Analysis of Malaysia Stock Return Using Mixture of Normal Distributions

In this paper, two component univariate mixtures of Normal distributions is proposed to accommodate the non-normality and asymmetry characteristics of financial time series data as found in the distribution of monthly rates of returns for Bursa Malaysia Index Series namely the FTSE Bursa Malaysia Composite Index (FBMKLCI) from July 1990 until July 2010. Firstly, we give some basic definitions and concepts of mixtures of Normal distributions. Next, we explore some of its distribution properties. In support of determining the number of components, we use the information criterion for model selection. The measures provide supporting evidence in favour of the two-component mixtures of Normal distributions. For parameter estimation, we apply the most commonly used Maximum Likelihood Estimation (MLE) via the EM algorithm to fit the two-component mixtures of Normal distributions using data set on logarithmic stock return of Bursa Malaysia index

Tests for normal mixtures based on the empirical characteristic function

Abstract. A goodness–of–fit test for two–component homoscedastic and homothetic mixtures of normal distributions is proposed. The tests are based on a weighted L2–type distance between the empirical characteristic function and its population counterpart, where in the latter, parameters are replaced by consistent estimators. Consequently the resulting tests are consistent against general alternatives. When moment estimation is employed and as the decay of the weight function tends to infinity the test statistics approach limit values, which are related to the first nonvanishing moment equation. The new tests are compared via simulation to other omnibus tests for mixtures of normal distributions, and are applied to several real data sets. Keywords. Characteristic function, Goodness-of-fit test, Mixtures of Normal Distributions

Tests for normal mixtures based on the empirical characteristic function

A goodness-of-fit test for two-component homoscedastic and homothetic mixtures of normal distributions is proposed. The tests are based on a weighted L2-type distance between the empirical characteristic function and its population counterpart, where in the latter, parameters are replaced by consistent estimators. Consequently, the resulting tests are consistent against general alternatives. When moment estimation is employed and as the decay of the weight function tends to infinity the test statistics approach limit values, which are related to the first nonvanishing moment equation. The new tests are compared via simulation to other omnibus tests for mixtures of normal distributions, and are applied to several real data sets. © 2004 Elsevier B.V. All rights reserved