]. This fusion aimed to enhance the precision of forecasting crude oil price fluctuations. Encouraging results were observed, demonstrating the model’s effectiveness in predicting four distinct time series indices. Barkan et al. [52] proposed a hierarchical RNN model to predict disaggregated inflation components of CPI. The model significantly outperformed existing inflation prediction baselines. Nasirtafreshi [53] proposed a LSTM-based RNN model for cryptocurrency transaction analysis. The model showed superior performance compared to other similar methods. Dey et al. [54] compared the performance of RNN, LSTM, and GRU models for predicting stock prices using three companies’ datasets. The study revealed that LSTM and GRU models outperformed RNN, with GRU producing fewer errors compared to LSTM. Hyunsun and Choi [55] proposed hybrid DL models combining RNN-based models such as CNN-LSTM, GRU-CNN, and ensemble models for forecasting stock market indices. The study also introduced averaging of high and low prices as a novel feature.

Pham et al. [16] used DL techniques to predict stock prices for 20 companies in the VN-index stock exchange over a period of 5 years, and evaluated the effectiveness of three different variations of LSTM (Vanilla, Stacked, Bi-directional). A comprehensive study by Lawi et al. [17] put forth a collection of eight novel architectural models for stock price forecasting. These models involved the fusion of LSTM and GRU models with four distinct NN block architectures. To gauge their effectiveness, the performance of these models was assessed using three different accuracy measures. Hum et al. [18] proposed a single layer LSTM model to forecast the closing price of the S&P 500 index for the following day. This model incorporated a combination of nine predictors to enhance its predictive capabilities. An LSTM enforced decision support system was created specifically for swing traders in the Indian stock market by Banik et al. [19]. This system was designed to provide accurate analysis and prediction of future stock values. By incorporating a range of technical indicators, the system demonstrated a high level of accuracy in forecasting future stock values.

Trend analysis is crucial in Forex markets for predicting currency pair movements, enabling informed trading decisions, risk management, and identifying up-trends and down-trends. DL techniques have been explored for Forex market forecasting and trend analysis. It provides an edge in trading, facilitates risk management by identifying support and resistance levels, and helps plan for the long term. Multiple studies have investigated the potential of deep learning-based techniques for Forex market and trend forecasting. Das et al. [44] proposed a deep network-based system to predict currency pairs’ closing prices and used technical indicators to validate the predictions. Dash et al. [45] developed a two-stage algorithmic framework that used a deep predictive coding network to predict exchange prices and trend analysis tools to identify market trends. Sadeghi et al. [56] combined ensemble multi-class support vector machine (SVM) and fuzzy NSGA-II to handle uncertainty in technical indicators and optimize hyper-parameters for better trading performance.

An intriguing study introduced a novel ensemble DL approach known as LSTM-B by Sun et al. [57]. This approach effectively combines LSTM and the bagging ensemble learning strategy, aiming to achieve precise forecasts of exchange rates and enhance profitability in exchange rate trading. The authors emphasize that previous research on exchange rate forecasts has predominantly focused on forecast validity, neglecting the broader perspective of professional trading advice. Accordingly, the authors argue that assessing how these ensemble learning approaches can inform trading decisions holds greater significance. These studies not only demonstrate the potential of DL-based techniques in Forex trading but also provide valuable insights for developing effective trading systems. Inspired by these findings, we have undertaken an empirical design of a two-stage Forex currency prediction model, as well as a market trend forecasting model.

3. Methodologies adopted

This section discusses the various trend-based indicators, DL based tools, techniques, strategies and optimization techniques used for the experimentation, result analysis and validation along with a detailed discussion on the design of improved DSN network for classification task.

3.1 Trend-based indicators

Forex traders employ trend-based indicators like MA, MACD, RSI, OBV, and Ichimoku Kinko Hyo [36, 37] to predict price movements. These indicators use past price data to calculate moving averages, momentum, and technical factors, generating buy or sell signals. For example, moving average crossovers are commonly used. Trend-based indicators provide information on price trend direction and strength based on mathematical calculations using historical data. This study focuses on MA, MACD, RSI, and OBV indicators for short-term predictions (5 and 15 days). MAs determine trends and generate signals, MACD compares exponential moving averages, RSI measures price action strength, and OBV gauges buying/selling pressure. Availability of price and volume data is crucial for calculating these indicators.

3.2 ARIMA, ANN, SVR, RNN, V-LSTM and Bi-LSTM for forecasting of forex market

ARIMA is a widely-used statistical model in finance for predicting future values based on observed trends and patterns. While effective for linear trends and seasonality, ARIMA struggles with non-linear patterns and needs additional data pre-processing. ANNs predict Forex market trends well but tend to overfit. SVR, using SVM, finds the best linear or nonlinear function for predicting future prices. It handles high-dimensional data and is robust to noise, making it suitable for Forex market prediction.

RNN models are used in Forex market prediction to learn patterns and relationships between market factors and price movements. Historical data and relevant market information are pre-processed and formatted into a sequence format. LSTM is commonly used due to its ability to handle long-term dependencies. The model is trained using a suitable loss function and optimization algorithm. The architecture includes recurrent layers processing input sequences and passing outputs to the next time step. Different types of recurrent cells can be used. Dense layers perform additional processing, with the last dense layer predicting the output [38, 39, 40]. V-LSTM is a powerful model for Forex market prediction, handling missing and noisy data. Historical price and volume data are pre-processed, normalized, and split. The V-LSTM model is trained using an appropriate loss function and optimization algorithm [13, 14, 15]. The architecture includes an input layer, an LSTM layer capturing long-term dependencies with memory cells, gates, and an output layer. This makes V-LSTM ideal for sequence prediction tasks [29, 30, 31]. A Bi-LSTM enhances context understanding by considering both past and future information. It consists of two LSTM layers: one processes the sequence in the forward direction, while the other processes it backward. At each time step, inputs from the current and previous time steps are processed by both layers, which contain memory cells and gating mechanisms. The outputs are concatenated and passed through a concatenation layer, combining forward and backward context for the current time step, resulting in a prediction [32].

3.3 The DeepSense network (DSN)

The DSN network is a DL architecture combining CNN and RNN layers to extract features and predict outcomes. Its advantage lies in learning features from raw data without manual engineering, beneficial for complex data modelling. The steps involve pre-processing, CNN feature extraction, RNN temporal modelling, fully connected layers for prediction, training on a large dataset, and making predictions on new data [20, 21, 22, 23, 24, 25, 26]. By combining CNNs and RNNs, spatial and temporal features are automatically extracted, resulting in a comprehensive representation that improves accuracy. The DSN outperforms traditional ML algorithms and other DL architectures for time series analysis by automatically learning features and temporal patterns. Its scalable architecture is suitable for real-world applications with substantial data [27, 28]. The working principle of the DSN network can be summarized as follows; (a) Input data: Time series data is taken as input, which can be single-channel or multi-channel. (b) Feature extraction: Convolutional layers extract spatial features, capturing patterns and structures. (c) Temporal modeling: Recurrent layers capture temporal dependencies, capturing long-term patterns. (d) Fusion of features: Convolutional and recurrent features are combined through fusion layer. (e) Classification: Fully connected layers with softmax or linear activation produce the final output. (f) Training: Back-propagation is used to update model weights based on loss function gradients. (g) Evaluation: Model performance is assessed on a separate test set using metrics like accuracy, precision, recall, F1 score, and MSE.

The key idea behind use of DSN network in this study is that, it utilizes in-built feature fusion by combining CNN and RNN layers to create a comprehensive feature representation for accurate predictions. On the other hand, feature ensemble strategies combine multiple models trained on different feature sets for improved robustness and accuracy. Feature fusion is ideal for complex time-series data, while feature ensemble is suitable for diverse or highly variable data [56, 57].

3.4 All Member-based optimizer (AMBO)

Member-based optimization algorithms, like AMBO, improve solution quality by gradually enhancing a population of potential solutions. Inspired by social animals, AMBO generates candidate solutions and leverages collective intelligence for superior results. It balances local and global search strategies to explore the search space effectively, avoiding local optima. Global search resembles birds flocking, adjusting positions based on neighbours, while local search mirrors bees investigating their local surroundings. AMBO draws inspiration from collective animal behaviour, allowing all members in the search space to contribute to population updates, distinguishing it from traditional meta-heuristics. The following is an illustration of the working principle of the AMBO algorithm [35]:

(a)
Initialization of parameters: The important parameters such as; Design variables or Dim, design constraints, search space boundaries (Lower Bound and Upper Bound), fitness function used for the population evaluation, population size or total number of search agents, current iteration and maximum iterations are initialized;
(b)
Initialization of population randomly in the search space: The algorithm starts by creating a population of candidate solutions, called members or search agents, randomly distributed in the search space using a population matrix (PM) as presented in Eq. (1), where the every row denotes a member of the population while each column corresponds to a variable of the optimization problem. Hence, the PM has a number of rows equivalents to the population size, and the number of columns equal to the number of variables in the optimization problem (Dim) where, $P_{i}$ is the $i^{th}$ population member or search agent, $p_{i}^{d}$ is the value of $d^{th}$ design variable or Dim suggested by the $i^{th}$ population member. The $X$ and $Y$ are the number of population members and number of design variables or Dim respectively.

$\displaystyle\textit{PM}=\left[{{\begin{array}[]{c}{P_{1}}\hfill\\ \vdots\hfill\\ {P_{i}}\hfill\\ \vdots\hfill\\ {P_{X}}\hfill\\ \end{array}}}\right]_{X\times Y}=\left\lfloor{\begin{array}[]{{20}c}{p_{1}^{1% }}\hfill\\ \vdots\hfill\\ {p_{i}^{1}}\hfill\\ \vdots\hfill\\ {p_{X}^{1}}\hfill\\ \end{array}}{\begin{array}[]{{20}c}\cdots\hfill\\ \ddots\hfill\\ \cdots\hfill\\ {\mathinner{\mskip 2.0mu \raise 1.0pt\hbox{.}\mskip 2.0mu \raise 4.0pt\hbox{.}% \mskip 2.0mu \raise 7.0pt\hbox{.}\mskip 1.0mu }}\hfill\\ \cdots\hfill\\ \end{array}}{\begin{array}[]{{20}c}{p_{1}^{d}}\hfill\\ \vdots\hfill\\ {p_{i}^{d}}\hfill\\ \vdots\hfill\\ {p_{X}^{d}}\hfill\\ \end{array}}{\begin{array}[]{{20}c}\cdots\hfill\\ {\mathinner{\mskip 2.0mu \raise 1.0pt\hbox{.}\mskip 2.0mu \raise 4.0pt\hbox{.}% \mskip 2.0mu \raise 7.0pt\hbox{.}\mskip 1.0mu }}\hfill\\ \cdots\hfill\\ \ddots\hfill\\ \cdots\hfill\\ \end{array}}{\begin{array}[]{{20}c}{p_{1}^{m}}\hfill\\ \vdots\hfill\\ {p_{i}^{Y}}\hfill\\ \vdots\hfill\\ {p_{X}^{Y}}\hfill\\ \end{array}}\right\rfloor_{X\times Y}$ (1)
(c)
Evaluation of initial population using fitness function: Each member is evaluated using a fitness function (FF), which assigns a fitness value ( $\textit{FF}_{1}\cdots\textit{FF}_{X})$ to each member based on how well it solves the optimization problem and the values of the FF are specified as a vector (FF(PM)) using Eq. (2);

$\displaystyle\textit{FF}\left({\textit{PM}}\right)=\left[{{\begin{array}[]{{2% 0}c}{\textit{FF}_{1}=\textit{PM}\left({P_{1}}\right)}\hfill\\ \vdots\hfill\\ {\textit{FF}_{i}=\textit{PM}\left({P_{i}}\right)}\hfill\\ \vdots\hfill\\ {\textit{FF}_{X}=\textit{PM}\left({P_{X}}\right)}\hfill\\ \end{array}}}\right]_{X\times 1}$ (2)
(d)
Local search and global search in the search space: Each member explores its local neighborhood to search for better solutions. The local search is inspired by the behavior of bees, where each bee investigates its local neighbourhood for food sources and in AMBO, each member in explores its local neighbourhood in search of better solutions. Similarly, the algorithm employs a global search strategy inspired by the behavior of birds flocking. In this strategy, each member or search agent adjusts its position based on the position of its neighbors in the search space. This adjustment is guided by two factors; attraction towards the best member in its neighborhood, and repulsion from other members in the same neighbourhood;
(e)
Updating of the position of member or agent in the search space: This PM undergo a two-stage update process. During the initial stage, each member’s update is determined by comparing their position with that of other members within the search space. If the new position improves the (FF value, it is considered acceptable for the population member. However, if the update fails to enhance the FF value, the member or search agent retains its previous position, as the update is deemed unacceptable. Equations (3), (4) and (5) are employed in these computations throughout the first phase.

$\displaystyle X_{s}=\textit{round}\left({X\times\left({1-\frac{\textit{Current% }_{\textit{Iteration}}}{\textit{Maximum}_{\textit{Iterations}}}}\right)}\right)$ (3) $\displaystyle\overline{p_{i}^{d}}=\left\{{{\begin{array}[]{l}{p_{i}^{d}+% \textit{Rand}_{\textit{number}}\left({p_{i}^{d}-p_{j}^{d}}\right),\textit{FF}_% {i}<\textit{FF}_{j}\ \textit{and}\ j=1\ \textit{to}\ X_{s}}\hfill\\ {p_{i}^{d}+\textit{Rand}_{\textit{number}}\left({p_{i}^{d}-p_{j}^{d}}\right),% \textit{else}}\hfill\\ \end{array}}}\right.$ (4) $\displaystyle P_{i}=\left\{{{\begin{array}[]{l}{\overline{P_{i}},\overline{% \textit{FF}}_{i}<\textit{FF}_{i}}\hfill\\ {P_{i},\textit{else}}\hfill\\ \end{array}}}\right.$ (5)

Where, $X_{s}$ is the selected search agents to lead the PM; $\textit{Current}_{\textit{Iteration}}$ and $\textit{Maximum}_{\textit{Iterations}}$ represents the current iteration number and the maximum number iterations of the algorithm respectively. The $\overline{p_{i}^{d}}$ is the new value of the position of $d^{\textit{th}}$ design variable (Dim) and $\overline{P_{i}}$ is the new position of $i^{\textit{th}}$ population member or search agent. $\textit{Rand}_{\textit{number}}$ is the random number generated within the range of [0,1] and $\overline{\textit{FF}}_{i}$ is the value of FF. The PM gets updated based on the obtained best member or best search agent during this second stage. In this stage also, like the first phase, the new position is acceptable to a population member or search agent if it improves the FF based on Eqs (6) and (7).

$\displaystyle\overline{\overline{p_{i}^{d}}}=p_{i}^{d}+\textit{Rand}_{\textit{% number}}\left({p_{\textit{Best}}^{d}-p_{i}^{d}}\right)$ (6) $\displaystyle P_{i}=\left\{{{\begin{array}[]{l}{\overline{\overline{{P_{i}}}},% \overline{\overline{\textit{FF}}}_{i}<\textit{FF}_{i}}l\\ {P_{i},\textit{else}}\hfill\\ \end{array}}}\right.$ (7)

Where, the new value for $d^{\text{th}}$ design variable (Dim) is $\overline{\overline{p_{i}^{d}}}$ , $p_{\textit{Best}}^{d}$ is the best member or search agent which achieves the best FF value, $\overline{\overline{P}}_{i}$ is the new position of the $i^{\textit{th}}$ population member on the second stage and $\overline{\overline{\textit{FF}}}_{i}$ represents the value of corresponding FF.
(f)
Termination: The algorithm continues to iterate through steps $d$ to $e$ until a termination criterion is met, such as reaching a maximum number of iterations or achieving a desired level of solution quality.

The AMBO algorithm employs a combination of local and global search strategies to explore the search space and avoid getting stuck in local optima. By harnessing the collective intelligence of the population of members, AMBO has shown promising results in solving a range of optimization problems.
3.5 Proposed enhanced DSN network with AMBO for forex market trend analysis

Figure 1.

Tailoring of DSN with AMBO (AMBO-DSN) classifier for trend forecasting model.

Figure 2.

Broad overview of the proposed two-stage Forex market trend forecasting model.

In the realm of Forex trading, trend analysis plays a crucial role in identifying patterns within the price movements of currency pairs over time. This analysis provides valuable insights into short and long term market behavior and aids in making informed trading decisions. In the second phase of this research, the optimization of parameters within the DSN network becomes a focus. Parameters such as the kernel size of the first convolution layer, the configuration of the second convolution layer, the number of cells within the gated recurrent unit (GRU-1), and the activation function type within GRU-2 are optimized using the AMBO algorithm. This iterative algorithm updates the members of the population based on their fitness value, which is determined by their performance in predicting trends. During the global search phase, each member adjusts its position in the search space, guided by attraction towards the best member in its neighborhood and repulsion from other members in the same neighborhood. By exploring various combinations of convolution layers and GRUs within the DSN network, the population members gradually enhance their ability to predict market trends. The DSN network has been tailored incorporating the AMBO algorithm is illustrated in Fig. 1, representing the proposed approach for this work

Algorithm-1: AMBO-DSN classifier for forex trend predictio
Input:
DSN architecture;
Optimization parameters (Dim) [Kernel size of Convolution layer-; Convolution layer-2; Number of cells in GRU-1 and Type of activation function in GRU-2;
Number of iterations;
Output
Best member (solution) for each iteratio;
Step 1: Develop Fitness Function (FF) considering the provided DSN architectur
Step 2: Initialize optimization parameters (Dim)
Step 3: Create initial population matrix (PM)
$\textit{PM}=\left[{{\begin{array}[]{*{20}c}\hfil&\cdots\hfill&\hfil\\ \vdots\hfill&\ddots\hfill&\vdots\hfill\\ \hfil&\cdots\hfill&\hfil\\ \end{array}}}\right]_{X\times 4}\mbox{Where}\ X\ \mbox{is the number of % population and}\ Y=\textit{Dim}.$
Step 4: Evaluate the Fitness Function (FF) considering the initial population matrix (PM
For $t=$ 1 to number of iterations:
• Update $X_{s}$ using Eq. (3) • Find the Best Member • For each individual $P_{i}$ in the population:
If $i<X_{s}$ :
• Update the individual member and its score based on Eqs (3) to (5)
Else:
• Update the individual and its score based on Eqs (6) to (7)
End if
End for
• Save the best member for the current iteration $\textit{Current}_{\textit{Iteration}})$
End for

The Fig. 2 illustrates a two-stage forecasting model aimed at predicting future prices and trends for three currency pairs. This model utilizes Bi-LSTM, DSN, and AMBO techniques. The primary objective of this experimental phase is to enhance the DSN architecture to achieve precise Forex trend forecasting. The algorithm takes inputs such as the DSN architecture, optimization parameters (Dim), and the number of iterations. At each iteration; the algorithm produces an output known as the best member (solution), which represents an optimized DSN configuration. The algorithm employs the FF function to evaluate the DSN architecture’s performance. This function measures the accuracy of the model in predicting Forex trends based on the specified Dim values outlined in Section 3.5 (first paragraph). The inputs are then fed into the DSN architecture, as depicted in Algorithm 1. Initially, an initial PM is created, with each row representing an individual DSN configuration. The population size, denoted by $X$ , determines the number of individuals, while the number of design variables (Dim) is represented here as $Y=4$ . The FF evaluates the initial PM, assessing the performance of each individual and assigning a score based on their FF value. The algorithm proceeds with a loop for a specified number of iterations. In each iteration, the $X_{s}$ value is updated using Eq. (3), which involves selecting a subset of individuals from the population. The best member is determined based on the updated $X_{s}$ value. For each individual in the population, their member and score are updated using Eqs (3) to (7), depending on whether the individual is less than $X_{s}$ or not. Finally, the best member for the current iteration is saved, and the loop continues until the specified number of iterations is completed. The output of the algorithm is the best member (solution) for each iteration, representing an optimized DSN configuration that demonstrates improved accuracy in predicting Forex trends.

Table 1

Description of data samples and data range [58]

Datasets	Total samples	Date range	Data range
USD/EUR	2623	Feb 11, 2013 $\sim$ Feb 28 2023	0.7177 $\sim$ 1.0421
AUD/JPY	2623		62.36 $\sim$ 105.2
CHF/INR	2623		56.45 $\sim$ 89.97

4. Experimentation, model evaluation and result analysis

This section presents the results of experiments conducted on three Forex datasets US dollar (USD) to European currency (EUR), Australian dollar (AUD) to Japanese Yen (JPY), Swiss Franc (CHF) to Rupees of Indian (INR) as detailed in Table 1. The data for these currency pairs was collected from https://in.investing.com/currencies/ and accessed online on March 1, 2023. To mitigate the risk of multicollinearity, we specifically selected datasets with low correlation among the three currency pairs. This approach enables our proposed model to capture distinct factors for each pair, leading to improved prediction accuracy. Each dataset comprises 2623 samples and covers a specific date range. Four essential features, namely open price, close price, high price, and low price for specific time intervals, were included in each dataset. For the USD/EUR dataset, the data spans from February 11, 2013, to February 28, 2023, with the corresponding data range for this currency pair varying between 0.7177 and 1.0421. The AUD/JPY dataset covers a period from an unspecified starting date to February 28, 2023, and the data range for the AUD/JPY currency pair fluctuates between 62.36 and 105.2. Lastly, the CHF/INR dataset consists of 2623 samples and covers a date range starting at an unspecified date and ending on February 28, 2023. The data range for the CHF/INR currency pair falls between 56.45 and 89.97. By using these datasets with unique characteristics, we aim to enhance the effectiveness of our model in predicting Forex price movements. The study was divided into two phases: regression and classification. In the regression phase, a Bi-LSTM network predicted the closing price of three currency pairs for 5 and 15 days ahead. In the classification phase, trends were computed using HHs-HLs (up-trends) and LHs-LLs (down-trends) [40, 41, 42, 43] based on the predicted closing price from the first phase, and an enhanced version of DSN network with AMBO was proposed to observe the directional movements. The performance of the proposed model was compared with existing DL strategies and optimization techniques.

Table 2
Associated parameter values for predictive networks and optimization techniques

Models and techniques	Parameters and associated values
Bi-LSTM	Optimizer-Adam; Activation function-RLU; Weight regularization-L1 $=$ 0, L2 $=$ 0.01; Dropout-0.1; Batch size-16; Epochs $=$ 30
V-LSTM	Optimizer-Adam; Activation function-RLU; Weight regularization-L1 $=$ 0, L2 $=$ 0.01; Dropout-0.1; Batch size-16; Epochs $=$ 30
RNN	Optimizer-Adam; Activation function-RLU; Learning rate-0.001; Momentum-0.9; Dropout-0.1; Batch size-16; Epochs $=$ 30
SVR	Kernel-RBF; Tolerance $=$ 0.001; Regularization-L2
ANN	Activation function-Relu; Solver-Adam; Learning Rate-0.001; Tolerance-0.0001
DSN	Optimizer-SGD; Learning Rate-0.0001; Batch Size-16; Epochs $=$ 30
GA	Number of Decision Variables $=$ 3; Maximum Number of Iterations $=$ 50; Population size $=$ 10; Selection Method-Roulette Wheel
PSO	Number of Decision Variables $=$ 3; Maximum Number of Iterations $=$ 50; Number of Particles $=$ 10; Inertia Weight $=$ 1; Inertia Weight Damping Ratio $=$ 0.99; Personal Learning; Coefficient $=$ 1.5; Global Learning Coefficient $=$ 2.0
DE	Number of Decision Variables $=$ 3; Maximum Number of Iterations $=$ 50; Crossover Rate $=$ 0.7; Mutation Factor $=$ 0.5
AMBO	Number of Decision Variables $=$ 4; Maximum Number of Iterations $=$ 50; Number of Members $=$ 10

4.1 Parameters used

In this proposed approach, consistency is maintained by keeping all standard parameters constant throughout the experimental findings. The specific parameters and their corresponding values for the predictive networks, classification techniques, and optimization strategies are provided in Table 2, offering detailed insights into their configuration.

Table 3
Performance comparison of Bi-LSTM for USD/EUR with other predictive models for both 5 and 15 days forecasting horizons

Models	MS		MAPE		R ${}^{2}$		MP		MG
	5 days	15 day	5 days	15 day	5 days	15 day	5 days	15 day	5 days	15 day
Bi-LST	0.000134	0.000133	0.011618	0.0116	0.969778	0.969842	0.000154	0.000153	0.000178	0.00017765
V-LSTM	0.000751	0.000951	0.027529	0.030749	0.831285	0.783364	0.000842	0.001063	0.000951	0.001195
RN	0.000606	0.000807	0.0244	0.028528	0.863743	0.81	0.000679	0.000904	0.000766	0.001018
SV	0.0012	1.2874	0.04	0.0571	0.9319	0.9589	0.0019	0.0032	0.000847	0.0092
AN	0.0012	2.3124	0.0411	0.1016	0.9411	0.9455	0.0015	0.0074	0.000841	0.0099
ARIM	2.1451	1.3488	0.0421	0.0982	0.9455	0.9429	0.0325	0.0065	0.000369	0.0099

4.2 Phase #1: Regression: Forecasting of closing price

In the first phase of the study, the goal is to predict short-term closing prices of three currency pairs using a dataset spanning ten years of historical data, which includes open, close, high, and low prices of the currencies. To enhance the analysis, trend-based indicators such as; MA, MACD, RSI, and OBV are incorporated into the datasets to form the augmented currency pairs coined here as AAs. Initially, the Bi-LSTM model is employed as the forecasting model for this experiment. The performance of the Bi-LSTM model is assessed using several evaluation metrics, including mean square error (MSE), mean absolute percentage error (MAPE), R-squared (R ${}^{2})$ , mean Poisson deviance (MPD), and mean gamma deviance (MGD). These metrics are compared with few DL and ML based predictive networks such as; Bi-LSTM, V-LSTM, RNN, SVR, ANN, and ARIMA, and the results are presented in Tables 3, 4, and 5. While MSE provides a measure of accuracy in predicting outcomes, it alone may not offer a comprehensive evaluation of the model’s performance. Hence, additional metrics like MAPE, R ${}^{2}$ , MPD, and MGD are used in conjunction with MSE. MAPE is particularly useful when the predicted variables have varying scales, and a lower value indicates greater accuracy. R ${}^{2}$ measures the goodness of fit of the regression model to the data, with a higher value indicating a better fit. MPD assesses the fit of the Poisson regression model by comparing the observed data with the model’s predictions. A lower mean Poisson deviance suggests a better fit, while larger values indicate a poorer fit. MPD is commonly employed in model selection and comparison. MGD captures the discrepancy between the fitted model and a saturated model that perfectly fits the data. It is used in the context of generalized linear models with continuous and positively skewed response variables. These evaluation measures collectively provide a comprehensive assessment of the Bi-LSTM model’s performance in predicting short-term closing prices of currency pairs.

In Table 3, the Bi-LSTM model had the lowest MSE and MAPE values and highest R ${}^{2}$ scores for predicting USD/EUR currency pairs, making it the most accurate. The V-LSTM and RNN models also did well, with lower MSE and MAPE values than SVR, ANN, and ARIMA models, but had lower R ${}^{2}$ scores than Bi-LSTM. SVR and ANN had the highest MSE and MAPE values and were the least accurate in predicting Forex prices. The Bi-LSTM model is the best for predicting USD/EUR prices, followed by V-LSTM and RNN models. SVR, ANN, and ARIMA models performed poorly compared to DL models.

Table 4
Performance comparison of Bi-LSTM for AUD/JPY with other predictive models for both 5 and 15 days forecasting horizons

Models	MS		MAPE		R ${}^{2}$		MP		MG
	5 days	15 day	5 days	15 day	5 days	15 day	5 days	15 day	5 days	15 day
Bi-LST	0.332563	0.331806	0.005922	0.005901	0.994463	0.994461	0.003916	0.003906	0.000046	0.000046
V-LSTM	1.579326	1.953106	0.012767	0.014315	0.973706	0.967403	0.018332	0.022661	0.000215	0.000265
RN	1.588963	1.684497	0.012891	0.013177	0.973545	0.971886	0.018441	0.019569	0.000216	0.000229
SV	2.3214	4.1258	0.0362	0.0958	0.9578	0.9487	0.0321	0.1258	0.000362	0.0847
AN	2.3158	6.2147	0.0324	0.1419	0.9589	0.9228	0.0318	0.1914	0.000358	0.0901
ARIM	3.1245	5.2147	0.0417	0.1124	0.9421	0.9258	0.0451	0.1351	0.000491	0.0891

Table 5

Performance comparison of Bi-LSTM for CHF/INR with other predictive models for both 5 and 15 days forecasting horizons

Models	MS		MAPE		R ${}^{2}$		MP		MG
	5 days	15 day	5 days	15 day	5 days	15 day	5 days	15 day	5 days	15 day
Bi-LST	0.338614	0.3350	0.007091	0.007064	0.993247	0.993249	0.004736	0.004671	0.000066	0.000065
V-LSTM	1.489395	2.176376	0.014794	0.017722	0.9702	0.956217	0.020482	0.029868	0.000284	0.000413
RN	1.583962	1.8997	0.015136	0.016604	0.968383	0.961783	0.021771	0.026032	0.000302	0.0003
SV	0.7458	6.3624	0.0369	0.1458	0.94	0.9321	0.0361	0.1698	0.0004	0.0925
AN	2.6121	7.2214	0.0351	0.2015	0.9418	0.9158	0.0358	0.2115	0.000402	0.2011
ARIM	3.4125	6.3587	0.0973	0.1347	0.94	0.9211	0.0464	0.1698	0.000498	0.1211

The Table 4 shows that the models have high MSE and MAPE values and low R ${}^{2}$ scores for predicting AUD/JPY currency pair prices. The Bi-LSTM model is the most accurate among the selected models, with the lowest MSE and MAPE values and the highest R ${}^{2}$ scores for both 5 and 15 days forecasting horizons. The V-LSTM and RNN models have higher MSE and MAPE values but comparable R ${}^{2}$ scores to Bi-LSTM. The SVR, ANN, and ARIMA models have the highest MSE and MAPE values and lowest R ${}^{2}$ scores, with the ANN model having the largest prediction errors. The Bi-LSTM model is the best performing model, followed by V-LSTM and RNN models, while the SVR, ANN, and ARIMA models perform poorly for this AUD/JPY currency pairs.

Similarly, the Table 5 shows that the Bi-LSTM model performed best for all three currency pairs. For USD/EUR, Bi-LSTM had the lowest MSE and MAPE values and the highest R ${}^{2}$ value for 5 days prediction. For AUD/JPY, Bi-LSTM had the lowest MSE and MAPE values for both 5 and 15 days predictions and the highest R ${}^{2}$ value for 5 days prediction. For CHF/INR, Bi-LSTM had the lowest MSE and MAPE values for both 5 and 15 days predictions and the highest R ${}^{2}$ value for 5 days prediction. The SVR and ANN models had higher errors than the Bi-LSTM for all three currency pairs, but still performed better than the RNN, V-LSTM, and ARIMA models.

Figure 3.

Closing price prediction for USD/EUR based on original, AAs, and prediction errors observed 5 and 15 days ahead.

Figure 4.

Closing price prediction for AUD/JPY based on original, AAs, and prediction errors observed 5 and 15 days ahead.

Figure 5.

Closing price prediction for CHF/INR based on original, AAs, and prediction errors observed 5 and 15 days ahead.

In this phase of experimentation, the article analyzes different models for predicting Forex prices and concludes that the Bi-LSTM model outperformed the others, including V-LSTM, RNN, SVR, ANN, and ARIMA, in terms of accuracy. The Bi-LSTM model had the lowest MSE and MAPE values and the highest R ${}^{2}$ scores for predicting the USD/EUR, AUD/JPY, and CHF/INR currency pairs. The V-LSTM and RNN models also performed well but had lower R ${}^{2}$ scores than the Bi-LSTM, while the SVR, ANN, and ARIMA models performed poorly compared to the DL models. The Bi-LSTM model was the best-performing model for all three currency pairs, with the lowest MSE and MAPE values for both 5 and 15 days predictions. The article here summarizes that, the Bi-LSTM model is a promising approach for Forex price prediction, especially for the USD/EUR, AUD/JPY, and CHF/INR currency pairs, which are visualized in Figs 3, 4 and 5 respectively for both the predictive days of 5 and 15. These figures demonstrate that the currency pairs with AAs and the observed errors show almost equivalent results when compared to the currency pairs with the original set of features.

4.3 Phase #2: Forecasting of Forex market directional movements based on HHs-HLs and LHs-LLs

During this experimental phase, the primary objective is to observe the directional movement of currency pairs, focusing on identifying up-trends and down-trends. This analysis serves several purposes for traders and analysts, including trend identification, determining entry and exit points, assessing risk-reward ratios, and gauging market sentiment. The figures presented in this section illustrate the observed up-trends (depicted by green arrows) and down-trends (depicted by orange arrows) based on the analysis of HHs-HLs and LHs-LLs ranging from 2014 to 2023 using the predicted output of the Bi-LSTM model. Specifically, Fig. 6(a) and 6(b) display the observed up-trends and down-trends for the USD/EUR currency pair using currency pair datasets with AAs for both 5 and 15 days, respectively. Similarly, Fig. 7(a), 7(b), 8(a), and 8(b) showcase the observed up-trends and down-trends for the AUD/JPY and CHF/INR currency pairs using currency pair datasets with AAs for 5 and 15 days. To evaluate the performance of the observed trends derived from the Bi-LSTM model, the total count of trends based on HHs-HLs and LHs-LLs for both the original currency pairs and currency pair datasets with AAs is considered for further analysis and experimentation. The provided tables (Tables 6 to 11) facilitate a comparison between the observed trends in the original currency pairs and the predicted trends generated by the Bi-LSTM model. These tables offer valuable insights into the model’s accuracy in predicting price movements for the three currency pairs across both 5 and 15-day forecast periods.

Figure 6.

USD/EUR trends observed for based on HHs-HLs and LHs-LLs using Bi-LSTM network’s predicted closing price for (a) 5 days and (b) 15 days.

Tables 6 and 7 compare the observed price trends in the USD/EUR currency pair for 5-days and 15-days forecasting periods respectively. From Table 6, it can be seen that, the percentage of up-trends in the original currency pairs ranges from 42% in 2023 to 70% in 2017, while the percentage of down-trends varies from 30% in 2017 to 58% in 2023. The total number of trends observed based on HHs-HLs/LHs-LLs ranges from 34 in 2019 to 44 in 2020. The predicted output of the Bi-LSTM model shows a similar trend, with the percentage of up-trends ranging from 50% to 70% and the percentage of down-trends ranging from 30% to 58%. The total number of trends observed also follows a similar pattern. Table 7 presents a comparative analysis of observed price trends in the USD/EUR currency pair for different years. The Bi-LSTM model generally aligns with the observed trends. In most years, the model predicts a distribution of up-trends and down-trends that closely matches the observed trends. There are slight variations in the percentages, but the overall trend direction is consistent. The total number of trends observed by the model is also reasonably close to the observed trends. It can be inferred from those tables that, the Bi-LSTM model shows a reasonable alignment with the observed trends in the original currency pairs for the USD/EUR exchange rate over the forecast periods. It consistently captures the price movement direction over a 15-day forecast period across different years.

Table 6

Price trends observed in each year for USD/EUR original currency pairs vs. predicted output of Bi-LSTM for 5 days ahead

Year	Observations on original currency pairs			Observations on predicted output of Bi-LSTM
	Up-trends (%)	Down-trends (%)	Total (HHs-HLs/LHs-LLs) (numbers)	Up-trends (%)	Down-trends (%)	Total (HHs-HLs/LHs-LLs) (numbers)
2014	55	45	35	54	46	38
2015	60	40	39	60	40	39
2016	62	38	37	63	37	38
2017	70	30	36	70	30	38
2018	60	40	36	58	42	36
2019	58	42	34	61	39	38
2020	68	32	44	50	50	44
2021	68	32	37	68	32	37
2022	54	46	39	50	50	41
2023	42	58	42	42	58	42

Figure 7.

AUD/JPY trends observed for based on HHs-HLs and LHs-LLs using Bi-LSTM network’s predicted closing price for (a) 5 days and (b) 15 days.

Table 7

Price trends observed in each year for USD/EUR original currency pairs vs. predicted output of Bi-LSTM for 15 days ahead

Year	Observations on original currency pairs			Observations on predicted output of Bi-LSTM
	Up-trends (%)	Down-trends (%)	Total (HHs-HLs/LHs-LLs) (numbers)	Up-trends (%)	Down-trends (%)	Total (HHs-HLs/LHs-LLs) (numbers)
2014	54	46	41	56	44	42
2015	60	40	32	60	40	33
2016	63	37	38	65	35	36
2017	70	30	37	71	29	35
2018	58	42	40	56	44	40
2019	61	39	38	64	36	38
2020	50	50	40	50	50	40
2021	54	46	41	52	48	41
2022	38	62	35	40	60	36
2023	52	48	36	50	50	37

Figure 8.

CHF/INR trends observed for based on HHs-HLs and LHs-LLs using Bi-LSTM network’s predicted closing price for (a) 5 days and (b) 15 days.

Table 8

Price trends observed in each year for AUD/JPY original currency pairs vs. predicted output of Bi-LSTM for 5 days ahead

Year	Observations on original currency pairs			Observations on predicted output of Bi-LSTM
	Up-trends (%)	Down-trends (%)	Total (HHs-HLs/LHs-LLs) (numbers)	Up-trends (%)	Down-trends (%)	Total (HHs-HLs/LHs-LLs) (numbers)
2014	50	50	38	49	51	39
2015	61	39	35	59	41	32
2016	72	28	41	70	30	40
2017	46	54	34	46	54	34
2018	46	54	30	46	54	30
2019	48	52	31	46	54	31
2020	48	52	33	48	52	33
2021	52	48	36	50	50	38
2022	18	52	35	25	65	35
2023	46	54	36	46	54	36

Table 9

Price trends observed in each year for AUD/JPY original currency pairs vs. predicted output of Bi-LSTM for 15 days ahead

Year	Observations on original currency pairs			Observations on Predicted output of Bi-LSTM
	Up-trends (%)	Down-trends (%)	Total (HHs-HLs/LHs-LLs) (numbers)	Up-trends (%)	Down-trends (%)	Total (HHs-HLs/ LHs-LLs) (numbers)
2014	45	55	32	48	52	33
2015	72	28	34	68	32	34
2016	46	54	34	48	52	34
2017	46	54	33	46	54	33
2018	48	52	35	48	52	32
2019	48	52	31	48	52	30
2020	52	48	31	50	50	30
2021	46	54	34	46	54	34
2022	48	52	32	44	56	32
2023	50	50	32	50	50	31

Table 10

Price trends observed in each year for CHF/INR original currency pairs vs. predicted output of Bi-LSTM for 5 days ahead

Year	Observations on original currency pairs			Observations on predicted output of Bi-LSTM
	Up-trends (%)	Down-trends (%)	Total (HHs-HLs/LHs-LLs) (numbers)	Up-trends (%)	Down-trends (%)	Total (HHs-HLs/LHs-LLs) (numbers)
2014	53	47	31	58	42	40
2015	54	46	36	54	46	34
2016	40	60	31	45	55	32
2017	50	50	36	50	50	36
2018	60	40	35	58	42	35
2019	40	60	35	38	62	35
2020	50	50	40	50	50	41
2021	54	46	41	54	46	42
2022	38	62	34	40	60	34
2023	52	48	32	52	48	32

Table 11

Price trends observed in each year for CHF/INR original currency pairs vs. predicted output of Bi-LSTM for 15 days ahead

Year	Observations on original currency pairs			Observations on predicted output of Bi-LSTM
	Up-trends (%)	Down-trends (%)	Total (HHs-HLs/LHs-LLs) (numbers)	Up-trends (%)	Down-trends (%)	Total (HHs-HLs/LHs-LLs) (numbers)
2014	50	50	34	52	48	34
2015	54	46	32	52	48	33
2016	38	62	35	39	61	36
2017	52	48	35	52	48	35
2018	58	42	37	60	40	37
2019	38	62	40	40	60	40
2020	50	50	36	48	52	38
2021	54	46	36	56	44	37
2022	40	60	34	38	62	35
2023	52	48	31	50	50	30

Table 8 provides a comparison of observed price trends in the AUD/JPY currency pair and the predicted output of the Bi-LSTM model for a 5-day forecast period. Generally, the trends and predicted output align, but there are variations in the percentages of up-trends and down-trends. Some years show close percentages, while others have slight discrepancies. The Bi-LSTM model’s performance in capturing price movement direction in the AUD/JPY pair over a 5-day forecast period is mixed, with some years closely matching observed trends and others showing differences. Table 9 compares observed price trends and predicted output for a 15-day forecast period in the AUD/JPY currency pair. The percentages of up-trends and down-trends vary between observed trends and the model’s predictions. However, there are similarities and consistencies in certain years. In 2014, both observed and predicted trends had lower percentages of up-trends and higher percentages of down-trends. Similarly, in 2017, 2018, and 2021, both observed and predicted trends had the same percentages of up-trends and down-trends. But in other years, there are variations between observed and predicted trends. The predicted output of the Bi-LSTM model does not consistently align with observed trends in the AUD/JPY currency pair for a 15-day forecast period. There are variations in the distribution of up-trends and down-trends, indicating inconsistent performance in capturing price movement direction over this timeframe.

Similarly, the Table 10 compares observed price trends in the CHF/INR currency pair with the predicted output of the Bi-LSTM model for a 5-day forecast period. Overall, the model’s predictions aligned with the observed trends, although there were minor variations in the percentages of up-trends and down-trends. In some years, the distributions were equal, while in others, there were slight differences. However, the Bi-LSTM model consistently captured the direction of price movements for this currency pair across different years. Table 11 compares observed price trends with predictions made by the Bi-LSTM model for a 15-day forecast period in the CHF/INR currency pair. The predicted output closely aligned with observed trends, with slight variations in the percentages of up-trends and down-trends. In some years, the distributions were similar, while in others, the model’s predictions deviated from the observed trends. Overall, the Bi-LSTM model consistently captured the direction of price movements for the CHF/INR pair over the 15-day forecast period, demonstrating relatively consistent performance.

4.4 Phase #3: Classification: Forex market trend prediction based on DSN-AMBO

Table 12
Year wise USD/EUR classification results for training and testing phases based on RNN, CNN and DSN for 5 days ahead

Year	RN		CN		DS
	Training accuracy	Testin accuracy	Training accuracy	Testin accuracy	Training accuracy	Testin accuracy
2014	97.21	97.11	95.22	94.87	97.12	96.85
2015	97.11	96.98	94.89	91.65	96.98	96.57
2016	93.26	91.24	98.22	97.11	98.35	97.64
2017	92.15	90.21	97.15	96.01	98.46	98.02
2018	94.55	92.11	93.59	91.08	98.58	98.38
2019	93.21	90.87	94.11	91.28	94.89	94.21
2020	91.59	91.11	95.1	91.55	94.25	94.11
2021	97.22	96.58	92.14	90.03	97.89	95.94
2022	96.98	95.21	92.36	90	95.64	95.56
2023	95.96	92.67	92.87	92.09	97.99	97.81
Averag	94.92	93.4	94.56	92.56	97.01	96.5

Table 13

Year wise USD/EUR classification results for training and testing phases based on RNN, CNN and DSN for 15 days ahead

Year	RN		CN		DS
	Training accuracy	Testin accuracy	Training accuracy	Testin accuracy	Training accuracy	Testin accuracy
2014	95.32	94.38	93.87	91.03	96.25	96.03
2015	94.58	93.68	96.24	94.87	98.64	98.34
2016	94.85	93.25	91.87	90.68	96.87	95.67
2017	96.33	95.97	90.35	90.01	97.02	96.91
2018	91.89	90.62	91.66	91.24	98.88	97.22
2019	90.58	90.11	92.58	91.09	95.92	94.03
2020	97.64	96.37	96.59	94.55	96.94	96.22
2021	95.99	95.83	91.28	90.54	97.29	97.05
2022	95.54	94.38	93.48	91.35	98.19	97.86
2023	94.87	91.06	92.55	91.09	97.68	97.38
Average	94.75	93.56	93.04	91.64	97.36	96.67

During this phase, the prediction of Forex market trends has been achieved through a classification process, utilizing the DSN enhanced with AMBO, referred to as AMBO-DSN. The observed trends, derived from the predictive outcomes of Bi-LSTM, have been utilized as the class labels for the DSN classifier, distinguishing between up-trends and down-trends based on HHs-HLs and LHs-LLs. To assess the performance of the DSN classifier, including its training and testing predictive accuracies, a comparison has been made with two other DL based classifiers, namely RNN and CNN. These comparisons have been conducted for each year, and the average accuracies spanning from 2014 to 2023 have been obtained. The results of these comparisons are presented in Tables 12 to 17, encompassing all three currency pairs for both short-term predictive days.

The classification results for the USD/EUR currency pair using RNN, CNN, and DSN models for different forecast periods are presented in Tables 12 and 13. For a 5-day forecast period (Table 12), the RNN model achieved an average training accuracy of 94.92% and an average testing accuracy of 93.4%. The CNN model displayed an average training accuracy of 94.56% and an average testing accuracy of 92.56%. However, surpassing both models, the DSN model exhibited superior performance with an average training accuracy of 97.01% and an average testing accuracy of 96.5%. It consistently outperformed the other models, attaining the highest training accuracy in 2018 (98.58%) and the highest testing accuracy in 2023 (97.81%). In Table 13, for a 15-day forecast period, the RNN model demonstrated an average training accuracy of 94.75% and an average testing accuracy of 93.56%. The CNN model yielded an average training accuracy of 93.04% and an average testing accuracy of 91.64%. Once again, the DSN model showcased the highest accuracy, recording an average training accuracy of 97.36% and an average testing accuracy of 96.67%. It consistently outperformed the other models, achieving the highest training accuracy in 2018 (98.88%) and the highest testing accuracy in 2022 (97.86%). It can be inferred that, the DSN model consistently exhibited the highest accuracy, followed by the RNN and CNN models, highlighting their potential for accurate predictions in forecasting the USD/EUR currency pair over both 5 and 15-day periods.

Table 14

Year wise AUD/JPY classification results for training and testing phases based on RNN, CNN and DSN for 5 days ahead

Year	RN		CN		DS
	Training accuracy	Testin accuracy	Training accuracy	Testin accuracy	Training accuracy	Testin accuracy
2014	96.2	95.8	96.01	95.48	97.25	97.11
2015	98.1	98.0	97.11	96.89	98.54	98.01
2016	95.3	95.2	95.22	95.02	95.01	94.97
2017	95.6	94.3	96.54	96.13	97.22	97.11
2018	96.8	95.8	97.01	96.91	98.25	98.01
2019	96.7	95.6	96.89	96.74	97.14	96.89
2020	92.9	92.0	94.12	94.06	96.88	96.58
2021	94.6	94.5	95.22	94.89	96.56	96.38
2022	95.3	94.3	95.21	94.95	97.22	97.01
2023	96.5	96.2	97.52	97.25	98.58	98.19
Averag	95.8	95.2	96.08	95.83	97.26	97.02

Table 15

Year wise AUD/JPY classification results for training and testing phases based on RNN, CNN and DSN for 15 days ahead

Year	RN		CN		DS
	Training accuracy	Testin accuracy	Training accuracy	Testin accuracy	Training accuracy	Testin accuracy
2014	95.58	95.47	92.69	91.06	96.38	95.98
2015	94.89	94.03	94.32	94.24	97.29	96.93
2016	98.21	97.89	91.87	91.72	95.68	95.54
2017	93.25	92.34	91.54	91.22	92.54	92.34
2018	91.67	91.09	96.98	95.68	96.97	96.74
2019	90.33	90	96.37	91.68	97.06	96.34
2020	95.64	94.97	95.81	93.88	97.58	97.38
2021	96.21	97.95	95.38	94.38	96.88	96.49
2022	93.44	93.28	92.03	91.87	93.97	93.66
2023	91.68	91.31	91.09	90.09	98.98	98.67
Averag	94.09	93.83	93.8	92.58	96.33	96

Table 14 presents the classification results for the AUD/JPY currency pair using RNN, CNN, and DSN models for a 5-day forecast period. The models performed well, with consistently high accuracy scores. The DSN model achieved the highest accuracy, with an average training accuracy of 97.26% and an average testing accuracy of 97.02%. Table 15 displays the classification results for the AUD/JPY currency pair using the same models but for a 15-day forecast period. The models showed consistent performance with minor fluctuations. Again, the DSN model demonstrated the highest accuracy, with an average training accuracy of 96.33% and an average testing accuracy of 96%. It can be observed that, the DSN model consistently outperformed the RNN and CNN models in both the 5-day and 15-day forecast periods for the AUD/JPY currency pair.

The classification results for the CHF/INR currency pair using RNN, CNN, and DSN models for 5-day and 15-day forecast periods are provided in Tables 16 and 17. In Table 16, the RNN model achieved an average training accuracy of 95.45% and an average testing accuracy of 94.79%. The CNN model displayed an average training accuracy of 95.17% and an average testing accuracy of 93.68%. Surpassing both models, the DSN model showcased superior performance with an average training accuracy of 97.37% and an average testing accuracy of 96.59%. The DSN model consistently exhibited exceptional accuracy in both the training and testing phases, demonstrating minor fluctuations. It achieved its highest accuracy in 2023, with a training accuracy of 98.47% and a testing accuracy of 98.03%. In Table 17, the RNN model exhibited strong performance with an average training accuracy of 94.88% and an average testing accuracy of 94.45%. The CNN model attained an average training accuracy of 93.96% and an average testing accuracy of 93.28%. Once again, the DSN model outperformed both models with an average training accuracy of 96.67% and an average testing accuracy of 96.17%. The DSN model consistently performed well across different years, showcasing training accuracies ranging from 94.81% to 98.97% and testing accuracies ranging from 94.66% to 98.03%.

Table 16

Year wise CHF/INR classification results for training and testing phases based on RNN, CNN and DSN for 5 days ahead

Year	RN		CN		DS
	Training accuracy	Testin accuracy	Training accuracy	Testin accuracy	Training accuracy	Testin accuracy
2014	95.68	95.01	96.81	96.14	99.14	98.58
2015	96.88	95.71	95.11	94.21	98.25	98.21
2016	96.11	95.22	92.15	90.28	95.25	93.59
2017	92.25	92.12	92.58	90.99	96.54	94.25
2018	96.78	95.02	97.52	95.79	97.25	96.99
2019	92.98	92.88	95.89	94.21	97.22	96.89
2020	94.69	94.55	96.01	94.38	97.53	97.01
2021	95.32	94.92	95.99	94.11	96.56	96.13
2022	96.57	96.18	96.78	95.87	97.54	96.29
2023	97.25	96.33	92.94	90.85	98.47	98.03
Averag	95.45	94.79	95.17	93.68	97.37	96.59

Table 17

Year wise CHF/INR classification results for training and testing phases based on RNN, CNN and DSN for 15 days ahead

Year	RN		CN		DS
	Training accuracy	Testin accuracy	Training accuracy	Testin accuracy	Training accuracy	Testin accuracy
2014	95.37	94.88	92.59	92.14	95.87	95.64
2015	94.28	94.02	93.84	93.47	97.3	96.73
2016	91.36	91.05	95.17	94.59	97.01	96.37
2017	91.02	90.87	97.97	96.88	94.81	94.66
2018	94.89	94.29	92.95	90.37	95.98	95.38
2019	98.21	97.54	93.25	93.02	96.37	95.99
2020	97.15	96.68	91.67	91.25	98.97	98.03
2021	95.38	94.79	90.33	90	95.18	95.11
2022	96.03	96	95.64	95.47	96.57	95.94
2023	95.17	94.38	96.27	95.69	98.64	97.92
Averag	94.88	94.45	93.96	93.28	96.67	96.17

Overall, across all three currency pairs it can be inferred that, the DSN model consistently outperformed the RNN and CNN models for both 5 and 15 days forecast periods, showcasing its effectiveness in accurately predicting currency pair trends. For the USD/EUR currency pair, the DSN model exhibited the highest accuracy among the three models. In the 5-day forecast period, it achieved an average training accuracy of 97.26% and an average testing accuracy of 97.02%. Likewise, in the 15-day forecast period, the DSN model showcased an average training accuracy of 96.33% and an average testing accuracy of 96% for the AUD/JPY currency pair. Regarding the CHF/INR currency pair, for both the 5-day and 15-day forecast periods, the DSN model consistently outperformed the RNN and CNN models. For the 5-day forecast period, the DSN model achieved an average training accuracy of 97.37% and an average testing accuracy of 96.59%. In the 15-day forecast period, it demonstrated an average training accuracy of 96.67% and an average testing accuracy of 96.17%.

Figure 9.

Learning curve of GA-DSN, PSO-DSN, DE-DSN and AMBO-DSN for USD/EUR.

In this phase, the architectural enhancement of the DSN model has been addressed by incorporating the AMBO. To assess the learning ability of the AMBO, learning curves have been examined, providing valuable insights into the behaviour of the DSN model during the learning process. Comparisons have been made between the hybridized form of DSN with genetic algorithm GA, particle swarm optimization (PSO) and differential evolution (DE) [59, 60] (AMBO-DSN vs. GA-DSN and PSO-DSN and DE-DSN models), and the results are presented in Figs 9, 10, and 11 for the augmented currency pairs of USD/EUR, AUD/JPY, and CHF/INR, considering both predictive days. These figures demonstrate that the AMBO-DSN model converges within 22 to 32 iterations, outperforming the other compared models, except for the learning ability of USD/EUR in the 5-day predictive period.

Table 18

Comparison of USD/EUR price trend prediction using optimized classifiers with trends observed on original currency pair datasets for 5 and 15 days ahead

Optimized predictive models	Predictive days	Original currency pairs trends observed		Predicted trends observed
		Up-trends (%)	Down-trends (%)	Up-trends (%)	Down-trends (%)
GA-DSN	5 Days	59.7	40.3	56.8	41.6
PSO-DSN		59.7	40.3	56.3	43.2
DE-DSN		59.7	40.3	56.1	43.7
AMBO-DSN		59.7	40.3	57.6	42.4
GA-DSN	15 Days	56	44	56.2	42.3
PSO-DSN		56	44	53.4	44.8
DE-DSN		56	44	55.1	43.5
AMBO-DSN		56	44	56.4	43.6

Figure 10.

Learning curve of GA-DSN, PSO-DSN, DE-DSN and AMBO-DSN for AUD/JPY.

Figure 11.

Learning curve of GA-DSN, PSO-DSN, DE-DSN and AMBO-DSN for CHF/INR.

Table 19

Comparison of AUD/JPY price trend prediction using optimized classifiers with trends observed on original currency pair datasets for 5 and 15 days ahead

Optimized predictive models	Predictive days	Original currency pairs trends observed		Predicted trends observed
		Up-trends (%)	Down-trends (%)	Up-trends (%)	Down-trends (%)
GA-DSN	5 Days	48.7	48.3	46.9	50.2
PSO-DSN		48.7	48.3	47.8	50.3
DE-DSN		48.7	48.3	47.8	51.4
AMBO-DSN		48.7	48.3	48.5	50.5
GA-DSN	15 Days	50.1	49.9	48.3	51.1
PSO-DSN		50.1	49.9	48.4	51.2
DE-DSN		50.1	49.9	48.6	51.4
AMBO-DSN		50.1	49.9	49.6	50.4

Table 20

Comparison of CHF/INR price trend prediction using optimized classifiers with trends observed on original currency pair datasets for 5 and 15 days ahead

Optimized predictive models	Predictive days	Original currency pairs trends observed		Predicted trends observed
		Up-trends (%)	Down-trends (%)	Up-trends (%)	Down-trends (%)
GA-DSN	5 Days	49.1	50.9	48.3	50.3
PSO-DSN		49.1	50.9	45.9	54.3
DE-DSN		49.1	50.9	48.4	51.2
AMBO-DSN		49.1	50.9	49.9	50.1
GA-DSN	15 Days	48.6	51.4	48.1	49.2
PSO-DSN		48.6	51.4	45.3	52.6
DE-DSN		48.6	51.4	48.6	50.3
AMBO-DSN		48.6	51.4	48.7	51.3

Furthermore, the Tables 18, 19, and 20 provide a comprehensive analysis of the USD/EUR, AUD/JPY, and CHF/INR price trend predictions. These tables compare the predictions made by four optimized predictive models: GA-DSN, PSO-DSN, DE-DSN, and AMBO-DSN, for both 5-day and 15-day predictive periods. Each model’s predictions are evaluated against the trends observed on the original currency pair datasets. Upon analyzing the observations, it becomes apparent that the AMBO-DSN model emerges as the most reliable and accurate model for both the 5-day and 15-day ahead predictions. It consistently demonstrates the highest accuracy levels and closely aligns with the observed trends for both up-trends and down-trends. In the 5-day ahead predictions, the AMBO-DSN model consistently outperforms the other models in terms of accuracy. Similarly, when considering the 15-day ahead predictions, the AMBO-DSN model maintains its position as the most accurate model, closely resembling the observed trends. While the other models display varying degrees of alignment with the observed trends, the AMBO-DSN model consistently performs better across the board. Based on these observations, we can confidently conclude that the AMBO-DSN model is the optimal choice for predicting price trends in the given context. Its consistent high accuracy and close resemblance to the observed trends make it the preferred model among the evaluated options.

In the previous phase of experimentation, the effectiveness of the AMBO-DSN approach has been evaluated for currency pairs USD/EUR, AUD/JPY, and CHF/INR. The evaluation involved analyzing training and testing accuracies, learning curves, as well as referencing Tables 6 to 17 and Figs 9 to 11. Once the quality of the AMBO-DSN approach was established, it was employed for trend forecasting. To assess its performance, the trend percentages observed on the original datasets were compared with those obtained from the AMBO-DSN. The primary objective is to demonstrate that the proposed AMBO-DSN approach achieves a similar level of result quality as the trends observed from the original currency pair.

Table 21

Comparison of USD/EUR price trend prediction using AMBO-DSN classifier with trends observed on original currency pair datasets and HHs-HLs/LHs-LLs for 5 and 15 days ahead

Year	Trends observed on AMBO-DSN (5 predictive days ahead)		Trends observed on AMBO-DSN (15 predictive days ahead)
	Up-trends (%)	Down-trends (%)	Up-trends (%)	Down-trends %)
2014	55	45	52	48
2015	61	39	60	40
2016	64	46	61	39
2017	72	28	70	30
2018	65	35	60	40
2019	58	42	60	40
2020	65	35	50	50
2021	68	32	52	48
2022	55	45	40	60
2023	44	56	50	50

To analyze and compare the trends observed on the USD/EUR currency pair with those obtained from the AMBO-DSN classifier for 5 and 15 days ahead of trend forecasting, we will examine the data presented in Table 21 in relation to Tables 6 and 7, respectively.

(a)

The trends observed on the original datasets for USD/EUR show variations from year to year. The percentages of up-trends range from 42% in 2023 to 70% in 2017, while the percentages of down-trends vary from 30% in 2017 to 58% in 2023. The total number of observed trends, categorized as HHs-HLs/LHs-LLs, also fluctuates over the years (as indicated in Table 6 for 5 days). Similarly, for the 15 days prediction, the percentages of up-trends range from 38% in 2022 to 70% in 2017, and the percentages of down-trends vary from 30% in 2017 to 62% in 2022. The total number of observed trends, categorized as HHs-HLs/LHs-LLs, also fluctuates over the years (as indicated in Table 7 for 15 days).

(b)

The AMBO-DSN approach demonstrates a similar trend pattern compared to the trends observed on the original datasets, indicating its effectiveness in forecasting trends (as depicted in Table 21) for both 5 and 15 days of prediction.

Table 22

Comparison of AUD/JPY price trend prediction using AMBO-DSN classifier with trends observed on original currency pair datasets and HHs-HLs/LHs-LLs for 5 and 15 days ahead

Year	Trends observed on AMBO-DSN (5 predictive days ahead)		Trends observed on AMBO-DSN (15 predictive days ahead)
	Up-trends (%)	Down-trends (%)	Up-trends (%)	Down-trends (%)
2014	49	51	47	53
2015	65	35	70	30
2016	65	35	46	54
2017	46	54	46	54
2018	46	54	46	54
2019	45	55	48	52
2020	55	45	54	46
2021	52	48	46	54
2022	48	52	46	54
2023	54	46	50	50

The comparison of trends observed on the AUD/JPY currency pair with those obtained from the AMBO-DSN classifier for 5 and 15 days ahead of trend forecasting data presented in Table 22 in relation to Tables 8 and 9 respectively are discussed below.

(a)

The trends observed on the original datasets for AUD/JPY vary from year to year. The percentages of up-trends range from 46% in 2017 to 72% in 2016 and, the percentages of down-trends range from 28% in 2016 to 54% in 2018 (as given in Table 8). Similarly, for 15 days ahead of prediction, the percentages of up-trends range from 45% in 2014 to 72% in 2015. Similarly, the percentages of down-trends range from 28% in 2015 to 55% in 2014 (see Table 9). The total number of observed trends, categorized as HHs-HLs/LHs-LLs, also fluctuates over the years for both the predictive horizons.

(b)

Comparing these trends to the ones observed based on the AMBO-DSN classifier; we find that the percentages of up-trends and down-trends are generally close. The AMBO-DSN approach demonstrates a similar trend pattern compared to the trends observed on the original datasets, indicating its effectiveness in forecasting trends (as depicted in Table 22) for both 5 and 15 days of prediction.

When analyzing the trends observed on the CHF/INR currency pair and comparing them with the trends obtained from the AMBO-DSN classifier for 5 and 15 days ahead of trend forecasting, we can gain a comprehensive understanding of the observed trends and their relationship with the forecasting approach based on (Tables 10, 11 and 13).

(a)

The trends observed on the original datasets for CHF/INR exhibit variations from year to year. The percentages of up-trends range from 38% in 2022 to 60% in 2018 and the percentages of down-trends range from 40% in 2018 to 62% in 2022 (see Table 10). Similarly, the percentages of up-trends range from 38% in 2019 to 58% in 2018 and, the percentages of down-trends range from 42% in 2018 to 62% in 2019 for 15 days ahead of prediction (see Table 11). For both the predictive days, the total number of observed trends, categorized as HHs-HLs/LHs-LLs, also fluctuates over the years.

(b)

Comparing these trends to the ones observed based on the AMBO-DSN classifier for 5 days ahead; we find that the percentages of up-trends and down-trends generally align with the trends observed on the original datasets for both the predictive days considered here (see Table 23).

Table 23

Comparison of CHF/INR price trend prediction using AMBO-DSN classifier with trends observed on original currency pair datasets and HHs-HLs/LHs-LLs for 5 and 15 days ahead

Year	Trends observed on AMBO-DSN (5 predictive days ahead)		Trends observed on AMBO-DSN (15 predictive days ahead)
	Up-trends (%)	Down-trends (%)	Up-trends (%)	Down-trends (%)
2014	48	52	51	49
2015	59	41	52	48
2016	70	30	40	60
2017	48	52	55	45
2018	52	48	45	55
2019	45	55	37	63
2020	48	52	50	50
2021	52	48	55	45
2022	48	52	40	60
2023	51	49	52	48

Table 24

The statistical significance test (K-S test) 5 and 15 days ahead

5 days ahead of prediction
Datasets	p/h VALUES	AMBO-DSN/ AMBO-DE	AMBO-DSN/ AMBO-PSO	AMBO-DSN/ AMBO-GA	AMBO-DSN/ DSN	AMBO-DSN/ CNN	AMBO-DSN/ RNN
USD/EUR	$p$	0.0	0	0	0	0.001	0.001
	$h$	0.9984	0.9867	0.9847	0.9767	0.9582	0.9549
AUD/JPY	$p$	0.0	0	0	0	0	0
	$h$	0.9899	0.9868	0.9587	0.9588	0.9428	0.9421
CHF/INR	$p$	0.001	0	0	0.01	0.001	0.002
	$h$	0.9877	0.9854	0.9726	0.9721	0.9582	0.9584
15 days ahead of prediction
USD/EUR	$p$	0.0	0	0	0	0.001	0
	$h$	0.9768	0.9723	0.9511	0.9437	0.9387	0.9382
AUD/JPY	$p$	0.001	0.001	0	0	0.001	0
	$h$	0.9707	0.9599	0.9489	0.9411	0.9387	0.9384
CHF/INR	$p$	0.0	0	0.001	0.001	0	0
	$h$	0.9837	0.9768	0.9742	0.9627	0.9548	0.9544

The AMBO-DSN classifier demonstrates a comparable level of result quality when compared to the trends observed on the original currency pairs. While slight differences may exist in the percentages, the overall trend direction remains consistent. This indicates the effectiveness and reliability of the AMBO-DSN approach in forecasting trends for the considered currency pairs, namely USD/EUR, AUD/JPY, and CHF/INR.

Figure 12.

Execution time comparison between AMBO-DSN with GA-DSN, PSO-DSN, DE-DSN and for USD/EUR, AUD/JPY and CHF/INR for 5 days ahead of prediction.

4.5 Model validation

The purpose of conducting the K-S (Kolmogorov-Smirnov) statistical test in the context of Forex trend forecasting is to evaluate the fit between observed Forex datasets and reference distributions. The test statistic represents the maximum vertical distance between cumulative distributions, while the $p$ -value indicates the level of significance. A lower $p$ -value signifies a higher level of significance, and typically, a $p$ -value below 0.05 (with an $h$ value of 0) is considered statistically significant. In this analysis, the K-S test is employed to assess the proposed AMBO-DSN empirical model, alongside GA-DSN, PSO-DSN, DE-DSN, basic DSN, RNN, and CNN models. The results, provided in Table 24, offer a quantitative measure indicating the strength of evidence supporting the proposed model for various prediction days across the three currency pairs. The $p$ -values obtained from the test represent the probability of observing the data under the assumption that the predicted distribution matches the actual distribution, with lower $p$ -values indicating higher statistical significance. In the case of the 5-day prediction, all currency pairs have very low $p$ -values (close to 0), indicating strong statistical significance. This suggests that the predicted distributions align well with the actual data distributions. Similarly, for the 15-day prediction, the $p$ -values remain consistently low across all currency pairs, reinforcing the significance of the predictions. Furthermore, the h-values are all above 0.05, indicating that the distributions of the predicted and actual data are not significantly different. From this table, it is evident that, the K-S test results validate the effectiveness of the proposed model in making accurate predictions for both short-term (5 days) and longer-term (15 days) Forex price movements for the given currency pairs

Figure 13.

Execution time comparison between AMBO-DSN with GA-DSN, PSO-DSN, DE-DSN and for USD/EUR, AUD/JPY and CHF/INR for 15 days ahead of prediction.

Furthermore, an assessment of computational efficiency in terms of execution speed (measured in minutes) was conducted on the proposed AMBO-DSN, as well as GA-DSN, PSO-DSN, DE-DSN, basic DSN, RNN, and CNN models. This evaluation aimed to determine the advantage of the proposed forecasting model in terms of its speed and suitability for real-time decision-making. The recorded data from Figs 12 and 13 indicate that the proposed model offers valuable insights for making informed decisions in Forex trend forecasting, considering efficiency aspects.

The proposed AMBO-DSN trend forecasting model has undergone validation through both the K-S non-parametric statistical test and execution time analysis. The results of these evaluations indicate that the AMBO-DSN model achieves a favourable balance between accuracy and computational speed, thereby enhancing the efficiency of decision-making processes. The validation process confirms the model’s reliability and suitability for Forex trend forecasting, providing confidence in its ability to provide accurate predictions in a timely manner.

5. Discussions on key observations

The key findings from the analysis of Forex market directional movement forecasting based on up-trends and down-trends for USD/EUR, AUD/JPY, and CHF/INR using the AMBO-DSN approach for both 5 and 15 days ahead of prediction are as follows;

(a)
The Bi-LSTM model consistently demonstrated the highest accuracy and performed the best among the selected models for all three currency pairs with AAs (USD/EUR, AUD/JPY, and CHF/INR). The V-LSTM and RNN models also showed relatively good performance, while the SVR, ANN, and ARIMA models performed poorly in terms of accuracy and prediction errors (evident from Tables 3 to 5).
(b)
The results depicted in Figs 3 and 4 demonstrates that the Bi-LSTM model accurately predicts the values of currency pairs, showing a strong alignment with the actual values. Additionally, when incorporating additional features (referred to as AAs), the predictive accuracy of the model remains consistent with the original dataset’s predictive ability. These findings highlight the robustness and effectiveness of the Bi-LSTM model in accurately forecasting Forex price movements.
(c)
The trends derived from the analysis of HHs-HLs and LHs-LLs are plotted (Figs 6 to 8) to get valuable insights into the directional movements of the currency pairs based on the predictions generated by the Bi-LSTM model for all three currency pairs and for both the predictive days.
(d)
The performance of the Bi-LSTM model is evaluated by comparing the obtained trends (up-trends and down-trends) from the model with the original currency pairs and currency pair datasets with AAs. Tables 6 to 11 present the total count of trends based on HHs-HLs and LHs-LLs for both the original and augmented datasets, allowing for an assessment of the model’s performance. These observed trends are then used as class labels for further processing with the DSN classifier.
(e)
The DSN model consistently outperformed the RNN and CNN models in accurately predicting currency pair trends for both 5 and 15 day forecast periods. It achieved the highest accuracy for the USD/EUR pair (Tables 12 and 13), with average training and testing accuracies of 97.26% and 97.02% (5 day) and 96.33% and 96% (15 day). For the AUD/JPY pair (Tables 14 and 15), the DSN model had an average training accuracy of 96.33% and testing accuracy of 96% in the 5 and 15 day respectively. Similarly, for the CHF/INR pair (Tables 16 and 17), the DSN model also outperformed the other models, with average training and testing accuracies of 97.37% and 96.59% (5 day) and 96.67% and 96.17% (15 day).
(f)
The learning curves were analyzed to evaluate the AMBO’s learning ability and to understand the behaviour of the DSN model during the learning process. Comparisons were made between the AMBO-DSN, GA-DSN, and PSO-DSN models (Figs 9 to 11) indicating the AMBO-DSN model’s performance in terms of convergence.
(g)
Comparing price trend predictions using optimized classifiers for USD/EUR, AUD/JPY, and CHF/INR over 5-day and 15-day periods (Tables 18 to Table 20), the AMBO-DSN model consistently achieves the highest accuracy and closely matches observed trends for both up-trends and down-trends. It outperforms other models in accuracy for 5-day predictions and maintains accuracy for 15-day predictions. The AMBO-DSN model’s superior performance establishes it as the optimal choice for predicting price trends, given its high accuracy and resemblance to observed trends.
(h)
The AMBO-DSN approach was employed for trend forecasting, comparing the trend percentages from original datasets with those generated by AMBO-DSN. For USD/EUR, the AMBO-DSN classifier showed a trend pattern similar to the original datasets, despite slight differences in percentages. The same consistency was observed for AUD/JPY, where the AMBO-DSN approach aligned with the original dataset trends. Similarly, for CHF/INR, the AMBO-DSN approach effectively forecasted trends that generally matched the original dataset trends for both 5 and 15 days ahead of prediction (Tables 6 to 11 and Tables 21 to 23).
(i)
The proposed AMBO-DSN trend forecasting model has been validated through K-S non-parametric statistical test and the time of execution (Table 21, Figs 12 and 13). The straight forward comparisons sates that AMBO-DSN is able to maintain favourable balance between accuracy and computational speed, enhancing the efficiency of decision-making processes.

The proposed methodology, the AMBO-DSN approach, seems to work well for Forex market directional movement forecasting for several reasons. Firstly, the Bi-LSTM model consistently demonstrated the highest accuracy and outperformed other selected models for all three currency pairs (USD/EUR, AUD/JPY, and CHF/INR). Additionally, the model’s predictions showed a strong alignment with the actual values of the currency pairs, even when incorporating additional features, highlighting its robustness. The analysis of trends based on the model’s predictions further validated its accuracy in forecasting directional movements. Secondly, the DSN model, used as a classifier, consistently outperformed other models (RNN and CNN) in accurately predicting currency pair trends for both 5 and 15-days forecast periods. It achieved high accuracy levels for all three currency pairs, indicating its effectiveness in classifying up-trends and down-trends. Thirdly, the learning curves analysis showed that the AMBO-DSN model exhibited good learning ability and convergence, making it reliable for the forecasting task. Moreover, the AMBO-DSN approach effectively forecasted trends that generally matched the original dataset trends for all three currency pairs, further validating its forecasting capability. Furthermore, the proposed AMBO-DSN trend forecasting model was validated through the K-S non-parametric statistical test, which demonstrated the model’s ability to maintain a favorable balance between accuracy and computational speed, enhancing the efficiency of decision-making processes. The combination of the Bi-LSTM model for accurate predictions and the DSN classifier for trend forecasting, along with the robustness and validation through statistical tests, contributes to the success of the proposed AMBO-DSN approach in accurately forecasting Forex market directional movements for different currency pairs and forecast periods.
6. Conclusion and future scope

This study focused on successful trading in the Forex market by emphasizing the importance of identifying market trends and utilizing trend analysis for informed decision-making. The proposed AMBO-DSN model, incorporating Bi-LSTM for price forecasting and trend change identification, demonstrated promising results in Forex trend forecasting. The model outperformed other ML, DL and statistical approaches, such as SVR, ANN, ARIMA, V-LSTM, and RNN, in terms of accuracy and prediction errors. The analysis of directional movement forecasting for USD/EUR, AUD/JPY, and CHF/INR currency pairs showed that the Bi-LSTM model consistently achieved the highest accuracy, accurately predicting currency pair values. The incorporation of additional features (AAs) further enhanced the predictive accuracy of the model, while the HHs-HLs and LHs-LLs trends provided valuable insights into directional movements. The DSN model, outperforming RNN and CNN, accurately predicted currency pair trends for both short-term (5-day) and medium-term (15-day) forecast periods. The DSN model’s high accuracy rates for all currency pairs confirmed its effectiveness in trend forecasting. The learning curves demonstrated the AMBO-DSN model’s learning ability and convergence behaviour, showcasing its performance. The AMBO-DSN approach effectively forecasted trends, aligning with the original dataset trends for USD/EUR, AUD/JPY, and CHF/INR currency pairs. The model maintained a favorable balance between accuracy and computational speed, enhancing decision-making efficiency. The validation through K-S statistical test and execution time analysis further supported the effectiveness and reliability of the AMBO-DSN model.

While our current work focuses on a specific set of currency pairs and incorporates certain market factors, there are several limitations that warrant consideration and exploration in subsequent research endeavours. Firstly, an important direction for future research could involve extending the application of our proposed model to encompass a broader array of currency pairs. By analyzing a more extensive range of currency pairs, we could attain a more comprehensive understanding of the model’s effectiveness and its adaptability across various market dynamics. Furthermore, our study currently integrates a selection of market factors into the model, but there is potential to enhance its robustness by quantifying additional variables. For instance, macro-economic factors, political scenarios, inflation rates, geopolitical events, central bank actions, market sentiment and risk appetite, etc. could all be systematically included. Additionally, the exploration of new nature-inspired optimization strategies could also yield valuable insights. This expanded scope would provide a more comprehensive analysis of currency market trends and their drivers.

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Forex market directional trends forecasting with Bidirectional-LSTM and enhanced DeepSense network using all member-based optimizer

Abstract

Keywords

1. Introduction

3. Methodologies adopted

3.1 Trend-based indicators

3.2 ARIMA, ANN, SVR, RNN, V-LSTM and Bi-LSTM for forecasting of forex market

3.3 The DeepSense network (DSN)

3.4 All Member-based optimizer (AMBO)

Table 2 Associated parameter values for predictive networks and optimization techniques

Table 3 Performance comparison of Bi-LSTM for USD/EUR with other predictive models for both 5 and 15 days forecasting horizons

Table 4 Performance comparison of Bi-LSTM for AUD/JPY with other predictive models for both 5 and 15 days forecasting horizons

Table 12 Year wise USD/EUR classification results for training and testing phases based on RNN, CNN and DSN for 5 days ahead

References

Table 2
Associated parameter values for predictive networks and optimization techniques

Table 3
Performance comparison of Bi-LSTM for USD/EUR with other predictive models for both 5 and 15 days forecasting horizons

Table 4
Performance comparison of Bi-LSTM for AUD/JPY with other predictive models for both 5 and 15 days forecasting horizons

Table 12
Year wise USD/EUR classification results for training and testing phases based on RNN, CNN and DSN for 5 days ahead