Pure Moving Average Vector Bilinear Time Series Model and Its Application

Most time series assume both linear and non linear components because of their random nature. Thus, the classical linear models are not appropriate for modeling series with such behaviour. This work was motivated by the need to propose a vector moving average (MA) bilinear concept that caters for the linear and non linear components of a series on the basis of the ‘orders' of the linear MA process. To achieve this, a matrix that preserved the ‘orders' of the linear processes was formulated with given conditions. With the introduction of diagonal matrix of lagged white noise processes, some special bilinear models emerged and the ‘orders' of the pure linear MA processes were maintained in both the linear and non linear parts. The derived vector bilinear models were applied to revenue series, and the result showed that the models gave a good fit which depicted its validity.