The Effect of Misspecification in Vector Autoregressive Moving Average Models on Parameter Estimation and Forecasting

In this study, the effect of incorrect order identification on parameter estimation and forecasting for the vector autoregressive moving average model has been conducted via a Monte Carlo simulation. Five parameter sets, labeled A to E, for a bivariate ARMA(1,1) model were specified within the feasible regions of stationarity and invertibility. It was found that the estimated parameter values for the ARMA(2,1) and ARMA(1,2) models had biases approaching zero, while those for the ARMA(2,0), ARMA(1,0) and ARMA(0,1) models exhibited persistent biases. The forecast findings for the underfitted models are contrary to the univariate results of Ledolter and Abraham (1981) and Kunitomo and Yamamoto (1985). However the findings are consistent with Akaike's (1969). This study has shown that an underfitted model is less desirable than an overfitted one in term of forecast error variances.