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

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.