Predicting Stock Index Time Series Based On Nonlinear Dynamics And Asymmetrical Support Vector Regression

As an essential part in the economic life, the stock market is a complicated nonlinear dynamic system which decides the difficulties in predicting stock price. However, due to the great economic influences, predicting stock price is always an important issue in financial investment and is always a focus of people's attention.In the end of last century, many economists discovered and proved the existence of chaos in the stock market. After then, many methods used to predict chaotic time series have been employed to predict stock price and achieve great achievements. This dissertation selects Hong Kong Heng Seng Index and American Dow Jones Industrial Average as the samples. After stationarizing the data, we use C-C Algorithm to compute two key parameters in the state space reconstruction: the delay time and the embedding dimension. Then G-P Algorithm and Small Data Sets Algorithm are employed respectively to compute the correlation dimension and the largest Lyapunov exponent. These two parameters are used to assess the quality of state space reconstruction. The results of the experiments show that the reconstructions of the stock index time series are satisfactory.Recently, with the development of Artificial Intelligence, Support Vector Regression (SVR) has been successfully applied to model stock market. This dissertation focuses on the application of SVR and its extension in predicting stock index time series. Firstly, we use standard SVR to predict the four stock index time series which have been processed by state space reconstruction. The experiments show that within the predictable time scale, we can obtain a good prediction result. However, stock index time series is always noisy and highly volatile. If fixed the margins of the loss function, the model would be failed to capture the information of the stock market promptly. Therefore, the SVR with asymmetrical margins is used to improve the prediction. The margin is consisted of the standard deviation of the input data which reflects the volatility of the stock market and the difference of the adjacent points which reflect the developing trend of the stock market. The experiments show that this asymmetrical SVR improves the predictive results. It obtains higher prediction accuracy, and furthermore, reduces the downside risk as well as extends the predictable time scale to some extend. Therefore, the asymmetrical SVR is more effective than the standard SVR in predicting stock index time series. We also derive the relation between the decision function and the margins of the loss function. The result we got is that under certain conditions, decision function is monotone decreasing to the up margin and is monotone increasing to the down margin. Therefore, we may control the downside risk by tuning the up and down margins.In the end, this dissertation proposes some problems existed in this research and put forward some possible research directions in this field.