Updated Vector Autoregressive Model Incorporating new Information Using the Bayesian Approach

Abstract

Vector Autoregressive (VAR) models have been applied extensively in modeling time series due to their high precision when used to forecast. In the VAR development, if we have information up to time t, then a VAR(p) model is fitted. However, if new information at time t + 1, is obtained, then a new VAR(p) model has to be fitted which makes one to go through the process again. Therefore, despite their good performance, a need would arise to incorporate new information that could be obtained after the model has been fitted to update the model instead of fitting a new model each and every time a new information is obtained. This study, therefore, considers incorporating the new information to update the vector autoregressive model of order p using Bayesian approach. First, a VAR model of order 1 is formulated after which this is generalized to the VAR model of order p. We assume that the VAR model is the prior while new information is the likelihood. The performance of updated model is compared with corresponding VAR(p) models and the model is found to perform well based on the small values of the root mean square error (RMSE) in the update and in the prediction for the plots obtained.