Temperature in the Iberian Peninsula: Trend, seasonality, and heterogeneity

In this paper, we propose fitting unobserved component models to represent the dynamic evolution of bivariate systems of centre and log-range temperatures obtained monthly from minimum/maximum temperatures observed at a given location. In doing so, the centre and log-range temperature are decomposed into potentially stochastic trends, seasonal, and transitory components. Since our model encompasses deterministic trends and seasonal components as limiting cases, we contribute to the debate on whether stochastic or deterministic components better represent the trend and seasonal components. The methodology is implemented to centre and log-range temperature observed in four locations in the Iberian Peninsula, namely, Barcelona, Coru\~na, Madrid, and Seville. We show that, at each location, the centre temperature can be represented by a smooth integrated random walk with time-varying slope, while a stochastic level better represents the log-range. We also show that centre and log-range temperature are unrelated. The methodology is then extended to simultaneously model centre and log-range temperature observed at several locations in the Iberian Peninsula. We fit a multi-level dynamic factor model to extract potential commonalities among centre (log-range) temperature while also allowing for heterogeneity in different areas in the Iberian Peninsula. We show that, although the commonality in trends of average temperature is considerable, the regional components are also relevant.