Modelling intervals of minimum/maximum temperatures in the Iberian Peninsula

In this paper, we propose to model intervals of minimum/maximum temperatures observed at a given location by fitting unobserved component models to bivariate systems of center and log-range temperatures. In doing so, the center and logrange temperature are decomposed into potentially stochastic trends, seasonal and transitory components. We contribute to the debate on whether the trend and seasonal components are better represented by stochastic or deterministic components. The methodology is implemented to intervals of minimum/maximum temperatures observed monthly in four locations in the Iberian Peninsula, namely, Barcelona, Coruña, Madrid and Seville. We show that, at each location, the center temperature can be represented by a smooth integrated random walk with time-varying slope while the log-range seems to be better represented by a stochastic level. We also show that center and log-range temperature are unrelated. The methodology is then extended to model simultaneously minimum/maximum temperatures observed at several locations. We fit a multi-level dynamic factor model to extract potential commonalities among center (log-range) temperature while also allowing for heterogeneity in different areas. The model is fitted to intervals of minimum/maximum temperatures observed at a large number of locations in the Iberian Peninsula.