Analyzing stock market tick data using piecewise nonlinear model

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Abstract

Trading in stock market indices has gained unprecedented popularity in major financial markets around the world. However, the prediction of stock price index is a very difficult problem because of the complexity of the stock market data. This study proposes stock trading model based on chaotic analysis and piecewise nonlinear model. The core component of the model is composed of four phases: The first phase determines time-lag size in input variables using chaotic analysis. The second phase detects successive change-points in the stock market data and the third phase forecasts the change-point group with backpropagation neural networks (BPNs). The final phase forecasts the output with BPN. The experimental results are encouraging and show the usefulness of the proposed model with respect to profitability.

Introduction

Predicting stock market's movements is quite difficult because many factors including political events, general economic conditions, and investors' expectations influence stock markets. Previous studies on stock market prediction using artificial neural networks (ANNs) have been executed during the past decades. The earliest studies are mainly focused on applications of ANN to stock market prediction (Ahmadi, 1990, Choi et al., 1995, Kamijo and Tanigawa, 1990, Kimoto et al., 1990, Trippi and DeSieno, 1992, White, 1994). Recent research tends to hybridize several artificial intelligence (AI) techniques (Hiemstra, 1995, Tsaih et al., 1998). Some researchers included novel factors in the learning process. Kohara, Ishikawa, Fukuhara, and Nakamura (1997) incorporated prior knowledge to improve the performance of stock market prediction. In addition, Quah and Srinivasan (1999) proposed an ANN stock selection system to select stocks that are top performers from the market and to avoid selecting under performers. They concluded that the portfolio of the proposed model outperformed the portfolios of the benchmark models in terms of compounded actual returns overtime. Kim and Han (2000) proposed a genetic algorithms approach to feature discretization and the determination of connection weights for ANN to predict the stock price index. They suggested that their approach reduced the dimensionality of the feature space and enhanced prediction performance. Those studies have tended to use statistical and AI techniques in isolation. However, an integrated approach, which makes full use of statistical approaches and AI techniques, offers the promise of better performance than each method alone.

This study proposes the integrated neural network model based on the statistical change-point detection. In general, macroeconomic time series data is known to have a series of change-points since they are controlled by government's monetary policy (Mishkin, 1995, Oh and Han, 2001). The government takes intentional action to control the currency flow that has direct influence upon fundamental economic indices. For the stock price index, institutional investors play a very important role in determining its ups and downs since they are major investors in terms of marking and volume for trading stocks. They respond sensitively to such economic indices like stock price indices, the consumer price index, anticipated inflation, etc. Therefore, we can conjecture that the movement of the stock price index also has a series of change-points. In this study, we show how we have applied ANN as a nonlinear statistical modeling technique to the task of stock market index prediction, attempt to capture the significant nonlinear relationships in the indices, and reflect them into the stock trading model.

The proposed model is composed of four phases: the first phase is to determine time-lag size in input variables, the second phase is to detect successive change-points in the stock price index dataset, the third phase is to forecast the change-point group with BPN, and the final stage is to forecast the output with BPN. This study then examines the predictability of the proposed stock trading model. To explore the predictability, we divided stock market data into the training data over one period and the testing data over the next period. The predictability of stock trading model is examined using three metrics.

In Section 2, we outline the development of piecewise nonlinear model and its application to the financial economics. Section 3 describes the proposed stock trading model. 4 Experiments, 5 Results and discussions report the processes and the results of the simulated trading. Finally, the concluding remarks are presented in Section 6.

Section snippets

Chaos analysis

Increasing evidence over the past decade indicates that stock market show chaotic behavior. A chaotic system can be modeled by a number of coupled nonlinear first-order differential equations. The minimum number of differential equations is equal to the integer that embeds the fractal dimension. The dimension of the phase space that spans the minimal number of differential equations is called the embedding dimension (Embrechts, 1994).

In addition, the level of chaos in a time series data can be

Research design

There has been much research interest of integrating statistical techniques and neural network learning methods. It has been widely recognized that combining multiple techniques yield synergism for discovery and prediction (Gottman, 1981, Kaufman et al., 1991). In this section, we discuss the architecture and the characteristics of our model to integrate the change-point detection and BPN. The BPN is applied to our model since it has been used successfully in many applications such as

Experiments

Research data used in this study comes from the daily KOSPI 200 from January 1990 to August 2000. The total number of samples includes 3069 trading days. From Phase I, the results of chaos analysis in Fig. 1 indicate a saturating tendency for the correlation dimension, leading to a fractal dimension of about 5. The embedding dimension is 6. The embedding dimension of 6 indicates that 5 time-lags may be shown to a neural network to predict the 6th data point of the time series.

The training phase

Examining the significance of the proposed model on the forecasting errors

Numerical values for the performance metrics by the predictive model are given in Table 1. According to RMSE, MAE and MAPE, the results indicate that Prop_NN is superior to Basic_NN for all of 10 testing days.

We use the pairwise t-test to examine whether the differences exist in the predicted values of models according to the absolute percentage error (APE). This metric is chosen since it is commonly used (Carbone & Armstrong, 1982) and is highly robust (Armstrong and Collopy, 1992, Makridakis,

Concluding remarks

This study has suggested the stock trading model based on chaotic analysis and piecewise nonlinear model. The proposed model consisted of four phases. The first phase selects the time-lag size for input variable based on the chaos theory. The second phase conducts the nonparametric statistical test to construct the homogeneous groups. The third phase applies BPN to forecast the change-point group in the third phase. The final phase applies BPN to forecast the output.

The proposed trading model

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