| As the rapid development of China's securities market, the research of the un- certainty in the stock market and the empirical analysis of the stock price have become the core of modern financial research problems. In the process of securities investment, people often want to create and apply models to analyze the stock market. In 1982, Engle, a famous professor, proposed the ARCH model, which is a dynamic and non- linear time series model, reflecting the particular and uncertainty relationship of eco- nomic variables: the variance changes over time. Since then, ARCH model has got a very rapid development in recent years. It has been widely used in the description of rules of finance theory and the forecasting of financial market.However, in practice, financial data are usually non-linear. Therefore, parameter models often lead to large deterioration. But non-parametric models do not make any special assumptions for the regression function, which makes them more flexible in terms of reducing bias. That's why more and more attention are paid on non-parametric models.In this paper, a non-parametric FAR-ARCH is introduced. And also the empirical analysis on the Shanghai stock index is done. The key findings are as following:1 The paper applies FAR to the estimation of the conditional variance in the ARCH, and estimate the model by the local polynomial techniques;2 To test the result of the proposed method, a simulation example is introduced. The comparison, between the estimated functions and the real functions, show that the proposed method gives a good estimate of the true coefficient functions.3 In empirical part, firstly, the data are carried out smoothly, and then the paper establishes the ARCH model of the composite index of Shanghai. Secondly, the non-parametric FAR-ARCH model is established. At last, the paper compares the effect of fitting and prediction of two models. The Results indicate that the model introduced in this paper is more accurate. |
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