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The Shifting Seasonal Mean Autoregressive Model and Seasonality in the Central England Monthly Temperature Series, 1772-2016

Author

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  • Changli He

    (Tianjin University of Finance and Economics)

  • Jian Kang

    (Tianjin University of Finance and Economics)

  • Timo Teräsvirta

    (CREATES and Aarhus University, C.A.S.E, Humboldt-Universität zu Berlin)

  • Shuhua Zhang

    (Tianjin University of Finance and Economics)

Abstract

In this paper we introduce an autoregressive model with seasonal dummy variables in which coefficients of seasonal dummies vary smoothly and deterministically over time. The error variance of the model is seasonally heteroskedastic and multiplicatively decomposed, the decomposition being similar to that in well known ARCH and GARCH models. This variance is also allowed to be smoothly and deterministically time-varying. Under regularity conditions, consistency and asymptotic normality of the maximum likelihood estimators of parameters of this model is proved. A test of constancy of the seasonal coefficients is derived. The test is generalised to specifying the parametric structure of the model. A test of constancy over time of the heteroskedastic error variance is presented. The purpose of building this model is to use it for describing changing seasonality in the well-known monthly central England temperature series. More specifically, the idea is to find out in which way and by how much the monthly temperatures are varying over time during the period of more than 240 years, if they do. Misspecification tests are applied to the estimated model and the findings discussed.

Suggested Citation

  • Changli He & Jian Kang & Timo Teräsvirta & Shuhua Zhang, 2018. "The Shifting Seasonal Mean Autoregressive Model and Seasonality in the Central England Monthly Temperature Series, 1772-2016," CREATES Research Papers 2018-15, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2018-15
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    References listed on IDEAS

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    1. Silvennoinen Annastiina & Teräsvirta Timo, 2016. "Testing constancy of unconditional variance in volatility models by misspecification and specification tests," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 20(4), pages 347-364, September.
    2. Song, Peter X.K. & Fan, Yanqin & Kalbfleisch, John D., 2005. "Maximization by Parts in Likelihood Inference," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1145-1158, December.
    3. Timo Teräsvirta & Marcelo C. Medeiros & Gianluigi Rech, 2006. "Building neural network models for time series: a statistical approach," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(1), pages 49-75.
    4. van Dijk, Dick & Franses, Philip Hans & Lucas, Andre, 1999. "Testing for ARCH in the Presence of Additive Outliers," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(5), pages 539-562, Sept.-Oct.
    5. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-430, March.
    6. Franses Philip Hans & de Bruin Paul, 2000. "Seasonal Adjustment and the Business Cycle in Unemployment," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 4(2), pages 1-14, July.
    7. Daniel Buncic, 2019. "Identification and Estimation Issues in Exponential Smooth Transition Autoregressive Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 81(3), pages 667-685, June.
    8. Terence C. Mills & David I. Harvey, 2003. "Modelling trends in central England temperatures," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 22(1), pages 35-47.
    9. Baek, Yae In & Cho, Jin Seo & Phillips, Peter C.B., 2015. "Testing linearity using power transforms of regressors," Journal of Econometrics, Elsevier, vol. 187(1), pages 376-384.
    10. Oberhofer, W & Kmenta, J, 1974. "A General Procedure for Obtaining Maximum Likelihood Estimates in Generalized Regression Models," Econometrica, Econometric Society, vol. 42(3), pages 579-590, May.
    11. Tommaso Proietti & Eric Hillebrand, 2017. "Seasonal changes in central England temperatures," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(3), pages 769-791, June.
    12. Dick van Dijk 1 & Birgit Strikholm & Timo Teräsvirta, 2003. "The effects of institutional and technological change and business cycle fluctuations on seasonal patterns in quarterly industrial production series," Econometrics Journal, Royal Economic Society, vol. 6(1), pages 79-98, June.
    13. Craig, Lee A. & Holt, Matthew T., 2008. "Mechanical refrigeration, seasonality, and the hog-corn cycle in the United States: 1870-1940," Explorations in Economic History, Elsevier, vol. 45(1), pages 30-50, January.
    14. Amado, Cristina & Teräsvirta, Timo, 2013. "Modelling volatility by variance decomposition," Journal of Econometrics, Elsevier, vol. 175(2), pages 142-153.
    15. Ahdi Ajmi & Adnen Ben Nasr & Mohamed Boutahar, 2008. "Seasonal Nonlinear Long Memory Model for the US Inflation Rates," Computational Economics, Springer;Society for Computational Economics, vol. 31(3), pages 243-254, April.
    16. Wooldridge, Jeffrey M., 1990. "A Unified Approach to Robust, Regression-Based Specification Tests," Econometric Theory, Cambridge University Press, vol. 6(1), pages 17-43, March.
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    Cited by:

    1. He, Changli & Kang, Jian & Teräsvirta, Timo & Zhang, Shuhua, 2021. "Comparing long monthly Chinese and selected European temperature series using the Vector Seasonal Shifting Mean and Covariance Autoregressive model," Energy Economics, Elsevier, vol. 97(C).
    2. He, Changli & Kang, Jian & Silvennoinen, Annastiina & Teräsvirta, Timo, 2024. "Long monthly temperature series and the Vector Seasonal Shifting Mean and Covariance Autoregressive model," Journal of Econometrics, Elsevier, vol. 239(1).
    3. He, Changli & Kang, Jian & Silvennoinen, Annastiina & Teräsvirta, Timo, 2023. "Long monthly European temperature series and the North Atlantic Oscillation," Energy Economics, Elsevier, vol. 126(C).
    4. Proietti, Tommaso & Pedregal, Diego J., 2023. "Seasonality in High Frequency Time Series," Econometrics and Statistics, Elsevier, vol. 27(C), pages 62-82.
    5. Webel, Karsten, 2022. "A review of some recent developments in the modelling and seasonal adjustment of infra-monthly time series," Discussion Papers 31/2022, Deutsche Bundesbank.

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    More about this item

    Keywords

    global warming; nonlinear time series; changing seasonality; smooth transition; testing constancy;
    All these keywords.

    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
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • Q54 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Climate; Natural Disasters and their Management; Global Warming

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