Comparison of the Out-of-Sample Forecast for Inflation Rates in Nigeria Using ARIMA and ARIMAX Models

This book chapter compares the out-of-sample forecast for inflation rates in Nigeria using ARIMAX and ARIMA models. To achieve this, Annual Data on Exchange Rate, Inflation Rate, Interest Rate and Unemployment Rate from 1981 to 2017 was sourced from Central Bank of Nigeria (CBN). The analysis used data from 1981 to 2010 while 2011 to 2017 was used to valid the forecast from the ARIMA and ARIMAX models. The preliminary analysis revealed that natural log transform of inflation rate is normally distributed and stationary at first difference while Exchange Rate, Inflation Rate, Interest Rate and Unemployment Rate were used as exogenous variables in the ARIMAX models. The following models ARIMA(1,1,0), ARIMA(1,1,1), ARIMA(0,1,1), ARIMAX(1,1,0), ARIMAX(1,1,1) and ARIMAX(0,1,1) were compared for both in-sample and out-of-sample forecasts. Using the Root Mean Square Error (RMSE) as selection criteria, ARIMAX(0,1,1) with RMSE of 0.6810 emerged as superior model for the in-sample forecast for forecasting inflation rate in Nigeria while ARIMA(1,1,1) emerged as a superior model for the out-of-sample forecast for inflation rate in Nigeria and its forecast for inflation revealed a negative growth in inflation in Nigeria. This study therefore recommended ARIMA(1,1,1) model be used for out-of-sample forecast for inflation rate in Nigeria.