A periodic mixed linear state-space model to monthly long-term temperature data

In recent decades, the world has been confronted with the consequences of global warming; however, this phenomenon is not reflected equally in every part of the globe. Thus, the warming phenomenon must be monitored in a more regional or local scale. This paper analyzes monthly long-term time series of air temperatures in three Portuguese cities: Lisbon, Oporto, and Coimbra. We propose a periodic state-space framework, associated with a suitable version of the Kalman filter; which allows for the estimation of monthly warming rates taking into account the seasonal behavior and serial correlation. Results about the monthly mean of the daily midrange temperature time series show that there are different monthly warming rates. The greatest annual mean rise was found in Oporto with 2.17 degrees C, whereas in Lisbon and Coimbra, it was respectively 0.62 degrees C and 0.55 degrees C per century.