Statistical analysis and modeling in financial time series

Abstract

In this thesis, we propose several methods to analyze the statistical characteristics of real capital markets, and propose a simple stochastic model to simulate teh real capital markets. Firstly, we study the unconditional return distributions for real stock markets by Histogram method and Adaptive-Kernel method. Then we check whether it can be described by the normal distribution or not. In addition, probability of returning to origin is studied to explore the difference between the time series of real stock prices and that of a random walk. Secondly, we employ the Hurst exponent method to measure the correlations in real capital markets. And we also propose two new methods, conditional return distribution and conditional average of price changes, for studying the volatility correlations in stock markets. Finally, we construct a simple intuitive stochastic model incorporating the features of short-term trend, trend reversal, and long-term volatility correlation and compare the results from the model with the real data, as well as with that of the GARCH(1,1) model.