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Random‐coefficient periodic autoregressions

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  • Philip Hans Franses
  • Richard Paap

Abstract

We propose a new periodic autoregressive model for seasonally observed time series, where the number of seasons can potentially be very large. The main novelty is that we collect the periodic parameters in a second-level stochastic model. This leads to a random-coefficient periodic autoregression with a substantial reduction in the number of parameters to be estimated. We discuss representation, estimation, and inference. An illustration for monthly growth rates of US industrial production shows the merits of the new model specification.
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Suggested Citation

  • Philip Hans Franses & Richard Paap, 2011. "Random‐coefficient periodic autoregressions," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 65(1), pages 101-115, February.
  • Handle: RePEc:bla:stanee:v:65:y:2011:i:1:p:101-115 DOI: j.1467-9574.2010.00477.x
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    File URL: http://hdl.handle.net/10.1111/j.1467-9574.2010.00477.x
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    References listed on IDEAS

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    1. Philip Hans Franses & Richard Paap, 1994. "Model Selection In Periodic Autoregressions," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 56(4), pages 421-439, November.
    2. Franses, Philip Hans & Paap, Richard, 2004. "Periodic Time Series Models," OUP Catalogue, Oxford University Press, number 9780199242030.
    3. Wolak, Frank A., 1989. "Local and Global Testing of Linear and Nonlinear Inequality Constraints in Nonlinear Econometric Models," Econometric Theory, Cambridge University Press, vol. 5(01), pages 1-35, April.
    4. Helmut Herwartz, 1999. "Performance of periodic time series models in forecasting," Empirical Economics, Springer, pages 271-301.
    5. Ghysels,Eric & Osborn,Denise R., 2001. "The Econometric Analysis of Seasonal Time Series," Cambridge Books, Cambridge University Press, number 9780521565882, November.
    6. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
    7. Boswijk, H. Peter & Franses, Philip Hans & Haldrup, Niels, 1997. "Multiple unit roots in periodic autoregression," Journal of Econometrics, Elsevier, pages 167-193.
    8. Osborn, Denise R & Smith, Jeremy P, 1989. "The Performance of Periodic Autoregressive Models in Forecasting Seasonal U. K. Consumption," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(1), pages 117-127, January.
    9. Franses, Philip Hans, 1994. "A multivariate approach to modeling univariate seasonal time series," Journal of Econometrics, Elsevier, pages 133-151.
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    Cited by:

    1. Kiygi Calli, M. & Weverbergh, M. & Franses, Ph.H.B.F., 2008. "Modeling the Effectiveness of Hourly Direct-Response Radio Commercials," ERIM Report Series Research in Management ERS-2008-019-MKT, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    2. Aknouche, Abdelhakim & Guerbyenne, Hafida, 2009. "Periodic stationarity of random coefficient periodic autoregressions," Statistics & Probability Letters, Elsevier, pages 990-996.
    3. Aknouche, Abdelhakim & Al-Eid, Eid & Demouche, Nacer, 2016. "Generalized quasi-maximum likelihood inference for periodic conditionally heteroskedastic models," MPRA Paper 75770, University Library of Munich, Germany, revised 19 Dec 2016.

    More about this item

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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