Vector bilinear autoregressive time series model and its superiority over its linear autoregressive counterpart

Abstract

In this research, a vector bilinear autoregressive time series model was proposed and used to model three revenue series (X₁, X₂, X₃) . The “orders” of the three series were identified on the basis of the distribution of autocorrelation and partial autocorrelation functions and were used to construct the vector bilinear models. The estimates obtained from the bilinear fits were compared graphically with those obtained from fitting linear (autoregressive) models. Residual variance and Box-Ljung Q statistic comparisons were also made. The result showed that vector bilinear autoregressive (BIVAR) models provide better estimates than the long embraced linear models.

Keywords: Linear time series, Autoregressive process, Autocorrelation function, Partial autocorrelation function, Vector time series and bilinear vector process