Mixture Models and Modelling Volatility of Returns - A Study on Gaussian and Heterogeneous Heavy Tail Mixtures

Abstract. This paper proposes several mixture models for describing return series of Pakistan Stock Exchange Index (PSX-100) and Pakistani Rupee (PKR) exchange rate against the US dollar. We implement Gaussian mixtures, heterogeneous mixtures and Heavy-tailed models of return distributions. The following models have been employed for this purpose: (i) Gaussian mixture up to three components, (ii) heterogeneous mixtures such as Normal-Logistic, Normal-Laplace, Logistic-Laplace, Normal-Normal inverse Gaussian (NIG), Logistic-NIG, Laplace-NIG, and Logistic-Skewed Generalized T distribution, and (iii) non-Gaussian heavy-tailed returns distributions such as Student T, Skewed-Generalized T, Logistic, Laplace, Generalized Hyperbolic and its sub-family such as NIG and Variance Gamma distribution. In addition, GARCH models and Value-at-Risk measure are used to assess the contribution of leverage effect, volatility clustering and asymmetric nature of the underlying returns series. Finally, we investigate the detrended correlation coefficient analysis to evaluate the integration level of the two markets and their role in the country’s economy.