Abstract: Previous studies proved that the distributions of stock returns exhibit fat-tail and skewness. The normal mixture distribution provides a practical extension of the normal distribution for modelling stock market returns with the above mention stylized facts. It has been successfully applied in financial time series modelling and the application is still expending not only in asset-return modelling but in other applied fields. In this study, normal mixture distribution is proposed to accommodate the non-normality and asymmetry characteristics of financial time series data as found in the distribution of returns for Bursa Malaysia index series namely the FTSE Bursa Malaysia EMAS Shariah Index (FBMS) from October 2006 until July 2012. Empirical analysis is conducted across frequencies (monthly, weekly and daily) to demonstrate the proposed method. Firstly, we present the basic definitions, concepts and distribution properties of normal mixture distribution. In support of determining the number of components in the mixture, we use the information criterion for model selection. The goodness-of-fit measures provide supporting evidence in favour of the two-component normal mixture distribution at all frequency levels. For parameter estimation, we use the most commonly used Maximum Likelihood Estimation (MLE) via the EM algorithm to fit the two-component normal mixture distribution. Also, the empirical results indicate that the normal mixture distributions offer a plausible description of the data. It also shown to be more superior compare to the use of other distributions.
Zetty Ain Kamaruzzaman and Zaidi Isa, 2015. Modelling Stock Market Return via Normal Mixture Distribution. Research Journal of Applied Sciences, 10: 324-333.