Autoregressive moving average vector models and their application to revenue data

The multivariate time series modeling carried out in this work considers four vector series, a response and three predictor vectors. The response vector ‘X_1t’ and one of the predictor vectors ‘X_4t’ follow a pure autoregressive process of order 3 and 2 respectively, while X_2t and X_3t predictor vectors follow a pure moving average process of order ‘1’ and ‘2’ respectively. This gives the basis for the choice of mixed autoregressive moving average vector (ARMAV) models for the vector series. A model for each of the vector series was obtained as a function of distributed lags of both the response and predictor vectors. This implies that every vector, be it response or predictor vector is modeled with respective feed-forward and feedback parameters. The estimates are given in appendix ‘2’, and are graphically shown in figures ‘1’, ‘2’, ‘3’ and ‘4’.