Modeling the Autocorrelated Errors in Time Series Regression: A Generalized Least Squares Approach

Abstract

This study considered Gross Domestic Product (N’ Billion) as the dependent variable (denoted by Yt),  the Money Supply (N’ Billion) as the independent variable (denoted by X1t ) and the Credit to Private Sector as another independent variable (denoted by X2t). The data were obtained from the Central Bank of Nigeria Statistical Bulletin for a period ranging from 1981 to 2014. Each series consists of 34 observations. The study aimed at applying the generalized least squares to overcome the weaknesses of ordinary least squares to ensure the efficiency of the model parameters, unbiased standard errors, valid t-statistics and p-values, and to account for the presence of autocorrelation. Based on ordinary least squares fitted regression model, our findings revealed that X1t and X2t contributed significantly to Yt and were able to explain about 67.95% of the variance in Yt. However, the diagnosis of the fitted regression model using Breusch and Godfrey test, ACF, and PACF showed that the residuals are correlated, hence the need for generalized least squares. Further findings from the results of generalized least squares estimation revealed that their estimates are better and that the additional information in the error terms (autocorrelation) could be explained and captured by AR (2). Thus, it could be deduced that generalized least squares provides better estimates than the ordinary least squares and also accounts for autocorrelation in time series regression analysis.