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On trends and constants in periodic autoregressions

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  • Richard Paap
  • Philip Hans Franses

Abstract

Periodic autoregressions are characterised by autoregressive structures that vary with the season. If a time series is periodically integrated, one needs a seasonally varying differencing filter to remove the stochastic trend. When the periodic regression model contains constants and trends with unrestricted parameters, the data can show diverging seasonal deterministic trends. In this paper we derive explicit expressions for parameter restrictions that result in common deterministic trends under periodic trend stationarity and periodic integration.

Suggested Citation

  • Richard Paap & Philip Hans Franses, 1999. "On trends and constants in periodic autoregressions," Econometric Reviews, Taylor & Francis Journals, vol. 18(3), pages 271-286.
  • Handle: RePEc:taf:emetrv:v:18:y:1999:i:3:p:271-286
    DOI: 10.1080/07474939908800446
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    Cited by:

    1. del Barrio Castro, Tom s & Osborn, Denise R., 2008. "Cointegration For Periodically Integrated Processes," Econometric Theory, Cambridge University Press, vol. 24(01), pages 109-142, February.
    2. Franses, Philip Hans & van Dijk, Dick, 2005. "The forecasting performance of various models for seasonality and nonlinearity for quarterly industrial production," International Journal of Forecasting, Elsevier, vol. 21(1), pages 87-102.
    3. Pami Dua & Lokendra Kumawat, 2005. "Modelling and Forecasting Seasonality in Indian Macroeconomic Time Series," Working papers 136, Centre for Development Economics, Delhi School of Economics.
    4. Eiji Kurozumi, 2002. "Testing For Periodic Stationarity," Econometric Reviews, Taylor & Francis Journals, vol. 21(2), pages 243-270.
    5. Christiano, Lawrence J. & Todd, Richard M., 2002. "The conventional treatment of seasonality in business cycle analysis: does it create distortions?," Journal of Monetary Economics, Elsevier, vol. 49(2), pages 335-364, March.
    6. del Barrio Castro Tomás & Osborn Denise R, 2011. "Nonparametric Tests for Periodic Integration," Journal of Time Series Econometrics, De Gruyter, vol. 3(1), pages 1-35, February.
    7. Eugen Ursu & Pierre Duchesne, 2009. "Estimation and model adequacy checking for multivariate seasonal autoregressive time series models with periodically varying parameters," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 63(2), pages 183-212.

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