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Seasonality with trend and cycle interactions in unobserved components models

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  • Siem Jan Koopman
  • Kai Ming Lee

Abstract

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, 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.

Suggested Citation

  • Siem Jan Koopman & Kai Ming Lee, 2009. "Seasonality with trend and cycle interactions in unobserved components models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 58(4), pages 427-448.
  • Handle: RePEc:bla:jorssc:v:58:y:2009:i:4:p:427-448
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    References listed on IDEAS

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    Cited by:

    1. Altug, Sumru & Çakmaklı, Cem, 2016. "Forecasting inflation using survey expectations and target inflation: Evidence for Brazil and Turkey," International Journal of Forecasting, Elsevier, vol. 32(1), pages 138-153.
    2. Sumru Altug & Cem Cakmakli, 2014. "Inflation Targeting and Inflation Expectations: Evidence for Brazil and Turkey," Koç University-TUSIAD Economic Research Forum Working Papers 1413, Koc University-TUSIAD Economic Research Forum.
    3. Paul Alagidede, 2012. "Trends And Cycles In The Net Barter Terms Of Trade For Sub-Saharan Africa's Primary Commodity Exporters," Journal of Developing Areas, Tennessee State University, College of Business, vol. 46(2), pages 213-229, July-Dece.

    More about this item

    JEL classification:

    • 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; Diffusion Processes

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