Forecasting and signal extraction with misspecified models

This paper evaluates multistep estimation for the purposes of signal extraction, and in particular the separation of the trend from the cycle in economic time series, and long-range forecasting, in the presence of a misspecified, but simply parameterized model. Our workhorse models are two popular unobserved components models, namely the local level and the local linear model. The paper introduces a metric for assessing the accuracy of the unobserved components estimates and concludes that multistep estimation can be valuable. However, its performance depends crucially on the properties of the series and the paper explores the role of the order of integration and the relative size of the cyclical variation. On the contrary, cross-validation is usually not suitable for the purposes considered.