A memetic-based technical indicator portfolio and parameters optimization approach for finding trading signals to construct transaction robot in smart city era

Abstract

With the development of smart cities, the demand for personal financial services is becoming more and more importance, and personal investment suggestion is one of them. A common way to reach the goal is using a technical indicator to form trading strategy to find trading signals as trading suggestion. However, using only a technical indicator has its limitations, a technical indicator portfolio is further utilized to generate trading signals for achieving risk aversion. To provide a more reliable trading signals, in this paper, we propose an optimization algorithm for obtaining a technical indicator portfolio and its parameters for predicting trends of target stock by using the memetic algorithm. In the proposed approach, the genetic algorithm (GA) and simulated annealing (SA) algorithm are utilized for global and local search. In global search, a technical indicator portfolio and its parameters are first encoded into a chromosome using a bit string and real numbers. Then, the initial population is generated based on the encoding scheme. Fitness value of a chromosome is evaluated by the return and risk according to the generated trading signals. In local search, SA is employed to tune parameters of indicators in chromosomes. After that, the genetic operators are continue employed to generate new offspring. Finally, the chromosome with the highest fitness value could be provided to construct transaction robot for making investment plans in smart city environment. Experiments on three real datasets with different trends were made to show the effectiveness of the proposed approach, including uptrend, consolidation, and downtrend. The total returns of them on testing datasets are 26.53% 33.48%, and 9.7% that indicate the proposed approach can not only reach risk aversion in downtrends but also have good returns in others.

Keywords

Genetic algorithm memetic algorithms simulated annealing algorithm stock trend prediction technical indicators

1. Introduction

In recent years, with the popularization of wireless networks and mobile devices, the construction of smart cities has become a development trend [39, 5, 16, 14, 29]. There are many services should be prepared for building the smart cities, and one of the services required by smart cities is personalized financial service, e.g., asset allocation [22], stock recommendation [23]. For investors, stock price information is the key point that must be understood before investing, and accurate prediction of stock price is the goal that investors have been pursuing. Because stock prices are inherently volatile, dynamic, messy, and influenced by a multitude of factors, stock price forecasting has been and is still a difficult challenge [3]. Therefore, how to judge the current stock market trend, minimize the risk, and be able to obtain good performance in the unpredictable market is a topic of great concern to investors.

The research of stock market analysis can be divided into three analytic types: (1) fundamental analysis, (2) chip analysis, (3) technical analysis [27]. Fundamental analysis can be used to known fundamental information of a company based on different indicators, e.g., price-earnings ratio, return on equity, and price-book ratio, from various financial reports that could be the monthly revenue, quarterly report, annual report, etc. Hence, the stock price may be reacted and the time to enter the market may be too late. In other words, if using those fundamental analytic indicators to predict the company’s future prospects, it may have bias on the prediction result. Chip analysis can be used to observe the possible directions of institutional investors or market leaders. Following the operations of them, parts of investors believe considerable profits can also be obtained. But institutional investors or market leaders are always one step faster, and the early layout also ends early, so that the profit margin is limited and even getting loses. Technical analysis can use different types of technical indicators to find the behavioral model of the stock price as the basis for buying and selling decisions. Using of technical indicators to determine stock price trends must rely on extensive investment experience. Thus, it is not easily task for every investor to find a useful set of technical indicators to form the effective trading strategies.

In the stock market, the researches of technical indicators have always been one of the hotly discussed topics, and investors often use various technical indicators as the basis for stock trading. In recent years, many studies have shown that technical analysis can assist investors making trading decisions and getting profit in the financial markets [33, 19, 38, 9]. For instance, Zhong et al. indicate that financial variables, such as stock prices, stock market index values, and the prices of financial derivatives, are predictable [38]. Chong et al. also show that financial markets are to some extent predictable [9]. In addition, many studies present approaches to reveal that trading strategies can be formed to predict stock price trends using technical indicators. For example, Alsubaie et al. used classifiers to select the types of technical indicators to increase the investment income rate [1]. Uygun et al. established the trend of stock prices Model by using all possible combinations of technical indicators and various machine learning algorithms [25]. When the number of factors should be considered increases, it can be known that those factors tend to have collinearity and interfere with each other. The optimization algorithms are then suitable to be employed for solving the problems. For example, Li et al. considered the cross-entropy and the firefly algorithm to design a hybrid meta-heuristic algorithm for solving large scale optimization problems [18]. Utilizing genetic programming (GP), some approaches have also been designed for finding technical trading rules [17, 8, 28]. In those approaches, technical indicators such as the moving average and the rate of change and logical operations such as greater than and less than are used as variables in the tree structure to generate trading rules.

However, to generate effective and useful trading rules that can reduce the risk and increase return, the following two issues should be considered: (1) what technical indicators are suitable used together for a target stock to obtain more reliable trading signals; (2) what hyperparameters setting is appropriate for the used technical indicators to generate more accurate trading signals. In this paper, firstly, the memetic-based stock trend prediction framework that consists of three phases, including the data collection, data preprocessing, and optimization process, is proposed. In the third phase, an optimization algorithm is designed to obtain suitable technical indicators and their hyperparameters using the memetic algorithms (MAs). It utilizes the genetic algorithm (GA) and the simulated annealing algorithm (SA) for global and local searching. In GA, the technical indicators and their hyperparameters are encoded into a chromosome using a bit string and a real number array. Then, the risk and return values calculated by the generated trading signals from a chromosome are used as the fitness value. After reproduction process, the population is sent to SA for tuning hyperparameters of technical indicators. Next, the genetic operators are applied on the population to form new chromosomes. The process is repeated until reaching the termination conditions. Experiments on three datasets with different trends that are collected from Taiwan stock market were conducted to show the effectiveness of the proposed approach. Therefore, the contributions of this paper are listed as follows:

(1)
Firstly, the memetic-based stock trend prediction framework that consists of three phases, including the data collection, data preprocessing, and optimization process, is proposed for finding effective and useful trading rule.
(2)
Secondly, to obtain suitable technical indicators and their hyperparameters for target stock, an optimization algorithm based on MA that using GA and SA for global and local searching has been proposed so that more profitable trading signals can be generated.
(3)
Thirdly, empirical analysis on three real datasets with uptrend, sideway trend, and downtrend are given to show the merits of the proposed approach in terms of getting returns and avoiding risks.
(4)
Finally, the designed algorithm can be used to build investment robots to provide investment suggestions to users as part of personalized financial services in smart cities.

The rest of the paper is organized as follows. Section 2 presents the literature review. Section 3 describes the design framework and the proposed approach. Section 4 contains the results and analysis of the experiments. Conclusion and recommendation for future work are given in Section 5.
2. Literature discussion and memetic algorithms

Related literature discussion and MA are given in this section. Review of technical analysis is described in Section 2.1. MAs is introduced in Sections 2.2.

2.1 Review of technical analysis

Technical analysis attempts to use various patterns or quantitative indicators to analyze past trends based on historical stock price data, and then to speculate on future trends to get benefits. Technical analysis is based on the analysis of different historical data, e.g., stock price series, stock volume series. The characteristics of them are aggregated into technical indicators. In the following, literature of technical analysis is introduced.

About effectiveness of using technical indicators for trading, Ülkü et al. studied the gap between 22-day, 56-day, and 200-day moving average and obtained that macroeconomic fluctuations increase the profitability of technical trading rules, especially long-term rules such as 200-day moving average [32]. In other words, the interaction of the return volatility with the return persistence and macroeconomic volatility has a significant positive effect on profitability of technical rules. It is consistent with the view that technical signals are correlated with new information arrivals rather than noise. Metghalchi et al. used various technical indicators, including moving average (MA), relative strength index (RSI), moving average convergence divergence (MACD) and breakthrough (TBO), to show their prediction ability [21]. The results indicated that trading rules formed by technical indicators were effective and better than the buy-and-hold strategy. Ni et al. also indicated that the Taiwan weighted index (TWSE) could be beaten with the trading signals issued by Taiwan 50 through the Bollinger bands [24].

To generate more robust trading signals for target stock, it is necessary to combine multiple technical indicators. It can be reached by relying on the trained investment models for finding optimal parameters for these models based on one or several criteria. The other is to use the selected technical indicators to determine the appropriate trading time point. For instance, Ye et al. proposed a forecasting method for stock trend prediction by utilizing technical analysis, multi-order fuzzy time series and GA [37]. In their approach, technical indicators such as rate of change (ROC), MACD, and stochastic oscillator (KD) are used to construct the multi-variable fuzzy time series. In their approach, in order to get good performance, GA is used to find appropriate domain partition for the time series. Huang et al. proposed an approach which combined the biclustering pattern mining and fuzzy modeling, named the BM-FM approach, to automatically discover trading rules from a combination of technical indicators in the financial markets using particle swarm optimization [15]. Yazeed et al. investigated in how to select suitable number of technical indicators to build prediction model [1]. In that approach, five feature selection approaches were applied on fifty technical indicators to obtain appropriate features to construct nine classifiers based on cost-sensitive concept. As a result, authors suggest that naïve Bayes classifier is better than others. Besides, Li et al. proposed a multi-indicator feature selection method for stock price prediction based on Pearson correlation coefficient and the broad learning system to show trading based on a small number of technical indicators can outperform the broader market [20].

Because deep learning is popular in recent years, Peng et al. used three feature selection methods, including sequential forward floating selection, tournament screening, and LASSO, to obtain a suitable set of technical indicators to build prediction model using neural networks [26]. Next, Alotaibi proposed a hybrid red deer-grey algorithm that consisted of three main steps that are feature extraction, optimal feature selection, and prediction, for Saudi stock market prediction [2]. In the algorithm, it first generated related attributes using statistic measurements. For instance, they could be mean and variance, etc. Then, technical indicators were calculated using those generated data. The red deer adopted wolf algorithm which is a hybrid model was used to find crucial features. At last, using crucial features, the ensemble approaches were used to build prediction model.

2.2 Memetic algorithms

GA has been proposed in 1975 by John Holland, which is an optimization algorithm used to find near optimal solution for optimization problem. The main concept comes from Darwin’s characteristics of “Natural selection and survival of the fittest”. By simulating the competition between organisms, it has a strong ability to adapt to the environment. The parents in a population can generate next population through selection, reproduction, crossover, mutation, and other processes. The offspring will continue to evolve through the above process until the population reaching adaptive capacity. GA is not only applied in the financial field, but also in many different fields, such as engineering design [34], electrical engineering [31], investment portfolio [10], etc.

To enhance the searching ability of optimization algorithm, MAs, also known as cultural genetic algorithms, which consists of the population-based global search and individual-based local search phases, has been proposed for solving optimization problems. According to “The Selfish Gene” published by Dawkins [12], meme is the unit of information exchange between people, and it is everywhere. The reason why it is called meme is that information will be changed along with time, and leave only the important part of the process. In other words, the main concept of MAs is to used heuristic approaches together so that more useful solution can be found during the evolution process. For instance, in the population-based global search phase, the global search optimization algorithms can be used, including GA [7], particle swarm optimization [40], whale optimization algorithm [30], etc. In individual-based local search phase, the local search optimization algorithms can be used, including SA [36], hill climbing, tabu search [13], etc. The applications of MAs are very wide. For example, Chen et al. used MAs to solve the travelling salesman problem which is using a given series of cities and the distance between each pair of cities, the goal is to find the shortest path that the traveling salesman must pass through each city without repeating it, and return to the starting city [11]. Based on company-wide insurance simulation model, Yu et al. proposed a hybrid algorithm for solving multi-period asset allocation problem [35]. They indicated that the asset allocations derived by their proposed approach is better than existing investment strategies. Afsar et al. proposed an enhanced memetic algorithm by combining multiobjective evolutionary algorithm, called MOEMA, for solving green job shop scheduling [4]. The results also showed that their approach is effective to discover the good scheduling.

3. Proposed algorithm

3.1 Proposed memetic-based stock trend prediction framework

Using the given technical indicators and stock price series, the proposed memetic-based stock trend prediction framework is shown in Fig. 1.

From Fig. 1, we can know that the framework is divided into three phases. In first phase, the stock price datasets are collected from the Internet. Once the data collection is done, based on the technical indicators, the trading signals are calculated and marked in the second phase. The technical indicators used in this study cover both price and volume indicators. The main reason for using them is that they are commonly used to analyze behaviors of investors in the stock market. They include relative strength index (RSI), moving average (MA), stochastic oscillator (KD), money flow index (MFI), commodity channel index (CCI), rate of change (ROC), bias rate (BIAS), directional movement index (DMI), moving average convergence & divergence (MACD) and several other technical indicators. As a result, the trading signals for every day in the given time period are stored in a matrix. In the third phase, the proposed memetic algorithm is employed to find suitable technical indicators and their parameters for the desired target stock for trading. The proposed approach utilizes GA and SA for global and local searching to find appropriate technical indicators and tuning their parameters. In phase 3.1, it first encodes the technical indicators and corresponding parameters into a chromosome using a bit string and real numbers. Then, according to trading signals generated from a chromosome, the return and risk are calculated and set as the fitness value. After selection, the local searching is started for tuning the parameters using SA. In phase 3.2, parameters for the technical indicators will be tuned one by one to find the most suitable setting, and local optimized parameters are updated to the population. At last, the evolution process is repeated to obtain not only suitable technical indicators but also their parameters for the given target stock for trading.

Table 1
Stock information

Data	Shares	Amount	Open	High	Low	Close	Change	Turnover	StockNo	Month
2016/12/1	1170762	41662761	35.9	35.95	35.5	35.5	$-$ 0.4	786	2492	12
2016/12/2	1263373	44137048	35.15	35.15	34.8	34.85	$-$ 0.65	825	2492	12
2016/12/5	804108	27910155	34.85	35.15	34.6	34.6	$-$ 0.25	567	2492	12
2016/12/6	635955	22284225	35.1	35.2	34.9	34.9	0.3	381	2492	12
2016/12/7	3188753	115313641	35.35	36.5	35.3	36.4	1.5	1934	2492	12
2016/12/8	3342992	123367535	36.8	37.4	36.35	36.4	0	1805	2492	12
2016/12/9	836482	30276946	36.55	36.6	36.05	36.05	$-$ 0.35	631	2492	12
2016/12/12	774430	27754249	36.15	36.3	35.55	35.7	$-$ 0.35	516	2492	12
2016/12/13	2336685	85106412	35.9	36.9	35.7	36.9	1.2	1384	2492	12
2016/12/14	3759965	138936165	37.1	37.4	36.2	36.36	$-$ 0.55	1928	2492	12

Figure 1.

Proposed memetic-based stock trend prediction framework.

3.2 Data preprocessing

The relevant stock information is captured from the Taiwan Stock Exchange (TWSE), and three characteristics including upward trend, consolidation trend, and downward trend are collected as experimental datasets. Details of data preprocessing are described in the following sections.

3.2.1 Stock information crawler

The datasets used for training and testing the stock trend prediction approach is collected from the following link: https://www.twse.com.tw. It is a website which is issued by TWSE and provides stock information in Taiwan. For instance, the stock information, including shares, amount, open, high, low, close, etc., can be downloaded for subsequent used, and partial instances in December 2016 that are suitable to explain how to generate trading signals are shown in Table 1.

3.2.2 Technical indicators

The trading signals generated in this study by the used technical indicators that are determined according to the related literature and those commonly used by investors, including price and volume indicators, include RSI, MA, KD, MFI, CCI, ROC, BIAS, DMI, MACD. Continue using the collected instances in Table 1, according to the formulas of technical indicators, values of them are calculated and shown in Table 2.

Table 2
Calculated values of the used technical indicators

Date	MA5		MA20		RSI		CCI		MFI		ROC		Bias		K		D		MACD
2016/12/1	35.	77	35.	4	46.	88	5.	16	61.	99	2.	30	$-$ 0.	37	47.	81	54.	54	$-$ 0.	202
2016/12/2	35.	6	35.	36	42.	99	$-$ 126.	32	53.	48	$-$ 0.	71	$-$ 2.	09	25.	09	39.	82	$-$ 0.	258
2016/12/5	35.	43	35.	3	41.	56	$-$ 122.	8	47.	26	$-$ 3.	21	$-$ 2.	77	12.	54	26.	18	$-$ 0.	318
2016/12/6	35.	15	35.	305	43.	97	$-$ 80.	21	57.	83	$-$ 3.	32	$-$ 1.	88	13.	09	19.	63	$-$ 0.	338
2016/12/7	35.	25	35.	45	54.	14	66.	48	69.	03	1.	39	2.	17	47.	45	33.	54	$-$ 0.	23
2016/12/8	35.	43	35.	505	54.	14	142.	7	77.	67	1.	39	2.	1	55.	87	44.	7	$-$ 0.	143
2016/12/9	35.	67	35.	58	51.	61	63.	46	73.	33	0.	98	1.	08	53.	82	49.	26	$-$ 0.	101
2016/12/12	35.	89	35.	5975	49.	13	8.	75	66.	12	0.	7	0.	15	46.	55	47.	91	$-$ 0.	095
2016/12/13	36.	29	35.	67	56.	79	101.	8	66.	81	1.	65	3.	22	64.	34	56.	13	0.	006
2016/12/14	36.	28	35.	7225	52.	86	109.	98	74.	15	1.	25	1.	47	63.	42	59.	77	0.	041

Table 3

Trading rules of used technical indicators

Technical indicators	Buying rule	Selling rule
MA	MA5 $>$ MA20 & MA20 $>$ MA5 last day	MA5 $<$ MA20 & MA20 $<$ MA5 last day
RSI	RSI $>$ 30 & RSI $<$ 30 last day	RSI $<$ 70 & RSI $>$ 70 last day
CCI	CCI $>$ $-$ 100 & CCI $<$ $-$ 100 last day	CCI $<$ 100 & CCI $>$ 100 last day
MFI	MFI $>$ 20 & MFI $<$ 20 last day	MFI $<$ 80 & MFI $>$ 80 last day
ROC	ROC $>$ 0 & ROC $<$ 0 last day	ROC $<$ 0 & ROC $>$ 0 last day
BIAS	BIAS $>$ $-$ 10 & BIAS $<$ $-$ 10 last day	BIAS $<$ 10 & BIAS $>$ 10 last day
KD	K $>$ D & K $<$ D last day	K $<$ D & K $>$ D last day
K	K $>$ 20 & K $<$ 20 last day	K $<$ 80 & K $>$ 80 last day
MACD	MACD $>$ MACD(signal) &	MACD $<$ MACD(signal)
	MACD $<$ MACD(signal) last day &	MACD $>$ MACD(signal) last day
	MACD(histogram) $>$ 0 &	MACD(histogram) $<$ 0
DMI	$+$ DI $>$ $-$ DI & $+$ DI $<$ $-$ DI last day & ADX $>$ $-$ DI	$+$ DI $<$ $-$ DI & $+$ DI $>$ $-$ DI last day

Table 4

Generated trading signals

Date	KD_buy	KD_sell	CCI_buy	CCI_sell	ROC_buy	ROC_sell
2016/12/1	0	0	0	0	0	0
2016/12/2	0	0	0	0	0	1
2016/12/5	0	0	0	0	0	0
2016/12/6	0	0	1	0	0	0
2016/12/7	1	0	0	0	1	0
2016/12/8	0	0	0	0	0	0
2016/12/9	0	0	0	1	0	0
2016/12/12	0	1	0	0	0	0
2016/12/13	1	0	0	0	0	0
2016/12/14	0	0	0	0	0	0

3.2.3 Trading signals

Based on the calculated values and trading rules of each technical indicator, buying and selling signals can be generated. The trading rules used in the proposed approach are shown in Table 3.

In Table 3, take the strategy using MA: “When $MA({5})>MA({20})$ , then buying signal, and when $MA({5})>MA({20})$ , then selling signal.” as an example. It means when 5-day MA value is larger than 20-day MA value, a buying signal is generated. On the contrary, a selling signal is generated. Utilizing the trading strategies, the generated trading signals on the same time period are given in Table 4.

Using trading signals showed in Table 4, the trading results can then be calculated based on what technical indicators are used and their buying and selling signals. To find appropriate technical indicators and their parameters will have influenced on the trading results, in this paper, we attempt to design an optimization algorithm to solve the problem.

3.3 Components of proposed trend prediction approach

3.3.1 Encoding scheme and initial population

In designing an optimization algorithm, how to encode a solution into a chromosome is important. The goal of the proposed approach is to find a set of appropriate technical indicators as well as their parameters to identify trading signals for a certain stock. Hence, the given technical indicators and their parameters are encoded into a chromosome. The chromosome representation is shown in Fig. 2.

Figure 2.

Chromosome encoding scheme.

Figure 2 shows that $n$ technical indicators, $T_{1},T_{2},\ldots,T_{n}$ , are considered and every technical indicator is represented by a bit, $b_{i}$ , which is used to indicate whether using the $i$ -th technical indicator and a set of real numbers, $p_{i1},p_{i2},\ldots,p_{ij},\ldots,p_{ih}$ , that are used to represent its parameters. Below, an example is given in Fig. 3 to illustrate how to represent a possible solution.

Figure 3.

An example for chromosome representation.

From Fig. 3, we can see that ten technical indicators are encoded in a chromosome. According to the $b_{i}$ values, it indicates that MA, CCI, and ROC are used as the technical indicator portfolio to identify the trading signals. The parameters of the ten indicators are shown in the third row. Take MA as an example. Two parameters, 5 and 20, are used for MA which means that the 5-day MA and 20-day MA are utilized to find trading signals. Based on the encoding scheme, the initial population can be generated randomly. In this paper, the ten technical indicators are used to form a chromosome, and every chromosome should have at least a technical indicator being used. When the number of generated buying signals is greater than half of the total number of technical indicators used in a chromosome, a buying action is executed. If a buying action is encountered before a selling action, the holding status remains unchanged. In other words, when the number of generated selling signals is greater than half of the total number of used technical indicators, a selling action is executed. If there is no selling action before the end of the test data after the last purchasing of a stock, the stock will be sold on the last trading day.

3.3.2 Fitness function

After the initial chromosomes are created, the fitness function of each chromosome is calculated to determine the fitness score in the evolution process. In this study, two factors are utilized to evaluate a chromosome. The first one is the average rate of return of a chromosome which is calculated according to its used technical indicators, and the second one is the risk for a chromosome which is set as the maximum rate of decline in returns. Thus, the fitness function of a chromosome $f(C_{q})$ is defined in Eq. (1):

$\displaystyle f(C_{q})=\frac{\sum_{i=1}^{n}{R^{q}_{i}}}{n*\textit{risk}^{q}},$ (1)

where $R^{q}_{i}$ is the return rate of the $i$ -th transaction, and the $\textit{risk}^{q}$ is the risk of the chromosome. $R^{q}_{i}$ is calculated by the $i$ -th selling price $S_{i}$ and the $i$ -th buying price $B_{i}$ , which is defined in Eq. (2):

$\displaystyle R^{q}_{i}=\frac{S_{i}-B_{i}}{B_{i}}*100\%$ (2)

Let there are $n$ transactions, $\textit{risk}^{q}$ is set as the difference between the maximum return $R_{\max}$ and the minimum return $R_{\min}$ that generated from the $n$ transactions.

Figure 4.

Evolutionary process including used genetic operators.

3.3.3 Genetic operators used in genetic algorithm

In GA, genetic operators are employed to generate new offspring. In general, crossover and mutation operators are used to form new chromosomes, and selection operator is utilized to form next population. In this paper, the flowchart of the evolutionary process including the used genetic operators is shown in Fig. 4.

In Fig. 4, using Eq. (1), the fitness values of all chromosomes are calculated. Then, the selection operator is performed. The top- $n$ % chromosomes are selected as offspring of next population according to their fitness scores. Let population size is ten, the selection operator is shown in Fig. 5.

Figure 5.

Selection operation.

In Fig. 5, chromosomes are sorted based on their fitness values, and when $n$ is set at 50%, five chromosomes are chosen and kept in next population. Then, the crossover operator is employed to generate other five chromosomes. It will select two distinct chromosomes from the top-5 chromosomes as parent. According to a randomly generated crossover point, the first half of first chromosome and last half of second chromosome are merged as a new chromosome. An example is given to show crossover operator in Fig. 6.

Figure 6.

An example of crossover operation to generate a new offspring.

From Fig. 6, the crossover point is located at “ROC”. Hence, the genes from “MA” to “MFI” of first chromosome, and “ROC” to “DMI” of second chromosome are combined as a new offspring. The crossover is repeated until generating requirement number of chromosomes for next population. After that, the mutation operator is applied on the population to get new offspring, and it gives ability for the proposed algorithm to avoid falling into local optimal solution. An example for mutation is given in in Fig. 7.

Figure 7.

An example of mutation operation.

From Fig. 7, it mutated on the gene “MACD”, therefore, the value is changed from 1 to 0, which means that the technical indicator “MACD” doesn’t use to find trading signal. The evolutionary process is repeated until reaching the termination condition.

3.3.4 Local search using simulated annealing

In this study, the parameters of the technical indicators are tuned in the local searching phase using the SA algorithm. For a chromosome, it will randomly generate values based on the given domains of technical indicators to replace the original parameters. Then, fitness value of the new offspring is calculated. If the fitness value of new offspring is better than original, the new one will replace the old one. However, when the fitness value of the new offspring is worse than the original one, SA still can accept it with a certain probability. The probability of accepting a poor solution decreases as the number of iterations increases, or as the temperature $T$ decreases. The parameters used in SA is described as follows: Tmax: Initial maximum temperature; Tmin: Minimum temperature; $a$ : Attenuation coefficient (cooling coefficient); $\textit{Count}_{\textit{sta}}$ : Number of consecutive new solutions not used; $\textit{Count}_{\textit{end}}$ : Number of new solutions reached without being used and exited; $D$ : Probability of randomly generating a new solution (if the new solution is not better than the old solution), where the parameter $D$ is given using the following Eq. (3):

$\displaystyle D=e^{-de/\textit{Tmax}},$ (3)

where $e$ is the mathematical constant with a value of approximately 2.718, $d e$ is the difference between the old and new income rates(old income rate – new income rate), and Tmax is the parameter described above(initial maximum temperature). The pseudocode for SA used in the proposed approach in this paper is given in Algorithm 3.3.4.

SA used in the proposed approachPopulation population and predefined domains for parameters of technical indicators Dom. Initial temperature $T_{0}$ , minimum temperature $T_{\min}$ , maximum count $\textit{count}_{\max}$ and cooling coefficient $a$ . The chromosome with the tuned parameters. $S$ $=$ bestChromosome (population); $T\leftarrow{T}_{0}$ ; $(T>{T}_{\min})\ \&\&\ (\textit{count}<{\textit{count}}_{\max})$ (i in range 10) Generate new parameters for $i$ -th technical indicator in $S$ to form solution $S^{\prime}$ ; $f(S^{\prime})>f(S)$ $S\leftarrow S^{\prime}$ ; $\textit{count}=1$ ; $\textit{count}++$ ; $\Delta=f(S^{\prime})-f(S)$ ; $D=e^{-\Delta/T}$ ; $\textit{rand}()<D$ $S\leftarrow S^{\prime}$ ; $T=a\times T$ ;

In Algorithm 3.3.4, it first selects the current best chromosome $S$ from population (line 2). Then, SA is started to tune parameters of technical indicator (lines 3 to 20). For an iteration, new parameters are generated according to the given domains of technical indicators Dom to form new solution $S^{\prime}$ (line 6). The return is used as the evaluation function to calculate score of new chromosome (line 7). If return of $S^{\prime}$ is higher than $S$ , the old one is replaced by $S^{\prime}$ (line 8). On the contrary, the old one is replaced by new one with a probability of $D$ (lines 14 to 16). After that, the temperature $T$ is adjusted through the cooling coefficient $a$ (line 19). If the termination condition is not reached, it goes to next iteration (line 4).

3.3.5 Pseudo code of the proposed approach

Based on the descriptions in previous subsections, the pseudo code of the proposed memetic-based algorithm for finding suitable technical indicators and their parameters to identify trading signals for a target stock is shown in Algorithm 3.3.5.

[h] The proposed methodA stock price series ${S}=\{{s}_{1},{s}_{2},\ldots,{s}_{n}\}$ , technical indicators ${TI}=\{{ti}_{1},{ti}_{2},\ldots,{ti}_{n}\}$ , and predefined domains for parameters of technical indicators $\textit{Dom}=\{\textit{tdom}_{1},\textit{tdom}_{2},\ldots,\textit{tdom}_{n}\}.$ Iterations iter, population size pSize,and mutation rate ${m}_{\textit{rate}}$ , retain rate of selection $r_{\textit{rate}}$ . The chromosome with the highest fitness value. $\textit{population}\leftarrow$ InitialChro $(\textit{pSize},TI,\textit{Dom})$ ; $i\leftarrow 0$ iterchrominpopulation ${\textit{fitness}}_{j}\leftarrow$ calculateFitness $(\textit{chrom})$ ; $\textit{population}^{\prime}$ $\leftarrow$ executeSelection (population, pSize, $r_{\textit{rate}}$ ); $\textit{population}^{\prime\prime}$ $\leftarrow$ localSearchSA ( $\textit{population}^{\prime}$ , Dom); // Using Algorithm 3.3.4 $\textit{population}^{\prime\prime\prime}$ $\leftarrow$ executeCrossover ( $\textit{population}^{\prime\prime}$ , pSize);population $\leftarrow$ executeMutation ( $\textit{population}^{\prime\prime\prime}$ , ${m}_{\textit{rate}}$ ); $\textit{bestChro}\leftarrow$ theBestChro (population);

In Algorithm 3.3.5, lines 1 to 13 describes the entirety process of the proposed approach. It first initializes the population according to population size pSize, technical indicators $T I$ , and their parameters Dom (line 2). After that, it starts the evolutionary process (lines 3 to 11). Fitness values of Chromosomes are calculated by the Eq. (1) (lines 4 to 6). Then, selection operator is executed on population to generate next population based on the given retain rate $r_{\textit{rate}}$ (line 7). The SA algorithm is utilized to tune parameters of the used technical indicators (line 8). The crossover operator is then executed to generate offspring until reaching the required number of chromosomes (line 9). The mutation operator is performed on the population based on the mutation rate ${m}_{\textit{rate}}$ (line 10). At last, when the termination condition is reached, the best chromosome is outputted.

3.4 An example

In the following, an example is given to illustrate the proposed approach on the real stock dataset collected from Taiwan stock market from 2015 to 2019. The used dataset contains number of shares traded, amount traded, opening, high, low and closing prices, spread, and turnover, etc. The used technical indicators include RSI, $M A$ , $K D$ , MFI, CCI, ROC, BIAS, DMI, MACD, etc., as described in Section 3.2.

Step 1: Data Preprocessing. In data preprocessing, the values of the used technical indicators are first calculated, and the trading signals are then generated. Parts of results are shown in Tables 2, and 4.

Step 2: Chromosome encoding. Because ten technical indicators are used, a bit string contains 10 bits is used to represent them, where 1 and 0 means to use and not to use an indicator. As to parameters of technical indicators, they are encoded by a real number string. An example is shown in Table 5.

Table 5
An example of chromosome representation

MA		RSI		CCI		MFI		ROC	BIAS		KD		K		MACD	DMI
1		1		0		0		0	0		0		1		0	0
5	20	30	70	100	$-$ 100	20	80	0	$-$ 10	10	–	–	20	80	0	–	–

From Table 5, because there are three “1” in the bit string, it indicates that three technical indicators, MA, RSI and K, are used in the chromosome. According to their parameters shown in the real number vector, the indicators used to generate trading signals are $MA({5},{20})$ , $\textit{RSI}({30},{70})$ and $K({20},{80})$ , respectively.

Step 3: Generating the initial population. Let population size is 10, the initial population with 10 chromosomes are generated randomly according to the encoding scheme.

Step 4: Calculating Fitness function. After the initial population is generated, the designed fitness function is employed to calculate fitness value of each chromosome. Continue using the chromosome showed in Step 2, the trading rules are formed as follows:

•

$M A$ : Buying when $MA{5}>MA{20}$ ; Selling when $MA{5}<MA{20}$ .

•

RSI: Buying when $\textit{RSI}<{30}$ and the RSI value goes over 30 from bottom to top; Selling when $\textit{RSI}>{70}$ and the RSI value goes over 70 from top to bottom.

•

$K$ : Buying when $K<{20}$ and the K value goes over 20 from bottom to top; Selling when $K>{80}$ and the K value goes over 80 from top to bottom.

Based on the trading rules, buying and selling signals can be generated. When the number of buying signals is greater than half of the number of used indicators, a buying action is suggested. On the contrary, when the number of selling signals is greater than half of the number of used indicators, a selling action is suggested. After the last buying action is executed, if there is no selling action before the end of the testing data, a selling action is executed on the last trading day, and vice versa. In the five-year training data, a total of 22 transactions were made, and the average return rate is 68%.

Step 5: Selection operation. Assume the retain rate is set at 50%, the selection operator is selected top-50% chromosomes based on their fitness values. For other half chromosomes, they will be generated via crossover operator.

Step 6: Using SA for tuning parameters. The SA algorithm is used to tune parameters for the technical indicators. An example for parameter tuning of MA is given in Fig. 8.

From Fig. 8, the return rate of MA using original parameters, $MA{5}$ and $MA{20}$ , is 330.15% during the training period. According to the predefined domain of MA, SA then generates randomly two new values that are 6 and 21 to replace the old values as shown in the right hand side figure, and the return rate of the new chromosome is 338.54%. Because the return rate of the new one is better than original one, the new one is updated to population. However, when the new one is worse, it still has the chance to replace the original one through a given threshold. Using the same way, parameters of other technical indicators are also tuned. Then, the iteration is repeated until the temperature $T$ is smaller than minimum temperature $T_{\min}$ .

Step 7: Crossover operation. In this step, the goal is to generate not only new offspring but also enough number of chromosomes for population. Two different chromosomes were selected from the top-50% chromosomes as the parent chromosome. It then generates a crossover point randomly. First half genes of first chromosome are combined with last half genes of second chromosome according to the crossover point to form a new offspring, as shown in Fig. 6.

Step 8: Mutation operation. After crossover, based on the given mutation rate, genes in the population are randomly selected for mutation, with 0 becoming 1 and 1 becoming 0, as shown in Fig. 7. If the number of iterations is not yet finished, it will go back to Step 4 for calculating fitness of new chromosomes, and keep repeating the evolutionary process.

Step 9: Outputted final result. When reaching termination condition, the chromosome with the largest fitness value is selected as the best solution. In this example, the best one is shown in Table 6.

Table 6

The final best chromosome in this example

MA		RSI		CCI		MFI		ROC	BIAS		KD		K		MACD	DMI
1		1		0		0		1	0		0		1		0	1
6	21	30	70	98	$-$ 102	20	80	0	$-$ 15	15	–	–	20	80	0	–	–

Figure 8.

An example of parameter turning using SA.

In Table 6, it shows that the five technical indicators, including MA, RSI, ROC, K, and DMI, are used at the same time to find trading signals. The parameters used for the used technical parameters are shown in the second row of the table.

4. Experimental results

4.1 Experimental datasets and environment descriptions

To evaluate the effectiveness of the proposed approach, the three datasets, including uptrend, sideway trend, and downtrend, are collected from Taiwan stock market. The collected period is from 2015 to 2020, and time periods from 2015 to 2019, and 2020 are used for training and testing, respectively. The stock symbols for the collected companies are 2330, 2492, and 2498, and the stock prices series of them are shown in Figs 9–11.

Table 7
Information of experimental environment

Hardware device	Mac Book Air (13-inch, Early 2015)
	CPU 1.6 GHz Intel Core i5
	RAM 8 GB 1600MHz DDR3
	Intel HD Graphics 6000 1536MB
Operation system	macOS Catalina 10.14.6
Programming language	Python 3.7
DevelopmENT PLATForm	Anaconda 2020.02
	Spyder 4.1.5

Figure 9.

Uptrend dataset.

Figure 10.

Sideway trend dataset.

From Figs 9–11, the blue and gray areas are used as training and testing periods in the following experiments. As to the experimental environment, information of hardware and software is shown in Table 7.

Figure 11.

Downtrend dataset.

The parameters that used in SA are set as follows: initial maximum temperature Tmax is 5000, minimum temperature Tmin is $1e^{-8}$ , attenuation coefficient $a$ is 0.98, number of new solutions not used continuously $\textit{Count}_{\textit{sta}}$ is 0, number of new solutions not used and exited $\textit{Count}_{\textit{end}}$ is 100, and probability of generating new solutions randomly $D$ is $e^{-de/\textit{Tmax}}$ . The parameters used in GA are set as follows: population size pSize is 50, number of iterations (generations) iter is 100, mutation rate $m_{\textit{rate}}$ is 0.001.

4.2 Analysis of proposed approach on difference stock trends

Based on the collected three datasets, the experimental results are shown and discussed in this section.

4.2.1 Analysis on uptrend dataset

After generations, the best chromosome for the uptrend dataset obtained from 30 runes is shown in Table 8.

Table 8
Best chromosome of uptrend dataset

MA		KD		RSI		CCI		MFI		ROC	BIAS		K		MACD	DMI
1		1		0		1		0		0	0		0		1	0
8	23	–	–	9	85	112	$-$ 76	2	67	10	$-$ 5	15	22	80	6	–	–

From Table 8, it shows that four indicators are used to identify trading signals. In the training phase, the highest return is 78.35%. Then, using a-year (2020) testing dataset, the related trading results are shown in Table 9.

Table 9

Trading results in testing period on uptrend dataset

Total number of transactions	6 times
Saperate payoff rate	$-$ 3.12%, $-$ 2.01%, 20.6 %, 0.71%, 4.14%, 6.21%
Maximum payoff rate	20.6%
Minimum payoff rate	$-$ 3.12%
Total number of profits	4 times
Total number of losses	2 times
Winning rate	66.67%
Total return rate	26.53%
Average return rate	4.42%

From Table 9, it shows that the number of transactions is six in the year 2020, and returns of them are -3.12%, -2.01%, 20.6%, 0.71%, 4.14%, 6.21%, respectively. In other words, the cumulative return is 26.53% for the whole year. The winning rate is 66.67%.

4.2.2 Analysis on sideway trend dataset

Using the same parameter setting, after generations, the best chromosome discovered by the proposed approach is shown in Table 10.

Table 10
Best chromosome on sideway trend dataset

MA		KD		RSI		CCI		MFI		ROC	BIAS		K		MACD	DMI
1		1		0		0		0		1	1		0		0	0
7	24	–	–	24	72	116	$-$ 110	12	75	11	$-$ 12	16	19	77	$-$ 6	–	–

From Table 10, it suggests that the suitable technical indicators are MA, KD, ROC, and BIAS, and the return of it is 494.42%. Applying the obtained chromosome to the year of 2020 for testing, the related trading results are shown in Table 11.

Table 11

Trading results in testing period on sideway trend dataset

Total number of transactions	4 times
Saperate payoff rate	$-$ 2.43%, $-$ 4.79%, 15.79%, 20.05%
Maximum payoff rate	20.05%
Minimum payoff rate	$-$ 4.79%
Total number of profits	3 times
Total number of losses	1 times
Winning rate	75%
Total return rate	33.48%
Average return rate	8.37%

From Table 11, it shows that there are totally four transactions when the four technical indicators are used, and returns of them are 2.43%, $-$ 4.79%, 15.79%, and 20.05%, which also means that the cumulative return is 33.45% for the whole year. The winning rate is 60%.

4.2.3 Analysis on downtrend dataset

In downtrend dataset, after 100 generations, the best chromosome obtained by the proposed approach is shown in Table 12.

Table 12
Best chromosome on downtrend dataset

MA		KD		RSI		CCI		MFI		ROC	BIAS		K		MACD	DMI
1		0		1		1		0		0	0		1		1	0
7	20	–	–	24	86	98	$-$ 76	5	71	7	$-$ 10	18	16	82	$-$ 9	–	–

From Table 12, it shows that when using MA, RSI, CCI, and K together to find trading signals, the highest return which is 26.68% can be generated. The trading results on the testing period using the obtained chromosome are shown in Table 13.

Table 13

Trading results in testing period on downtrend dataset

Total number of transactions	5 times
Saperate payoff rate	$-$ 0.99%, 3.81%, 3.33%, $-$ 1.04%, 4.59%
Maximum payoff rate	4.59%
Minimum payoff rate	$-$ 1.04%
Total number of profits	3 times
Total number of losses	2 times
Winning rate	60%
Total return rate	9.7%
Average return rate	1.94%

In Table 13, it shows that number of transactions is five, and returns of them are $-$ 0.99%, 3.81%, 3.33%, $-$ 1.04%, which means that total return is 9.7% for the whole year. Because returns of three out of five transactions are positive, the winning rate is 60% for downtrend dataset.

4.3 Comparing to the buy and hold strategy

Next, to show the merits of the proposed approach, comparison results of the proposed approach and the well-known buy & hold strategy (BHS) [6] in terms of cumulative return were made on the three datasets, and the results are shown in Figs 12–14.

Figure 12.

Comparison results of proposed approach and BHS on uptrend dataset.

From Fig. 12, the red and blue dotted lines are cumulative returns of the proposed approach and BHS. It shows that the returns of the proposed approach and BHS are 26.53% and 53.24%, which means that BHS is better than the proposed approach on uptrend dataset. Besides, we can also see that HBS dropped significantly in March 2020 due to the impact of COVID-19. However, when using the obtained technical indicators for trading, it can avoid the event in that period of time. In other words, although the proposed approach provides less return than BHS, it has better ability to avoid risk.

Figure 13.

Comparison results of proposed approach and BHS on sideway trend dataset.

From Fig. 13, it shows that cumulative returns of the proposed approach and BHS are 33.48% and 8.19% on testing dataset. Based on the results, we can know that the proposed approach is better than BHS in terms of cumulative return and ability to avoid loss on sideway trend dataset.

Figure 14.

Comparison results of proposed approach and BHS on downtrend dataset.

From Fig. 14, it shows that the cumulative returns of the proposed approach and BHS are 9.7% and $-$ 14.62% on testing dataset, which indicates using BHS is risky in the bear market. However, when using the obtained technical indicators for trading, the results show again that reliable trading signals can be provided to get the profit and avoid massive loss in downtrend dataset.

4.4 Comparing proposed approach to GA

At last, experiments were conducted on the three datasets to show the effectiveness of the proposed approach with and without SA. When using the proposed approach without SA, it means that only GA is used. Experimental results on the three datasets are shown in Figs 15–17.

Figure 15.

Proposed approach with and without SA on uptrend dataset.

From Fig. 15, it shows that cumulative return of the proposed approach is similar or a little bit better than it without SA. As showed in previous section, its cumulative return and average return are 26.53% and 4.42%. When using only GA for optimization, five transactions are made, and cumulative return and average return are 25.44% and 5.09%. Besides, the interesting observation is that the first transaction of two approaches are both made after May which mean that the obtained technical indicators can successfully avoid the previous time interval with a large decline.

Figure 16.

Proposed approach with and without SA on sideway trend dataset.

From Fig. 16, it shows that the proposed approach is better than it without SA. Its cumulative return and average return are 33.48% and 8.37%. When using only GA for optimization, four transactions are made, and cumulative return and average return are 18.26% and 4.57%. The first transactions of them are again made after May, which shows their ability to avoid risk. Hence, based on the results, we can say that the proposed approach on sideway trend dataset is effective to find reliable trading signals.

From Fig. 17, it shows that the proposed approach is also better than it without SA. The cumulative return and average return of the proposed approach are 9.7% and 1.94%. When using only GA for optimization, six transactions are made, and its cumulative return and average return are 5.04% and 0.84%. In addition, it shows that when using SA for parameter tuning, the cumulative return is around two times better than that without SA. Based on the results, we can say that the obtained technical indicators and parameters by the proposed approach are effective on not only to avoid massive loss but also to get profit even the downtrend dataset used.

At last, the execution time of the proposed approach and GA with different population sizes of a generation is shown in Table 14.

Table 14

Comparison of the proposed approach and GA in terms of execution time (Sec.)

Population size	GA	Proposed approach
10	7.7	3431.1
30	22.2	7055.8

Figure 17.

Proposed approach with and without SA on downtrend dataset.

In Table 14, we can observe that when the population sizes are set at 10 and 30, the execution time for GA and the proposed approach are 7.7 and 22.2, and 3434.1 and 7055.8 seconds. It indicates that the execution time of finding appropriate technical indicators and their parameters by using the proposed approach is higher than that by GA. This results are reasonable because SA is used in the proposed approach as local search algorithm.

4.5 Summaries of observations

Based on the experimental results, following observations can be found: (1) The first one is that the final chromosomes derived by the proposed approach can reach positive returns no matter what trends of datasets are in training and testing phases; (2) The second observation is that different technical indicators and their parameters can be obtained for stocks with different trends to reduce the risk by using the proposed approach; (3) The third observation is that number of transactions by using the obtained chromosomes is few for the three datasets and the winning rates of them are around 60%, which mean that the used technical indicators can identify more profitable and safe trading signals; (4) Comparison results also indicate that the cumulative return of proposed approach is better than BHS and that using only GA. In other words, we can conclude that the proposed approach is effective.

5. Conclusions and future work

Due to the demand for personal financial services in smart cities, in this study, the memetic-based stock trend prediction approach has been proposed to find a set of technical indicators as well as their parameters for identifying more reliable trading signals for constructing the effective transaction robot. In the proposed approach, GA and SA are used as the global search and local search algorithm. In the global search, technical indicators and their parameters are encoded into a chromosome by a bit string and real numbers. Fitness value of a chromosome is evaluated by returns and maximum risk of transactions. In local search, SA is used to tune parameters of the used technical indicators. Then, genetic operators are executed to generate new offspring. The evolution process is repeated until reaching termination conditions. To show the merits of the proposed approach, experiments were conducted on the uptrend, sideway trend, and downtrend datasets, and reveal that: (1) Experimental results show that the proposed approach provides useful technical indicators and their parameters as well for target stock to increase profit and avoid massive loss; (2) Comparing to the proposed approach without SA shows that the proposed approach is effective in finding more useful parameters to increase profit. In the future, based on the proposed approach, we will continue to design more advanced algorithms. For instance, considering types of technical indicators to enhance the fitness function so that a more robust set of technical indicators and parameters can be found. In addition, different types of global and local search algorithms could be employed to enhance the proposed approach. Besides, we will also try to build a fair platform to compare the proposed approach to the existing approaches.

Footnotes

Acknowledgments

This research was supported by the National Science and Technology Council of the Republic of China under grant NSTC 111-2221-E-992-088-MY2.

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A memetic-based technical indicator portfolio and parameters optimization approach for finding trading signals to construct transaction robot in smart city era

Abstract

Keywords

1. Introduction

2.1 Review of technical analysis

2.2 Memetic algorithms

3. Proposed algorithm

3.1 Proposed memetic-based stock trend prediction framework

Table 1 Stock information

3.2.1 Stock information crawler

3.2.2 Technical indicators

Table 2 Calculated values of the used technical indicators

3.3 Components of proposed trend prediction approach

3.3.1 Encoding scheme and initial population

3.4 An example

Table 5 An example of chromosome representation

4.1 Experimental datasets and environment descriptions

Table 7 Information of experimental environment

4.2.1 Analysis on uptrend dataset

Table 8 Best chromosome of uptrend dataset

Table 10 Best chromosome on sideway trend dataset

Table 12 Best chromosome on downtrend dataset

5. Conclusions and future work

Footnotes

Acknowledgments

References

Table 1
Stock information

Table 2
Calculated values of the used technical indicators

Table 5
An example of chromosome representation

Table 7
Information of experimental environment

Table 8
Best chromosome of uptrend dataset

Table 10
Best chromosome on sideway trend dataset

Table 12
Best chromosome on downtrend dataset