A generalized conditional heteroscedastic model for temperature downscaling

Abstract

This study describes a method for deriving the time varying second order moment, or heteroscedasticity, of local daily temperature and its association to large Coupled Canadian General Circulation Models predictors. This is carried out by applying a multivariate generalized autoregressive conditional heteroscedasticity (MGARCH) approach to construct the conditional variance–covariance structure between General Circulation Models (GCMs) predictors and maximum and minimum temperature time series during 1980–2000. Two MGARCH specifications namely diagonal VECH and dynamic conditional correlation (DCC) are applied and 25 GCM predictors were selected for a bivariate temperature heteroscedastic modeling. It is observed that the conditional covariance between predictors and temperature is not very strong and mostly depends on the interaction between the random process governing temporal variation of predictors and predictants. The DCC model reveals a time varying conditional correlation between GCM predictors and temperature time series. No remarkable increasing or decreasing change is observed for correlation coefficients between GCM predictors and observed temperature during 1980–2000 while weak winter–summer seasonality is clear for both conditional covariance and correlation. Furthermore, the stationarity and nonlinearity Kwiatkowski–Phillips–Schmidt–Shin (KPSS) and Brock–Dechert–Scheinkman (BDS) tests showed that GCM predictors, temperature and their conditional correlation time series are nonlinear but stationary during 1980–2000 according to BDS and KPSS test results. However, the degree of nonlinearity of temperature time series is higher than most of the GCM predictors.