Modeling of Seasonal Multivariate Time Series Analysis; Using Gross Domestic Product (GDP) in Nigeria (January 1985- 2017)

The multivariate “Seasonal Vector Autoregressive Moving Average” was used to measure the growth rate of Gross Domestic Product (GDP) in five (5) sectors: Agriculture, Industries, Building/Construction, Wholesales/Retails, and Services. The data was gathered from the National Bureau of Statistics and spans 33 years, from 1985 to 2017. To evaluate the model, real (R) software was used. The variability statistics for the five variables show that all of the variables have a seasonality pattern that is not stationary. We difference the data series (once) to obtain stationary series and define the season order to indicate the seasonality pattern. We find the best model using Akaike information criteria and Bayesian information criteria. The best model was determined to be the SVARMA (4, 1, 1) (1, 0, 0)12. We also apply model simplification to the SVARMA (4, 1, 1) (1, 0, 0), 12 model, to exclude statistically insignificant parameters. The forecasts revealed that the rate of growth in the Agriculture sector is slowly growing, the rate of growth in the Industries sector is slowly decreasing, the rate of growth in the Building/Construction sector is increasing, the rate of growth in the Wholesales/Retails sector is not stable, and the rate of growth in the services sector is poor.