On Statistical Aspects of Modelling Financial Volatility

Abstract: This thesis is comprised of five papers that are all related to the subject of financial time series. We study statistical aspects of conditional heteroskedastic models commonly used in modelling financial volatility. Paper I discusses the performance of commonly known information criteria in the presence of various GARCH processes. The investigation has been performed using Monte Carlo simulations. All models are further simulated with a number of parameter combinations to study the possible effects of various volatile structures on these criteria. We noticed an impact from the volatility structure of the time series on the performance of these criteria. Paper II extends the idea of investigating the impact of a number of GARCH processes on volatility spillover. Various testing procedures are applied for testing the causality-in-variance. It is found that the causality pattern, due to causality between two series, is influenced by the intensity of volatility clustering. Moreover, we notice severe size distortion of volatility spillover tests, when the clustering parameter is high or when the GARCH process is near integration. In Paper III, we nest the concept of causality and jumps and investigate the effect of jumps on the causality pattern in mean and variance. When the jumps in the data are ignored, we see a significant change in the causation pattern. This indicates that jumps influence the transmission of information. It also shows that jumps in one series are transmitted to the other series with high probability. Paper IV applies the GARCH-MIDAS (Mixed Data Sampling) model to examine whether information contained in macroeconomic variables can help to forecast short-term and long-term future variances. A principal component analysis is used to incorporate the information contained in various variables. Our findings show that the GARCH-MIDAS model constitutes better forecast than the traditional GARCH model. Moreover, macroeconomic variables are found to have significant information about the volatility structure. In Paper V, we examine the dynamic conditional correlation structure of European countries in order to investigate the degree of integration. A DCC-MIDAS model is implemented due to the fact that it allows us to decompose the correlations into short-term and long-term components. We observe a significant increase in the integration since the introduction of the fixed currency regime. The joint relationship of volatility and correlation is also investigated, which indicates that both volatility and correlation move in the same direction.

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