On the Use of Marginal Likelihood in Time Series Model Estimation.

Abstract : This paper is concerned with the estimation of regression models with errors which follow an Autoregressive Integrated Moving Average (ARIMA) process. The effect of the regression upon the ARIMA model parameter estimates is considered and marginal likelihood investigated as a means of overcoming some small sample bias. Examples illustrate the importance of this effect even in samples of moderate size. The consequences regarding inference for the regression coefficients are also discussed.