Department of Economics and Business Economics

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

Research output: Working paperResearch


  • rp18_15

    Final published version, 660 KB, PDF document

  • Changli He, Tianjin University of Finance and Economics, China
  • Jian Kang, Tianjin University of Finance and Economics, China
  • Timo Terasvirta
  • Shuhua Zhang, Tianjin University of Finance and Economics, China
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.
Original languageEnglish
Place of publicationAarhus
PublisherInstitut for Økonomi, Aarhus Universitet
Number of pages41
Publication statusPublished - 25 Apr 2018
SeriesCREATES Research Papers

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