A Probabilistic Application of Generalized Linear Model in Discrete-Time Stochastic Series

Abstract

This study is aimed at identifying the problem associated with Ordinary Least Squares (OLS) in relation to the violation of assumptions of normality and constant variance. Mainly, the possible problem encountered when these assumptions are violated is the introduction of biases in the parameters of the fitted model thereby threatening the model’s efficiency. In this study, the Generalized Linear Model (GLM) is applied to overcome such problems and to ensure the efficiency of the model parameters. The major reasons being that the GLM does not require transformation and assumptions of classical regression. Instead, it employs a probabilistic approach in transforming the expected value of the dependent variable. The data used were obtained from the Central Bank of Nigeria Statistical Bulletin from 1981 to 2016, with each series consisting of 36 observations. The Gross Domestic Product (N’ Billion) was considered as the dependent variable (Yt) while Money Supply(X1t), and Credit to Private Sector(X2t)were considered as the independent variables (N' Billion). From the analysis, the results of the fitted regression model showed no significant relationship between the variables. The diagnosis on the residual series (using skewness, kurtosis, Jacque-Bera test and Breusch-Pagan-Godfrey test) provided sufficient evidence that both validity and efficiency of the model parameters are threatened. However, the results of the GLM procedure provided the much needed significance, validity, and efficiency of the model parameters. Further findings from GLM procedure revealed that the standard errors of the parameters of OLS were biased having been far larger in values than those of the GLM. Hence, for studies involving the regression of a discrete-time stochastic series such as GDP on Money Supply and Credit to Private Sector, the GLM is analytically tractable than the OLS.