On the Use of Marginal Likelihood in Time Series Model Estimation

SUMMARY In the context of time series regression, with an error model of the ARIMA type, the fitting of the regression can seriously bias the ARIMA model parameter estimates. Moreover, choosing between different error models on the basis of the smallest residual variance may lead to incorrect selection with a high probability, even in samples of moderate size. The marginal likelihood procedure is considered as a solution to these problems and examples are presented in the context of trend estimation, seasonal forecasting and mixed spectrum analysis.