Seasonality with trend and cycle interactions in unobserved components models
AbstractUnobserved 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, which is 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. 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. Copyright (c) 2009 Royal Statistical Society.
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Bibliographic InfoArticle provided by Royal Statistical Society in its journal Journal of the Royal Statistical Society: Series C (Applied Statistics).
Volume (Year): 58 (2009)
Issue (Month): 4 ()
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Other versions of this item:
- Siem Jan Koopman & Kai Ming Lee, 0000. "Seasonality with Trend and Cycle Interactions in Unobserved Components Models," Tinbergen Institute Discussion Papers 08-028/4, Tinbergen Institute.
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
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