New bootstrap methods for exchange rate prediction under GARCH(p,q) process

The price changes forms an important part of the financial time series analysis. Modeling of financial time series such as exchange rates, market indices, interest rates and option prices, succeeding accurate parameter estimations of the model and prediction of future values play a critical role in assessing risk and uncertainty. In foreign exchange market, the generalized autoregressive conditional heteroscedasticity model is one of the most commonly used techniques for modeling volatility and obtaining dynamic prediction intervals for returns as well as volatilities. Technically, construction of such prediction intervals requires some distributional assumptions which are generally unknown in practice. Moreover, the constructed prediction intervals along with the estimated parameter values can be affected due to any departure from the assumptions and may lead us to unreliable results. One of the remedy to construct prediction intervals without considering distributional assumptions is to use the well known resampling methods, e.g., the bootstrap. In this dissertation, two new block bootstrap based methods are proposed to obtain valid prediction intervals in conditionally heteroscedastic models. Firstly, the proposed block bootstrap methods are discussed in the context of linear time series models. Secondly, these methods are applied to heteroscedastic models to obtain prediction intervals. Performances of the proposed methods have been compared with the existing methods via both real-world examples and simulation studies. The results are reveal that our proposed methods outperform other existing methods for parameter estimation. Also, they produce better prediction intervals compared to existing ones.