Seasonality with Trend and Cycle Interactions in Unobserved Components Models

Siem Jan Koopman and Kai Ming Lee ()
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Kai Ming Lee: VU University Amsterdam

No 08-028/4, Tinbergen Institute Discussion Papers from Tinbergen Institute

Abstract: This discussion paper resulted in a publication in the Journal of the Royal Statistical Society Series C (2009). Vol. 58, pages 427-448. Unobserved components time series models decompose a time series into a trend, a season, a cycle, an irregular disturbance, and possibly other components. These models have been successfully applied to many economic time series. The standard assumption of a linear model, often appropriate after a logarithmic transformation of the data, facilitates estimation, testing, forecasting and interpretation. However, in some settings the linear-additive framework may be too restrictive. In this paper, we formulate a non-linear unobserved components time series model which allows interactions between the trend-cycle component and the seasonal component. The resulting model is cast into a non-linear state space form and estimated by the extended Kalman filter, adapted for models with diffuse initial conditions. We apply our model to UK travel data and US unemployment and production series, and show that it can capture increasing seasonal variation and cycle dependent seasonal fluctuations.

Keywords: Seasonal interaction; Unobserved components; Non-linear state space models (search for similar items in EconPapers)
JEL-codes: C13 C22 (search for similar items in EconPapers)
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Citations: View citations in EconPapers (2)

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Journal Article: Seasonality with trend and cycle interactions in unobserved components models (2009)
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