Modeling inflation in Kenya: Comparison of SARIMA and Generalized Least Squares models

Abstract

One desire by the policy makers in a country is to have access to reliable forecast of inflation rate. This is only achievable if the right model with high predictive accuracy is used. In this paper, seasonal auto regressive integrated moving average (SARIMA) and Generalized Least Squares regression models are developed to predict Kenya's inflation using quarterly data for the period 1981 to 2013. SARIMA (0,1,0)(0,0,1)₄ was chosen as the model with the least Akaike Information Criterion and Bayesian Information Criterion. The parameters were then estimated. The residuals were checked to find out if they follow a white noise process by using residual Q-Q and normality test plots. The Test for normality of residual was also done. Given the high p-values (0.0639237) associated with the statistics as compared to 0.05, we fail to reject the null hypothesis that an error is normally distributed in this residual series. Thus, we conclude that the model provides an adequate fit for the data. In an effort to improve this, inflation was also modeled using Generalized Least Squares regression model.. The data was first checked for heteroscedasticity using the Breusch-Pagan test. Based on the p-value=0.000, which is less than alpha (of 5%), we conclude that there is substantial amount heteroscedasticity in the data. A regression model that forecasts inflation using its lags was constructed. The residuals were checked for normality using q-q plot. Additionally, the Shapiro-Wilk normality test was carried out. Its p-value was 0.08178 and since its greater than 0.05, its concluded that the residuals does not deviate from normality

A comparison was made on the predictive ability of both models. SARIMA (0,1,0)(0,0,1)₄ model had the least values of MAPE, MAE and RMSE with the corresponding values given by MAPE=14.155, RMSE=0.2871and MAE=0.23692

Keywords: SARIMA, Generalized Least Squares, Akaike Information Criterion ,Bayesian Information Criterion, Shapiro-Wilk normality test and Breusch-Pagan test