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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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  • 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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    References listed on IDEAS

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    1. Franses, Philip Hans & Paap, Richard, 2004. "Periodic Time Series Models," OUP Catalogue, Oxford University Press, number 9780199242030.
    2. 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(1), pages 1-35, April.
    3. Ghysels,Eric & Osborn,Denise R., 2001. "The Econometric Analysis of Seasonal Time Series," Cambridge Books, Cambridge University Press, number 9780521565882.
    4. Maddala, G S, et al, 1997. "Estimation of Short-Run and Long-Run Elasticities of Energy Demand from Panel Data Using Shrinkage Estimators," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(1), pages 90-100, January.
    5. Wolak, Frank A., 1989. "Testing inequality constraints in linear econometric models," Journal of Econometrics, Elsevier, vol. 41(2), pages 205-235, June.
    6. Helmut Herwartz, 1999. "Performance of periodic time series models in forecasting," Empirical Economics, Springer, vol. 24(2), pages 271-301.
    7. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
    8. Franses, Philip Hans & Paap, Richard, 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.
    9. 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.
    10. Boswijk, H. Peter & Franses, Philip Hans & Haldrup, Niels, 1997. "Multiple unit roots in periodic autoregression," Journal of Econometrics, Elsevier, vol. 80(1), pages 167-193, September.
    11. Franses, Philip Hans, 1994. "A multivariate approach to modeling univariate seasonal time series," Journal of Econometrics, Elsevier, vol. 63(1), pages 133-151, July.
    12. Peter Bloomfield & Harry L. Hurd & Robert B. Lund, 1994. "Periodic Correlation In Stratospheric Ozone Data," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(2), pages 127-150, March.
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    Cited by:

    1. Aknouche, Abdelhakim & Guerbyenne, Hafida, 2009. "Periodic stationarity of random coefficient periodic autoregressions," Statistics & Probability Letters, Elsevier, vol. 79(7), pages 990-996, April.
    2. Paul L. Anderson & Farzad Sabzikar & Mark M. Meerschaert, 2021. "Parsimonious time series modeling for high frequency climate data," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(4), pages 442-470, July.
    3. Aknouche, Abdelhakim & Rabehi, Nadia, 2024. "Inspecting a seasonal ARIMA model with a random period," MPRA Paper 120758, University Library of Munich, Germany.
    4. Dennis Fok & Philip Hans Franses, 2013. "Testing earnings management," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 67(3), pages 281-292, August.
    5. 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.
    6. Kiygi Calli, Meltem & Weverbergh, Marcel & Franses, Philip Hans, 2012. "The effectiveness of high-frequency direct-response commercials," International Journal of Research in Marketing, Elsevier, vol. 29(1), pages 98-109.
    7. 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.
    8. Abdelhakim Aknouche & Eid Al-Eid & Nacer Demouche, 2018. "Generalized quasi-maximum likelihood inference for periodic conditionally heteroskedastic models," Statistical Inference for Stochastic Processes, Springer, vol. 21(3), pages 485-511, October.

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    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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