Recently the topic of global warming has become very popular. The literature has concentrated its attention on the evidence of such effect, either by detecting regime shifts or change points in time series. The majority of these methods are designed to find shifts in mean, but only few can do this for the variance. In this paper we attempt to investigate the statistical evidence of global warming by identifying shifts in seasonal mean of daily average temperatures over time and in seasonal variance of temperature residuals. We present a time series approach for modelling temperature dynamics. A seasonal mean Lasso-type technique based with a multiplicative structure of Fourier and GARCH terms in volatility is proposed. The model describes well the stylised facts of temperature: seasonality, intertemporal correlations and the heteroscedastic behaviour of residuals. The application to European temperature data indicates that the multiplicative model for the seasonal variance performs better in terms of out of sample forecast than other models proposed in the literature for modelling temperature dynamics. We study the dynamics of the seasonal variance by implementing quantile and expectile functions with confidence corridor to detrended and deseasonalized residuals. We show that shifts in seasonal mean and variance vary from location to location, indicating that all sources of trends other than mean and variance would rise trends over spatial scales. The local effects of temperature risk support the existence of global warming.
Weather temperature seasonality variance global warming expectile quantile