State space models for the analysis and forecasting of climatic time series

We analyse climatic time series with state space models in order to compute the forecast distribution. The task is challenging since the temperature series are characterised by large temporal and cross-sectional dimensions. We modify and apply the three-step method proposed in Li et al. Journal of Econometrics 2020, which exploit the cross information in order to improve prediction. We fit the linear Gaussian state space model to different univariate time series, estimating the model parameters with the Kalman filter and computing the prediction errors. The prediction error time series are then jointly analysed by means of a dynamic factor model. The estimation procedure follows the two-step approach suggested by Doz, Giannone, and Reichlin in the context of macro-economic time series nowcasting. Finally, the simulation smoother by Durbin and Koopman allows to sample scenarios conditional on the observed time series and to reconstruct the forecast distribution. The results we obtained are promising. They demonstrate the feasibility of the entire procedure. Our explorations involved just a climatic parameter (the maximum temperature) and a reduced sample of data (8 years on a weekly basis for twenty climatic stations) , but we preliminarily tested the whole approach on much longer time series - up to 150 years - with a richer cross-sectional structure - up to 10.000 stations - experiencing viable computational times and very promising estimation results.