A EMD-BP integrated model to forecast tourist number and applied to Jiuzhaigou

Abstract

This paper focuses on improving the accurate prediction of tourist capacity, which is the key to solve the contradiction of tourism economy development and ecological environment protection. EMD-BP integrated predictive model is proposed and uses Empirical Model Decompose method to decompose time-series data of visitors into several TMF, then forecasting each component by BP neural network. In order to shown the effective of our method, an empirical study of Jiuzhaigou is conducted, and the average error rate of EMD-BP integrated prediction model is 8.8%, among which the error within 1% accounts for 31.3% of the total predicted amount, the error within 5% accounts for 41.7%, the error above 10% accounts for 30.2% in slack seasons and 69.8% in busy seasons.

Keywords

Empirical Model Decompose BP neural network integrated prediction method JiuZhaigou

1 Introduction

In the development of tourism, the predication of tourist capacity is of great importance. An accurate prediction of tourist capacity can greatly improve the quantitative level of tourism economy, which is helpful to the formulation of the development plans and policies in tourist areas as well as solving the problems existing in scenic spots (especially the damage to ecological environment caused by tourism in the development of tourism) [1].

The research on tourism demand prediction made by western scholar’s dates from the 1960s, and it experienced a rapid development in the 80s. Most of their research literature lays particular emphasis on tourism demand model and empirical analysis. Relevant research in China didn’t start until the late 20th century, the existing literature is mainly the theoretical introduction and discussion based on the research in the west, and empirical studies are quite few [2]. At present, the prediction methods of tourist capacity can be divided into two types: qualitative method and quantitative method, among which the major research method is the quantitative method. The quantitative prediction method can be further classified into four types, including non-causal time series model, causal measurement model, artificial intelligence model and combined model.

Time series model believes that the dynamic state observed from historical data may sustain for a period of time in the future, so we can recur future according to the past [3], thus saving data collection cost. Major time series models include moving average method, exponential smoothing method, autoregressive moving average method and seasonal autoregressive moving average method, among which the most widely used in tourist capacity prediction is Autoregressive Integrated Moving Average (ARIMA) [4 –7]. However, there still exist disputes over whether ARIMA model is superior to other models. For example, Coh mentioned that ARIMA model was much better than other time series [8], and Smeral and Wuger made empirical analysis, which showed that SARIMA model or ARIMA model were not better than Native (no-change) [9]. Among the time series models, Generalized Autoregressive Conditional Heteroskedasticity (GARCH) is widely used in tourism demand prediction, such as Liang [10].

Relative to time series model, the superiority of measurement model is that it analyzes the causal relationship between tourist capacity and its influencing factors, which can provide reference to relevant measures and policies of administering authority of the scenic spots. However, traditional measurement models may experience spurious regression, so in order to break through this defect, Autoregressive Distributed Lag Model (ADLM), Error Correction Model (ECM), Vector Auto-regression Model (VAR) and Time Variable Parameter (TVP) Model appear successively and are widely used. For example, Fung-Thai [11], Koonnam [12] all use ECM to predict tourist demand; Tran [13], as well as Tsaur [14] use VAR model; in literature, the author also uses TVP model, and proves that TVP model is superior to other measurement models.

With the rise of artificial intelligence technology, artificial intelligence technology has also been introduced to the prediction of tourist capacity. It breaks through the limitation of linear prediction of the previous prediction method. In the middle and late 1990s, Rob Law introduces artificial neural network to the prediction area in order to predict the Japanese tourists’ tourism demand towards Hong Kong [15], which was widely used soon afterwards.

Various single prediction models have achieved relatively high prediction accuracy, but influenced by many factors, all single prediction methods usually can’t cover the overall and effective information of tourism demand, thus greatly reducing the accuracy of the prediction result [16]. Therefore, various combined prediction models become the research focus of many scholars. Through combination, the advantages of various single models are integrated, thus improving the effect of the prediction. For example, Liao et al. firstly used ARIMA combined model to predict the initial predicted value of Chinese inbound tourists, then used BP neural network to correct the error of the initial predicted value, thus improving the prediction accuracy [17] as well as Shao [18]. Wang Yong et al. used LOGISTIC model and regression iterative model to make combined prediction, thus improving the accuracy of the predicted result [19]. In order to break the limitation of quantitative method and improve the accuracy of prediction, some scholars combine the quantitative method with qualitative method, constituting the quantitative-qualitative combined model. But usually, in terms of the combination method, summing and weighting are made after the prediction with different prediction methods. However, there are many factors influencing tourist capacity and existing the feature of loud noise; in addition, various emergencies will also influence the result, so their relationship doesn’t just present a simple linear relation. Therefore, it exists limitations in the combination methods of the combined model, and its prediction accuracy also remains to be improved.

Accordingly, this thesis adopts the method of empirical model decomposition to decompose the time series of tourist capacity into multiple IMFs which can represent its internal features, and then makes use of BP neural network to predict the components.

2 EMD-BP network prediction model

2.1 EMD-BP integrated prediction idea

The basic idea about the prediction of tourist capacity in Jiuzhaigou based on EMD-BP integrated model is to make use of EMD to decompose the historical time series of tourist capacity in Jiuzhaigou into multiple IMFs which can represent its internal features, and then make use of BP neural network to predict the components [20].

The realization process based on EMD-BP integrated model prediction is shown in Fig. 1.

Fig.1

Flow chart based on EMD-BP integrated model prediction.

2.1.1 EMD decomposition course

According to the EMD method mentioned above, the tourist capacity time series x (t) (t = 1, 2, …, n) is divided into n IMF, c_i (t) (i = 1, 2, …, n) and a residual term r_n (t).

2.1.2 Frequency grouping stage

The extracted intrinsic model functions are classified from high to low. The intrinsic model functions with high frequency mean longer learning process while those with low frequency mean shorter learning process. Therefore, in order to construct network prediction model with short cycle and high accuracy, the classification of time series is very important.

2.1.3 Network prediction stage

Based on the preparation in step 1 and step 2, BP neural network model is respectively constructed in very component to do training and prediction, and finally all prediction results are added linearly to get the final predicted value.

2.2 Empirical model decomposition

Empirical Model Decomposition (EMD) is put forward by a Chinese American Huang in 1998. Its main idea is to make use of Hilbert transform to select the non-linear and unstable data series until the final data series is stable. Every data series is called Intrinsic Model Function, IMF for short. The definition of IMF is as follows:

In the whole time series, the difference between the extreme value amount (the maximum and the minimum) and the zero crossing point amount is no more than 1;

In any area of the time series, the mean value of the upper and the lower envelope line is zero.

The decomposition course of EMD is as follows:

Step 1, work out all local minimum and maximum of the original times series x (t);

Step 2, work out the lower envelope line composed of all minimum and the upper envelope line composed of all maximum (the upper and the lower envelope line should cover all data), which is respectively denoted by u₀ (t) and v₀ (t), and their mean value is denoted by m₁ (t); the difference of the signal x (t) and the mean value m₁ (t) is h₁ (t). Thus, $m_{1} (t) = \frac{u_{0} (t) + v_{0} (t)}{2}$ (1) $h_{1} (t) = x (t) - m_{1} (t)$ (2)

Step 3, judge whether h₁ (t) can satisfy the definition of IMF above. If so, h₁ (t) is IMF; otherwise, h₁ (t) is denoted by the next iterative signal x (t), so $h_{11} (t) = h_{1} (t) - m_{11} (t)$ (3)

Step 4, repeat step 1 to step 3 until the K iteration finds the first IMF, which is denoted by c₁ (t); $h_{1 k} (t) = h_{1 (k - 1)} (t) - m_{1 k} (t)$ (4) $c_{1} (t) = h_{1 k} (t)$ (5)

Step 5, the residual term r₁ (t) = x (t) - c₁ (t) is denoted as the new time series. Repeat step 1 to step 4 until we find the next IMF, which is denoted by c₂ (t), when the remainder term is r₂ (t) = r₁ (t) - c₂ (t). Repeat step 1 to step 5 until the residual term is less than the set threshold value, when the loop is ended. Finally, it is decomposed into nIMF and 1 residual term r_n (t). The original series x (t) can be indicated as $x (t) = \sum_{k = 1}^{n} c_{k} (t) + r_{n} (t)$ (6)

From the above iterative process, it can be seen that the original sequence can be decomposed into the sum of n intrinsic model functions and a residual term. The decomposition process is shown at Fig. 2.

Fig.2

Decomposition process of EMD.

2.3 BP neural network

BP neural network is also called error back propagation network, which is currently the most widely used neural network [21]. BP neural network is composed of input layer, output layer and hidden layer (usually one layer, or multiple layers). BP neural network structure is shown in Fig. 3.

Fig.3

BP neural network structure.

2.3.1 BP algorithm

Take the BP neural network structure in Fig. 3 as an example. The network is composed of N input layer nerve cells, K hidden layer nerve cells and M output layer nerve cells. Suppose O2_pm and O1_pk are respectively the output value of the output layer and the input layer, W2_km and W1_nk are respectively the connection weight from the hidden layer to the output layer and from the input layer to the hidden layer. Suppose the learning sample is x_pn and the corresponding target output value is t_pm.

The process of BP algorithm is shown at Fig. 4. The detailed procedure is shown as follows [22]:

Fig.4

BP Algorithm.

Step 1, initialize the weight. Suppose the learning rate is α, the error is ɛ, the maximum cycle index is max, and i = 0;

Step 2, feed forward calculation: Input x_p (x_p = { x_p1, …, x_pn }) into the network, calculate O2_pm and O1_pk according to the formula below: $O 1_{pk} (i) = f (\sum_{n + 1}^{N} w 1_{nk} (i) x_{pn})$ (7) $O 2_{pm} (i) = f (\sum_{n + 1}^{N} w 2_{km} (i) O 1_{pk} (i))$ (8)

The transfer function f usually uses sigmoid function. $f (x) = \frac{1}{1 + e^{- x}}$ (9)

Step 3, calculate the mean square error MSE. If MSE ≤ ɛ, the loop will end. Otherwise, it switches to step 4; $MSE = \frac{1}{M} \sum_{k = 1}^{M} {(t_{pm} - O 2_{pm})}^{2}$ (10)

Step 4, reverse calculation: calculate the variable quantity of the weight as below: $Δ w 1_{nk} (i + 1) = α \sum δ_{pk} (i) x_{pn}$ (11) $Δ w 2_{km} (i + 1) = α \sum δ_{pm} (i) O 1_{pk} (i)$ (12)

In the formula: $δ_{pm} (i) = (t_{pm} - O 2_{pm} (i) (1 - O 2_{pm} (i)))$ (13) $\begin{matrix} δ_{pk} (i) & = & O 1_{pk} (i) (1 - O 1_{pk} (i)) \\ \sum_{m = 1}^{M} δ_{pm} (i) w_{km} (i) \end{matrix}$ (14)

Reset the weight: $w 1_{nk} (i + 1) = w 1_{nk} (i) + Δ w 1_{nk} (i + 1)$ (15) $w 2_{km} (i + 1) = w 2_{km} (i) + Δ w 2_{km} (i + 1)$ (16)

Step 5, make i = i + 1, go back to step 2.

2.3.2 BP algorithm improvement

Though BP algorithm has been widely used, there are still some defects. For example, it needs lots of training samples, the learning efficiency is low and the rate of convergence is slow, the selection of parameters is sensitive and it is easy to get into local minimum value. BP neural network learning process includes BP network connection weight learning and network structure learning. Therefore, improvement can be done in those two aspects. Major improvement methods include simulated annealing algorithm, genetic algorithm, training sample normalization method, logical selection of initial weight value and threshold value as well as adjustment of network structure.

BP algorithm usually uses s shape function as the transfer function, whose range is [0,1]. The actual sample data may have great difference, making all training samples have no comparability. Therefore, in order to avoid the circumstance that the small value is “submerged” by the big one, normalization processing is adopted to normalize the sample input to the interval [0,1], and in the calculation process, use formula 19 to do data preprocessing: $\bar{x_{i}} = α + β \frac{x_{i} - x_{min}}{x_{max} - x_{min}}$ (17)

In the formula, α, β are constant, x_min, x_max respectively denote the minimum value and the maximum value in each sample group; x_i and $\bar{x_{i}}$ respectively denote the value before and after disposal. The procedure of improved BP algorithm is shown at Fig. 5.

Fig.5

Procedure of improved BP algorithm.

3 Prediction of tourist capacity in Jiuzhaigou

3.1 Data source

Jiuzhaigou is a famous natural scenic spot in China and has attracted millions of tourists at home and abroad. Therefore, to have an accurate prediction of its daily tourist capacity can provide basic data for the administrators of Jiuzhaigou, help decision-makers make overall arrangement of proper manpower resources, offer optimal configuration of relevant supply of catering and hotels, as well as formulate the regulation scheme of tourist transportation in advance.

In this thesis, the author takes the daily tourist capacity of Jiuzhaigou as the prediction object, and there are 365 data samples (from January 1, 2010 to December 31, 2010) from the access control system of Jiuzhaigou. In the earlier stage, we’ve cleared up the ticket checking data of the access control system and got the data table 1 of daily tourist scale in 2010 including data from January, 2001 to December, 2007, which is shown in Fig. 6.

Fig.6

Time series data of daily tourist capacity of Jiuzhaigou in 2010.

To ensure the validity of the evaluation model, this thesis sets the error evaluation method of tourist capacity prediction and uses average deviation rate as the statistics of error evaluation. $E = \frac{\sum_{i}^{N} \frac{| {\hat{y}}_{i} y_{i} |}{y_{i}}}{N}$ (18)

In the formula, ${\hat{y}}_{i}$ is the i predicted value, y_i is the actual value and N is the predicted sum.

3.2 Analysis of predicted results

In this thesis, the author firstly carries out EMD towards the original data. After decomposition, we get 11 intrinsic model functions and 1 residual term. Then, the three-layer neural network is used to construct the model so as to have an empirical prediction study of the tourist capacity in Jiuzhaigou. In the process of using EMD-BP prediction model, because of the huge number of 365 training sample data all year round, the number of neuron nodes in the hidden layer n₂ is supposed to be as many as possible, so the thesis chooses, n₂ = 150. Here the number of neuron nodes in the hidden layer is not fixed, which should be modified according to actual training. The number of neuron nodes in the input layer is n₁ = 1, and the number of neuron nodes in the output layer is n₃ = 1. This thesis adopts MATLAB test, the transfer functions both from the input layer to the interlayer and from the interlayer to the output layer are tangent functions, the learning rate is set as 0.5, training time 5000 and training target error 1 × 10^-10.

To use MATLAB to do neural network training and get the output data after normalization processing, we should firstly restore the data of the output layer and get the restoration formula according to the normalization formula. $Y = 10^{(y^{*} \times 10)}$ (19)

In the formula, Y is the output data of the restored neural network, y^* is the output data of the neural network.

Figure 7 is the comparison diagram of the predicted value of tourist capacity by making use of EMD-BP prediction model. From it we can find that the curve of predicted value of tourist capacity by means of EMD-BP prediction model is very close to the actual value curve of tourist capacity. These two curves are almost coincident.

Fig.7

Comparison between EMD-BP predicted value and actual value.

In order to further verify the validity of this prediction method, this thesis compares EMD-BP prediction model with the simple BP neural network prediction model. Figure 8 is the comparison diagram between predicted value and actual value of neural network. Figure 9 is the comparison of the prediction error of these two methods.

Fig.8

Comparison between the predicted value and the actual value of neural network.

Fig.9

Comparison between EMD-BP prediction error and BP neural network prediction error.

According to BP neural network prediction and EMD-BP integrated prediction model prediction, the variation trend of the predicted value and the actual value are basically consistent. From the comparison in Figs. 8 and 9, it can be seen that: 1. The actual touristy capacity of Jiuzhaigou every year presents multimodality; 2. The peak value of the actual tourist number and the predicted tourist number are basically consistent; 3. The comparison diagram of the two shows that the prediction of the two in number is basically correct. Besides, in terms of EMD-BP integrated model prediction (i.e. using empirical model decomposition to process data and then use BP neural network prediction), the predicted value and the actual value of tourist capacity are closer. Through calculation, we can find that after the correction of the predicted value through the neural network model, the error becomes smaller significantly. Through calculation, the average error rate of EMD-BP integrated prediction model and the actual value is 8.8%, among which the error within 1% accounts for 31.3% of the total predicted amount, the error within 5% accounts for 41.7%, the error above 10% accounts for 30.2% in slack seasons and 69.8% in busy seasons. Bigger error mainly lies in busy tourist seasons, when the predicted value is basically smaller than the actual value, probably because that at that time, factors influencing tourist amount are more complex.

4 Conclusion

Scholars’ research on the prediction of tourist capacity both at home and abroad dates back to the 1960 s. In recent years, domestic and overseas scholars have done lots of research on the prediction of tourist capacity, but most of them lay more emphasis on the prediction of yearly tourist capacity and there are quite a few studies on daily tourist capacity prediction. In this thesis, by constructing EMD-BP integrated prediction model, taking daily tourist capacity of Jiuzhaigou as research object, the author carries out empirical analysis and reaches the following conclusion: compared with simple BP neural network, the integrated prediction model of BP neural network based on empirical model decomposition has better prediction effect, which can accelerate the rate of convergence and improve the prediction accuracy. However, there are still some defects in this thesis. It doesn’t consider the influence of emergencies on tourist capacity. Thus, in future studies, the author will try to apply techniques like text mining and consider the influence of emergencies so as to seek for a more vivid prediction method.

Footnotes

Acknowledgments

The humanistic and social science of Sichuan Education Department (Tourism Studies) project “Research on Sichuan Tourism Enterprises’ Competitiveness from the Perspective of Industry Integration” (LYC15-35); Social Science Planning Fund Program of Sichuan Province “Research on relationship embedded model between agricultural e-commerce enterprises and customer under the trend of industrial convergence (SC16C022)”.

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