Year

2013

Degree Name

Doctor of Philosophy

Department

School of Mathematics and Applied Statistics

Abstract

The volatility modeling and forecasting of returns are essential for many areas of econometric and financial analysis. Volatility forecasting dramatically affects financial decisions, such as portfolio selection, option pricing, risk management and monetary policy making. Improving the modeling and forecasting of financial volatility remains an important issue. The Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model is the most successful model to use for volatility modeling and forecasting of financial returns (Zakaria and Abdalla, 2012).

However, it is well known that financial return series generally exhibit nonnormal characteristics while the typical GARCH model assumes a normal error distribution (Gokcan, 2000). Consequently, the typical GARCH model cannot well capture the stylized facts of return series such as heavy tails, excess kurtosis and skewness. This thesis will develop better GARCH models and use these models to improve the volatility forecasting of returns.

In this thesis, there are two main approaches for improving the volatility forecasting performance. The first approach combines GARCH model with various types of non-normal error distributions. There are a large number of non-normal distributions that can be applied to the error term in GARCH model. In this thesis, six different types of error distributions are considered. These are the normal, skewed normal, student-t, skewed student-t, generalized error and skewed generalized error distributions.

GARCH model with a normal error distribution is used as a benchmark to compare the volatility forecasting performance when competing GARCH models are fitted with the other five non-normal distributions. The impact of those error distributions on the best fitting model and the best performance model is studied in this thesis. The simulated results show that the best fitting GARCH(p,q) model is not necessarily the best volatility forecasting performance model. But the results from the paired t-test reveal that there are not greatly significant difference between the best fitting model and the best performance model in terms of Mean Square Error(MSE) and Mean Absolute Error(MAE). Therefore, it is still reliable in practice to use the best fitted model for volatility forecasting. The empirical results indicate that GARCH(p,q) models with non-normal distributions outperform GARCH(p,q) models with a normal distribution based on the three emerging indices from Thailand, Malaysia and Singapore.

The second approach considered in this thesis incorporates the GARCH error terms with the six types of error distributions into the cointegrating error terms in Error Correction Model (ECM). If the underlying financial time series are found to be cointegrated and each series can be well fitted by a univariate GARCH model with non-normal distributions, our study shows the knowledge of cointegration information among these series might result in further improvement in volatility forecasting based on univariate GARCH model.

There are several methods for detecting the cointegration relationships among financial time series. This thesis investigates which cointegration method is the most powerful to use for developing volatility forecasting models. The Johansen approach appears to provide superior results when the cointegrating errors are normally distributed. This thesis investigates whether the Johansen tests continue to be more powerful than another three tests when the cointegrating errors are non-normally distributed. The performance of the Johansen method is compared with another three tests, the Dickey-Fuller test, the Cointegrating Regression Durbin-Watson test and the Wild Bootstrap test in terms of the size and power of the tests.

The simulation results reveal that the power of the Johansen tests is higher than that of other cointegration tests. Furthermore, the power of the Johansen tests slightly increases when the errors of the GARCH(1,1) model is given by the skewed student-t error distribution.

To investigate whether the knowledge of cointegration information can be beneficial to volatility forecasting performance, simulation studies are conducted to compare the performance in terms of the volatility forecasting between an individual univariate GARCH(p,q) model and cointegration-based ECM by taking into account alternative non-normal distribution assumptions. The results indicate that the model which contains the knowledge of cointegration information can further improve the volatility forecasting performance and provide better forecasts than the best fitting univariate GARCH model. A model with the nonnormal error distributions tends to outperform a model with the normal error distribution. Therefore, the knowledge of cointegration relationship information among the underlying financial time series appears to provide certain benefits in volatility forecasting. Furthermore, using the non-normal error distributions such as skewed student-t and generalized error distributions in a GARCH model can improve accuracy of volatility forecasting.

This thesis also examines the comparisons of VaR estimations between the univariate GARCH model and the cointegration-based ECM by using the cointegrated indices of daily closing prices from Thailand and Malaysia. Two types of Backtesting used in this thesis for VaR evaluations are the unconditional coverage (LRuc) and conditional coverage (LRcc). VaR estimates calculated based on the knowledge of cointegration information (Model B) can produce adequate VaR forecasts for 1-step ahead for both SET and KLCI. The results of VaR forecasting reveal that, if time series are cointegrated, the knowledge of cointegration information will help to improve the volatility forecasting and VaR forecasting for 1-step ahead.

FoR codes (2008)

010401 Applied Statistics, 010406 Stochastic Analysis and Modelling, 140207 Financial Economics

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Unless otherwise indicated, the views expressed in this thesis are those of the author and do not necessarily represent the views of the University of Wollongong.