Stochastic behaviour of the daily minimum mean and maximum temperature in Modena,Italy

The minimum, mean and maximum daily temperature measured in Modena, Italy, since 1892 can be well represented by the sum of a deterministic and a fluctuating signal. The deterministic signal is given by a constant plus the first three harmonics having a fundamental period of one year: a total of seven constant parameters (four amplitudes and three phases). The fluctuating term is stationary and has a first-order probability density function which is normal with zero mean. The autocovariance of the fluctuating signal is well fitted by the sum of two decreasing exponentials for time lags up to 30 days. Since the second exponential is much smaller in amplitude and much slower, the autocovariance is approximated by a single decreasing exponential for time lags up to 7–10 days. Therefore the process is Markovian only initially.