A Modified Bl-garch Model for Distributions with Heavy Tails.

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Onyeka-Ubaka, J.N
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Most previous studies on Generalized Autoregressive Conditional Heteroskedastic (GARCH) Models have largely concentrated on modelling empirical characteristics present in high frequency financial time series data, especially volatility clustering between returns and conditional variance. Some of the works focus on leverage effect between returns and conditional variance with emphasis on relaxing the non-negativity constraints imposed by GARCH models. Nevertheless, they have not yet objectified the simultaneous capturing of volatility clustering and leverage effect within the non-Gaussian framework. This study, therefore, introduces a Bilinear Generalized Autoregressive Conditional Heteroskedastic-Volume (BL-GARCH (1, 1)-Volume) model which is capable of capturing simultaneously the volatility clustering and leverage effect present in high frequency financial data as exemplified with the daily stock returns of selected banks: First Bank of Nigeria (FBN), Guaranty Trust Bank (GTB), United Bank for Africa (UBA) and Zenith Bank (ZEB) for the sampled period (January, 2007-May, 2011). The theoretical framework of the study is based on some past results proved by various researchers such as Bollerslev (1986), Kleibergen and Van Dijk (1993) and Posedel, (2005) on GARCH model. The framework facilitates the identification, proofs of the stationary, positivity of the conditional variance and the interpretation of BL-GARCH models as reflected in texts. The hybrid Monte Carlo simulation experiment is used to see within sample performance of the BL-GARCH (1, 1) and BL-GARCH (1, 1)-Volume models within Gaussian and non-Gaussian frameworks. The results obtained through sequential estimation of parameters via particle filtering algorithms are consistent with Storti and Vitale (2003) within the Gaussian framework. The empirical results show that both GARCH (1, 1) and BL-GARCH (1, 1) models perform well in modelling the selected banks daily returns for the sampled period within the Gaussian framework. The study goes further to deduce that BL-GARCH (1, 1) model performs better in capturing volatility clustering as well as leverage effect using generalized Student t distribution for GTB, UBA and ZEB and with Student t distribution for FBN. The study has also deduced that there is a dynamic relationship between return volatility and daily trading volume. This is because the daily trading volume and volatility of returns contains information about upcoming trading volumes. Though the inclusion of the daily trading volume variable in the variance process provides information relating to the time-varying conditional volatility, the BL-GARCH model is still required to explain the hetereoskedasticity observed in the selected banks’ daily stock returns. This establishes that with or without the inclusion of the daily trading volume, a stronger and persistent BL-GARCH asymmetric variance effect with a negative error is expected to have a more significant impact on future variance. The study has, therefore, shown that the parameters of GARCH models especially BL-GARCH (1, 1) model can be estimated from Gaussian and non-Gaussian frameworks.
A Thesis Submitted to the School of Postgraduate Studies, University of Lagos.
GARCH Models , Heavy Tails , Volatility , Research Subject Categories::MATHEMATICS::Applied mathematics::Mathematical statistics
Onyeka-Ubaka, J.N (2014), A Modified Bl-garch Model for Distributions with Heavy Tails. A Thesis Submitted to University of Lagos School of Postgraduate Studies Phd Thesis and Dissertation, 136pp.