Temperature in the Iberian Peninsula: Common trends and heterogeneity
C. Vladimir Rodríguez-Caballero, Esther Ruiz
The Annals of Applied Statistics · 2026 · Volume 20 · Issue 1
Abstract
We propose a Multilevel Dynamic Factor Model (ML-DFM) to capture the common global and region-specific stochastic trends in monthly centre and log-range temperatures observed at 68 locations across the Iberian Peninsula from January 1930 to December 2020. The specification of common trends is based on the analysis of temperatures at each location using unobserved component models, which decompose temperatures into trend, seasonal, and transitory components. First, we show that the centre and log-range temperatures evolve independently. Second, we remove the seasonal component before analysing common trends. Third, we find that centre temperature trends are well approximated by a smooth, integrated random walk with a time-varying slope. In contrast, a stochastic level better captures the dynamics of the log-range. The ML-DFM is estimated using an EM algorithm extended here to accommodate nonstationary factors. We show that, although the commonality in centre-temperature trends is considerable, the regional components remain relevant, particularly at the log-range.
Keywords
Climate change; dynamic factor models; Kalman filter; state space models;
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