Advanced nonlinear and nonstationary methods for the analysis of financial time series

A broad range of advanced subjects and methods for nonstationary and nonlinear time series analysis comprises this thesis. These researches and their contents are summarized as follows. The wavelet coherence is investigated and applied on FTSE 100 and S&P 500 with several major Asian markets and major real estate markets. It is revealed that the developed economy stock markets have strong influences over Asian stock markets. These relationships are used to develop a VARMA based forecast model that shows less forecast errors than the models constructed with individual time series. Moreover, the multiple wavelet coherence is added for the analysis of dynamic correlations between three time series together. The chaos related properties of FIGARCH(p, d, q) processes are examined by computing the correlation dimension and the largest Lyapunov exponent from the stochastic difference equations directly and the simulated time series through mutual information, false nearest neighbour method, Wolf's algorithm, Kantz's algorithm and Jacobian algorithm. A new stochastic modelling and forecasting method for the chaotic noisy Duffing map series and for the financial time series with identical characteristics is introduced. The combination of telegraph process and the fractional Gaussian noise is fitted to the noisy Duffing map series that possesses regime switching and long-range dependent characteristics and then the real-world financial time series with identical features. Multiscale correlation dimension (MSCD) is proposed as a new method for chaotic properties of time series. Based on MSCD method, fractal dimension and Hurst exponent relationship is investigated in multiple scales on several time series.