10 Structural time series models

Abstract

Structural time series model is one which is set up in terms of components, which have a direct interpretation. Thus, for example, one may consider the classical decomposition in which a series is seen as the sum of trend, seasonal and irregular components. A model could be formulated as a regression with explanatory variables consisting of a time trend and a set of seasonal dummies. Typically, this would be inadequate. The necessary flexibility may be achieved by letting the regression coefficients change over time. A similar treatment may be accorded to other components such as cycles. The principal univariate structural time series models are therefore nothing more than regression models in which the explanatory variables are functions of time and the parameters are time-varying. The use of a regression framework opens the way to a unified model selection methodology for econometric and time series models. The key to handling structural time series models is the state space form with the state of the system representing the various unobserved components such as trends and seasonals. The estimate of the unobservable state can be updated by means of a filtering procedure as new observations become available. Predictions are made by extrapolating these estimated components into the future, while smoothing algorithms give the best estimate of the state at any point within the sample. A structural model can therefore not only provide forecasts, but can also, through estimates of the components, present a set of stylized facts.