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 confidence 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 affects the confidence intervals of seasonally adjusted data. We apply our extended BSM to monthly US unemployment and we show that the estimated confidence intervals for seasonally adjusted unemployment change with past changes in the oil price.

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Keywords business cycles, econometric models, economics, seasonality, time series, unemployment
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Koopman, S.J, & Franses, Ph.H.B.F. (2002). Constructing seasonally adjusted data with time-varying confidence intervals. Oxford Bulletin of Economics and Statistics, 64(5), 509–526+414. doi:10.1111/1468-0084.00275