Digital Object Identifier 10.1109/MCS.2009.934465 E conomic time series display features such as trend, seasonal, and cycle that we do not observe directly from the data. The cycle is of particular interest to economists as it is a measure of the fluctuations in economic activity. An unobserved components model attempts to capture the features of a time series by assum- ing that they follow stochastic processes that, when put to- gether, yield the observations. The aim of this article is thus to illustrate the use of unobserved components models in economics and finance and to show how they can be used for forecasting and policy making. Setting up models in terms of components of interest helps in model building; see the discussions in [1] and [2] for a comparison with alternative approaches. A detailed treatment of unobserved components models is given in [3]. The statistical treatment of unobserved components models is based on the state-space form. The unobserved components, which depend on the state vector, are related to the observations by a measurement equation. The Kalman filter is the basic recursion for estimating the state, and hence the unobserved components, in a linear state-space model (see “Kalman Filter”). The estimates, which are based on current and past observations, can be used to make predictions. Backward recursions yield smoothed estimates of components at each point in time based on past, current, and future observations. A set of one-step-ahead prediction errors, called innova- tions, is produced by the Kalman filter. In a Gaussian model, the innovations can be used to construct a likeli- hood function that can be maximized numerically with respect to unknown parameters in the system; see [4]. Once the parameters are estimated, the innovations can be used to construct test statistics that are designed to assess how well the model fits. The STAMP package [5] embodies a model-building procedure in which test statistics are pro- duced as part of the output. © DIGITAL STOCK Unobserved Components Models in Economics and Finance THE ROLE OF THE KALMAN FILTER IN TIME SERIES ECONOMETRICS ANDREW HARVEY and SIEM JAN KOOPMAN 1066-033X/09/$26.00©2009IEEE DECEMBER 2009 « IEEE CONTROL SYSTEMS MAGAZINE 71 Digital Object Identifier 10.1109/MCS.2009.934465