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

Publikation: Working paperForskning


  • rp18_15

    Forlagets udgivne version, 660 KB, PDF-dokument

  • Changli He, Tianjin University of Finance and Economics, Kina
  • Jian Kang, Tianjin University of Finance and Economics, Kina
  • Timo Terasvirta
  • Shuhua Zhang, Tianjin University of Finance and Economics, Kina
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.
UdgiverInstitut for Økonomi, Aarhus Universitet
Antal sider41
StatusUdgivet - 25 apr. 2018
SerietitelCREATES Research Papers


  • global warming, nonlinear time series, changing seasonality, smooth transition, testing constancy

Se relationer på Aarhus Universitet Citationsformater


Ingen data tilgængelig

ID: 126370998