Forecasting with Unobserved Components Time Series Models

Structural time series models are formulated in terms of components, such as trends, seasonals and cycles, that have a direct interpretation. As well as providing a framework for time series decomposition by signal extraction, they can be used for forecasting and for `nowcasting'. The structural interpretation allows extensions to classes of models that are able to deal with various issues in multivariate series and to cope with non-Gaussian observations and nonlinear models. The statistical treatment is by the state space form and hence data irregularities such as missing observations are easily handled. Continuous time models offer further flexibility in that they can handle irregular spacing. The paper compares the forecasting performance of structural time series models with ARIMA and autoregressive models. Results are presented showing how observations in linear state space models are implicitly weighted in making forecasts and hence how autoregressive and vector error correction representations can be obtained. The use of an auxiliary series in forecasting and nowcasting is discussed. A final section compares stochastic volatility models with GARCH.