PERFORMANCE OF ALL NIGERIA BANKS’ SHARES USING STUDENT-T MIXTURE AUTOREGRESSIVE MODEL

J. F. Ojo and R.O. Olanrewaju

Department of Statistics,

University of Ibadan, Ibadan, Nigeria.

E-mail: jfunminiyiojo@yahoo.com,rasakiolawale@gmail.com

Abstract

This study attempts to model the all Nigeria banks’ volume of shares using the Student-t Mixture Autoregressive (TMAR) and the Mixture Autoregressive (MAR) models because the series has been characterized by fluctuation, excessive kurtosis and excessive skewness that was justified by the Degree of Freedom (DF)that was  greater than four, that is,in each regime of the TMAR model. The TMAR model substituted the Student-t Probability Density Function (PDF) for the error term in contrast to Gaussian used by MAR in order to cater for positive or negative excess kurtosis that might have distorted the parameters’ estimation in MAR. Though the stylized traits of the shape changing means, variances (volatilities), and conditional distributions of the two models were still maintained. The approach adopted the E-step and M-step (Expected and Maximization) iterative procedure in parameters’ estimation and detection of kurtosis whenever the DF is greater than four. The all Nigeria banks’ shares were fitted using TMAR and MAR models, the density function plot of all Nigeria banks’ shares between 4 January, 2007 and 20 April, 2015 revealed a 5-regime shift and the best model was recorded at MAR (5: 2, 1, 6, 2, 2) and TMAR (5: 2, 1, 6, 2, 2).  Apart from the fact that the standard errors of estimates from TMAR model were smaller compared to standard errors of estimates from MAR model, the TMAR model  out-performed the MAR model with minimum Akaike Information Criterion and Bayesian Information Criterion  of (438.98 and 454.54) and (445.84 and 459), respectively. In addition, the TMAR model recorded a lesser predictive error of Residual Mean Square Error (RSME) of 8.2960 compared to10.6061 recorded for MAR. Lastly, the banks’ shares recorded a rapid change and unpredictably higher volatility (risk) of 10.4370 for TMAR and 20.6902 for MAR in the third and fifth regimes compared to other three regimes with lesser risk.