Constructing seasonally adjusted data with time-varying con dence intervals

Seasonal adjustment methods transform observed time series data into estimated data, where these estimated data are constructed such that they show no or almost no seasonal variation. An advantage of model-based methods is that these can provide con dence intervals around the seasonally adjusted data. One particularly useful time series model for seasonal adjustment is the basic structural time series [BSM] model. The usual premise of the BSM is that the variance of each of the components is constant. In this paper we address the possibility that the variance of the trend component in a macroeconomic time series in some way depends on the business cycle. One reason for doing so is that one can expect that there is more uncertainty in recession periods. We extend the BSM by allowing for a business-cycle dependent variance in the level equation. Next we show how this a ects the con dence intervals of seasonally adjusted data. We apply our extended BSM to monthly US unemployment and we show that the estimated con dence intervals for seasonally adjusted unemployment change with past changes in the oil price. We thank Jordi van Kessel for his excellent research assistance, and Marius Ooms for helpful discussions. Corresponding author: Department of Econometrics, Free University Amsterdam, De Boelelaan 1105, NL-1081 HV Amsterdam, email: [email protected] Econometric Institute, Erasmus University Rotterdam, P.O. Box 1738, NL-3000 DR, Rotterdam, The Netherlands, email: [email protected]