Prediction in Time Series Models and Model-free Inference with a Specialization in Financial Return Data
The main aim of this dissertation is to study the prediction of financial returns or squared financial returns. As is known, financial returns data have the distribution with fatter tails than the normal and often show significant correlation and the phenomenon of volatility clustering. To capture these features is the most challenging thing in modeling financial returns data. The most popular nonlinear time series models for financial returns data now are ARCH (Autoregressive Conditional Heteroscedasticity) and GARCH (Generalized Autoregressive Conditional Heteroscedasticity) models. Early this century, a Model-free prediction approach was also derived to understand this complex type of data. One application of the model-free approach, NoVaS (Normalizing and Variance-Stabilizing) transformation has been proved to outperform ARCH and GARCH models under stationary financial data. In Chapter 1, we extend the realm of application of NoVaS to non-stationary data and compare the performance with GARCH in the one-step point prediction and prediction intervals of squared financial returns. In addition, we show the applicability of NoVaS transformation for estimating realized volatility. A new approach to the multi-step ahead prediction of squared financial returns is defined and analyzed in Chapter 2. Our work on linear time series model such as Autoregression are shown in the last two chapters. Chapter 3 describes in detail the situations that a simplified autoregressive models should be considered and the theoretical support was also given there for further study. In the last Chapter, we construct the prediction intervals of regression with model selections in the bootstrap world, which give better performance than the standard bootstrap methods. All the work here are mainly focusing on financial returns time series.