Asian stock markets closing index forecast based on secondary decomposition, multi-factor analysis and attention-based LSTM model

Abstract

The analysis and prediction of stock markets in Asian is an important issue which can help to promote the integration and globalization of financial cooperation. However, owning to the non-stationary and complexity of the stock market fluctuation, it is challenging to predict the stock price accurately. Especially after the decomposition of the original series, how to solve the problem of pseudo information and filter the exogenous variables is often certain challenging. This paper presents a hybrid model based on secondary decomposition (SD), multi-factor analysis (MFA) and attention-based long short-term memory (ALSTM) to predict the stock market price trends of four major Asian countries. The original stock price series is preprocessed by two decomposition algorithms so as to capture further non-linear feature and better filter the noise. Multi-factor analysis is introduced as a supplement to the original data information. In the prediction stage, attention layer is added in long short-term memory model to increase the weights of effective information. Finally, four datasets about Asian stock markets and nine compared models were used to verify the performance of the proposed model. The empirical analysis results show that compared to the general long short-term memory, our proposed model can obtain higher 30% accuracy at least. The mean average percentage errors of the system were also the lowest among all models mentioned in this paper (0.612%, 0.903%, 0.606% and 0.402% respectively), which proves the effectiveness of the hybrid model.

Introduction

The stock markets, which are known as one of the most vital financial markets all over the world, have become the focus of many investors and professional researchers. Over the past three decades, with the continuous development of the economy, financial activities in Asia have increased day by day, and regional monetary and financial cooperation based on regional development has always been one of the important topics among Asia countries. From the Chiang Mai Initiative (CMI) signed in Thailand to the Chiang Mai Initiative Multilateralization (CMIM) agreement, the macroeconomic research office among Asean, China, Japan and South Korea has been established, which fully reflects the urgent need and bold practice of Asia to make up for the inadequacy of the international financial system.

The integration of Asian financial capital market is an important force to accelerate the financial cooperation in Asia. It is an irresistible trend that governments will vigorously promote the cooperation of Asian stock market after the proposal of new roadmap of Asian bond market. This strategy can promote the level of regional and global stock market integration in emerging and frontier Asian countries and expand the geographic reach of portfolio diversification strategies for more international investors participating (Mohti et al., 2019). Recently, the prediction of Asian stock markets has becoming a hot research field. Because using appropriate methods to forecast financial data can not only help investors and production enterprises to avoid risks and maximize profits, but also help the government sector to understand the operation status of national economy from the macro level and guide policymakers to formulate relevant industrial policies, thus promoting the steady and healthy economy development. In addition, because Asian stock markets are highly dynamic and fluctuating resulted from economic policies, investor sentiments, economic expectations and the political environment, it may be more realistic and practical to assume that the Asian stock market prices are nonlinear mixture data (Guegan, 2009).

In the early stage of time series research, most forecasting methods focus on traditional econometric models, which mainly includes autoregressive moving average model (ARMA) and generalized autoregressive conditional heteroscedasticity (GARCH) model (Jakubowski and Szewczak, 2021, Yang, 2018). Devi et al. (2013) predicted Nifty-Midcap by applying ARIMA model, and the results proved that ARIMA model had good flexibility in time series. Gu and Chen (2011) used five different GARCH models to predict the volatility of Shanghai composite index and Shenzhen composite index, and the GARCH (1,1) was found that it could describe the volatility of the stock index better. Although econometric models have made some achievements in the field of prediction, a large number of empirical studies also show that the linear assumption makes the models unable to comprehensively reflect the real distribution of data (Xu and Chen, 2010), which is difficult to obtain accurate prediction results on more complex dataset. Similarly, Liu and Morley (2009) also pointed out that only using the traditional econometric models for modeling would lead to very serious prediction deviation.

Apart from econometric models, artificial intelligence (AI) techniques are now widely applied in time series, which mainly includes support vector machine model (Richhariya and Tanveer, 2018, Atmaja and Akagi, 2021, Fan et al., 2016) and artificial neural network (ANN) (Yuan et al., 2021, Aras and Kocakoc, 2016, Rakesh et al., 2018). Traditional ANN has been proven to have more advantages in dealing with nonlinear data (Zhang, 2003). However, each coin has two sides. ANN is easy to fall into the problem of overfitting and local extremum, which greatly restricts its promotion (Chen and Hao, 2018). Additionally, stock price has the characteristic of autocorrelation, which means the current stock price will be affected by the historical data. Therefore, it is non-ignorable that changes in stock price do not satisfy the assumption of random walk but are well suitable for neural networks. If we only use current information to make prediction, the information carried by the early data will be lost, which makes it difficult to deal with complicated time series problems. To solve these problems, recurrent neural network (RNN) was proposed. RNN can keep memory of recent events well through fully connecting hidden neurons in networks and learning from internal feedback mechanism. But the fly in the ointment is that it also faces the problem of gradient disappearance. In order to capture both long-term and short-term information, long short-term memory (LSTM) model was established on the basis of RNN. The special gate structure is added in LSTM to filter more useful and important information from the training data, which makes it more suitable for time series problem. Ghosh et al. (2019) used the LSTM model to predict the future trend of the company’s stock price, and the final empirical results showed good accuracy. Baek and Kim (2018) used LSTM framework to predict S&P-500 index and KOSPI-200 index respectively, and the study found that LSTM could achieve better prediction performance than other comparison models. Nevertheless, the valid information cannot gain more weights to show its importance in LSTM, which needs to be further improved.

Combining AI techniques with data preprocessing methods can greatly improve the prediction accuracy, because relying solely on AI cannot consistently and stably output high-quality results in all cases. The complexity of the predictive model can be lowered by using the signal analysis methods which decompose the data and then model the sub-sequences respectively. The most typical signal decomposition method is empirical mode decomposition (EMD), which can not only transform non-stationary signal into stationary signal, but also have a good decomposition effect on nonlinear data. By decomposing the original signal into multiple intrinsic mode functions (IMFs) and trend items, the hidden information in the data can be mined well. Wang and Wang (2017) successfully applied EMD algorithm and stochastic time neural network to predict financial time series. However, there is an unavoidable problem in the application of EMD-modal aliasing. Generally speaking, it means that different IMFs contain similar features. In order to solve this, a non-recursive signal analysis method, variational mode decomposition (VMD), was created based on EMD. Bisoi et al. (2019) applied the most efficient VMD to decompose the original stock price series for seizing the vital information, which proved that it is a useful tool for feature selection. This paper also applied VMD algorithm as the first decomposition for the reason that it can integrate the decomposed signals into the real signals and separate similar frequencies. Additionally, it is of vital importance for researchers to determine the decomposition layers of VMD. Scholars need to stop the decomposition when the same features are encountered. Kullback–Leibler divergence (KLD) algorithm is adopted in this paper to find the optimal decomposition layers, and constitute an improved VMD (IVMD). Analogously, complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) is another improved version of EMD and has been widely used by researchers. Cao et al. (2019) combined different decomposition methods (EMD and CEEMDAN) with LSTM to compare their effectiveness. They found that CEEMDAN can extract more effective information compared with EMD. By adding a special kind of white noise, CEEMDAN has been improved continuously, which can reduce the residual noise to nearly zero. Therefore, this paper applied this relatively progressive algorithm to make the second decomposition for the high frequency sub-sequences.

In previous studies, one-off decomposition methods were widely used in the fusion models to improve prediction performance. In their decomposition-ensemble framework, the decomposition method was used to process the original data only once, and then the sub-sequences were modeled respectively. However, it should be noted that some of the decomposed sub-sequences may not be stable and even be pseudo-signals. In that case, the direct use of sub-sequences for modeling does not improve the accuracy, but reduces the efficiency of calculation. Compared with the single model, the hybrid model has greater superiority by integrating the advantages of multiple methods (Zhang et al., 2019a, Zhang et al., 2019b). Therefore, this paper applied with secondary decomposition (SD) method including improved VMD (IVMD) and improved CEEMDAN (ICEEMDAN) to solve the problem that decomposed modes still have pseudo-signals.

The role of exogenous variables is as important as data preprocessing part in time series forecasting field. For example, technical indicators such as moving average convergence divergence (MACD) and stochastics oscillator (KDJ) can act as exogenous variables in the stock price forecasting. Some studies have shown that technical indicators can not only effectively describe stock market changes, but also provide effective information for the establishment of model, which is also named multivariate analysis (Panigrahi and Behera, 2017, Zbikowski, 2015). It includes two stages, dimensionality reduction and feature selection. In the former stage, high dimensional data will be compressed and reconstructed into lower dimensional data since high dimensional data will lower the generalization ability, increase the amount of calculations, and reduce the final prediction performance. The Principal component analysis method (PCA) is used as the most classic and famous dimensionality reduction algorithm (Zhang et al., 2018). Wang and Wang (2015) combined PCA and neural network (NN) to predict financial time series and found that the introduction of PCA can effectually improve the accuracy of a single model. However, PCA can only achieve good results on linear data. In order to avoid this problem, this study uses auto encoder (AE) machine to compress high dimensional data. Chen et al. (2018) applied the combination of a deep-learning model, AE and a restricted Boltzmann machine to predict stock index price, whose results indicated that the novel hybrid model is a good choice for the index price prediction. The power of the AE is that it can reduce the dimensionality of non-linear data and guarantee the integrity of the information to a great extent. In the later stage, the most influential variables will be selected as the input from all collected variables. Feature selection is also a kind of data compression method as the same as dimensionality reduction. It can filter irrelevant variables in order to save computing time and improve the model’s efficiency. In this study, F test and mutual information (MI) are used to screen the relevant variables.

On the basis of the above analysis, this research comes up with a decomposition ensemble model for stock market price prediction, which combines the advantages of SD, multi-factor analysis (MFA) and attention-based LSTM (ALSTM) model. Firstly, the closing price in stock market is decomposed to corresponding sub-series by the IVMD algorithm. The high frequency components obtained from IVMD are inputted to secondary decomposition which adopts ICEEMDAN as the tool. For the further improvement, multiple exogenous variables are selected as influencing factors, and AE is used to compress these factors after screening out significant influencing factors. In the ensemble phase, the ALSTM model is utilized to predict the closing price data.

The innovations and contributions of this study are as follows:

(a) In the previous researches, the signal decomposition method is often used only once in the fusion models. Even though it can improve the prediction performance, its potential has not been fully tapped yet. The decomposed sub-sequences still have noise and unclear signals. In order to make up for this defect, this study establishes a model based on the secondary decomposition, which can reduce the influence of pseudo components on the prediction results and extract more effective information from the data.

(b) The parameters of VMD have rarely been determined scientifically before. This paper applied with KLD algorithm to improve VMD, which can determine the optimal number of sub-sequences’ layers according to the calculated value so as to improve the ability of feature extraction.

(c) The previous model only used closing price data for modeling, ignoring other relevant variables. In order to cover up this gap, this study introduces multiple related variables to build the model based on the closing price, and uses the multivariate analysis technologies including dimensionality reduction and variables selection to improve the prediction performance of the hybrid model.

(d) The proposed model uses the AE as the dimensionality reduction method instead of PCA because stock price has the nonlinear and nonstationary characteristics which are not suitable for PCA. Conversely, AE is a type of neural networks and it can adapt nonlinear data well. Additionally, the methods of feature selection applied with the combination of F test and MI to select the most correlated variables with stock market from underlying factors.

(e) The attention mechanism is introduced into the LSTM model in order to improve the prediction performance of the proposed model. The importance of input data is fully utilized to determine the weight assignment so as to improve the prediction accuracy of the model.

(f) The novel hybrid model is firstly proposed and achieves superior performance.

The remainder of this paper is organized as follows. Section 2 describes the basic methods used in this study. Section 3 presents the framework of the proposed hybrid model. Sector 4 describes the experimental process and empirical results in detail, and Section 5 summarizes the conclusion.