A stochastic model for the analysis of maximum daily temperature

In this paper, a stochastic model for the analysis of the daily maximum temperature is proposed. First, a deseasonalization procedure based on the truncated Fourier expansion is adopted. Then, the Johnson transformation functions were applied for the data normalization. Finally, the fractionally autoregressive integrated moving average model was used to reproduce both short- and long-memory behavior of the temperature series. The model was applied to the data of the Cosenza gauge (Calabria region) and verified on other four gauges of southern Italy. Through a Monte Carlo simulation procedure based on the proposed model, 105 years of daily maximum temperature have been generated. Among the possible applications of the model, the occurrence probabilities of the annual maximum values have been evaluated. Moreover, the procedure was applied for the estimation of the return periods of long sequences of days with maximum temperature above prefixed thresholds.