Non-Normality Issue and Hypothesis-Inferring: Testing the Monte Carlo Process

Abstract

Ordinary Least Square (OLS) estimator is assumed to be an unbiased
estimator and the errors are normally distributed. However often is the case
that stock returns characteristically have non-symmetric distribution which
leads to problems related to inferential part by using the estimates of
regression analysis. Markov-chain Monte Carlo simulation approach offers
advantage in better estimates of the model and has become an important tool
in risk management. In this article we compare the critical t-statistics
estimated by Monte Carlo Simulation process with the standard asymptotic tdistribution which subsist under the assumption that the error terms are
normally distributed. Sample of 6 stock companies from the Karachi Stock
Exchange (KSE) 100 index was taken. Daily data of 406 closing prices and
KSE 100 index from January 2010 to June 2011 is taken from Daily
“Business Recorder”. Jarque Bera Test shows that regression error terms in
all these six estimated models were not normally distributed. Following
Monte Carlo Simulation procedure, the critical t-values were simulated at
5% level of significance. These values were found to be almost closer to the
asymptotic standards of t-distribution. Thus it can be concluded that Monte
Carlo based simulation approach is a preferred one for assessing statistical
significance due to its property to transform unsymmetrical distribution into
symmetrical distribution.