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The shifting seasonal mean autoregressive model and seasonality in the Central England monthly temperature series, 1772–2016

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  • He, Changli
  • Kang, Jian
  • Teräsvirta, Timo
  • Zhang, Shuhua

Abstract

A new autoregressive model with seasonal dummy variables in which coefficients of seasonal dummies vary smoothly and deterministically over time is introduced. The error variance of the model is seasonally heteroskedastic and multiplicatively decomposed as in ARCH 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. The purpose of the model is to find out how the average monthly temperatures in the well-known central England temperature series have been varying during the period of more than 240 years. The main result is that warming has occurred but that there are notable differences between months. In particular, no warming is found for February, April, May and June.

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  • He, Changli & Kang, Jian & Teräsvirta, Timo & Zhang, Shuhua, 2019. "The shifting seasonal mean autoregressive model and seasonality in the Central England monthly temperature series, 1772–2016," Econometrics and Statistics, Elsevier, vol. 12(C), pages 1-24.
    • Handle: RePEc:eee:ecosta:v:12:y:2019:i:c:p:1-24
    DOI: 10.1016/j.ecosta.2019.05.005
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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. Changli He & Jian Kang & Timo Teräsvirta & Shuhua Zhang, 2019. "Long monthly temperature series and the Vector Seasonal Shifting Mean and Covariance Autoregressive model," CREATES Research Papers 2019-18, Department of Economics and Business Economics, Aarhus University.
    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; Time-varying error variance;
    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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