Generalised models for multivariate bilinear autoregressive moving average process

The objective of this work was to establish generalised bilinear models for the time series vectors assuming autoregressive and moving average processes. A multiple number of vectors were considered. The vectors included: X_1t, X_2t, X_3t, …, X_nt. The first vector ‘X_1t’ was considered a dependent vector, while others were considered independent vectors. Generalised Bilinear Autoregressive Moving Average Vector (BARMAV) models were established. The models have been confirmed valid for estimation of values of each vector in a multiple relationship between the dependent and independent vectors on the basis of the distribution of autocorrelation and partial autocorrelation functions.