Timo Terasvirta ( Aarhus University)

In this paper we introduce a new model, the Shifting Seasonal Mean Autoregressive Model, in which the seasonal dummy variables have deterministically time-varying coefficients. Seasonal error variances are also assumed time-varying. Asymptotic properties of maximum likelihood estimators of the parameters of the model are considered. Tests of constancy of coefficients of seasonal dummy variables against shifts in them are derived. Misspecification tests of the estimated model are discussed as well. The model is applied to describing variations in seasonality of the monthly Central England temperature series, studied by many authors, including Proietti and Hillebrand (2017). Results show, among other things, that there are three types of warming, tentatively named 19th century and 20th century warming, and no warming, respectively.

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