Application of Vector Autoregressive (VAR) Process in Modelling Reshaped Seasonal Univariate Time Series

Abstract

Seasonal Autoregressive Integrated Moving Averages (SARIMA) model has been applied in most research work to forecast seasonal univariate data. Less has been done on Vector Autoregressive (VAR) process. In this research project, seasonal univariate time series data has been used to estimate a VAR model for a reshaped seasonal univariate time series for forecasting. This was done by modeling a reshaped seasonal univariate time series data using VAR. The quarterly data is reshaped to vector form and analyzed to vector form and analyzed using VAR for the year 1959 and 1997 to fit the model and the prediction for the year 1998 is used to evaluate the prediction performance. The performance measures used include; mean square error (MSE), root mean square error (RMSE), mean percentage error (MPE), mean absolute percentage error (MAPE) and Theil’s U statistic. Forecasting future values from the fitted models in both SARIMA and VAR using Box Jenkins procedures, (Box and Jenkins; 1976) was done. The results showed that both models are appropriate in forecasting but VAR is more appropriate model than SARIMA model since its predictive performance was shown to be the best. Other data sets were also used for analysis and comparison purpose.