Forecasting mean squared error for Structural Time Series Models

A simulation study is carried out to examine the behaviour in small samples of various estimators of the forecasting mean square error (MSE) with estimated parameters. The attention is focused on the class of Structural Time Series Models. Two practical estimates of the forecasting MSE, one of which includes terms reflecting parameter estimation and one which excludes these terms, are compared to the mean squared error of forecast for the simplest structural model, the random walk plus noise model, considering different values of the parameters of the model and different sample sizes.