GNGTS 2022 - Atti del 40° Convegno Nazionale

GNGTS 2022 Sessione 1.2 121 Results. The results of 100 rolling forecasts calculated simultaneously for the 14 series at 1-, 5-, and 10-step are reported in Fig.1a in comparison with the corresponding observations. The values of RMSE increase at increasing the step of the forecast while R 2 values decreases, indicating a progressive decreasing reliability of the forecast. However, the values of the t-test performed on the slope and intercept indicate a likely significant (0.05 < p-value < 0.1) difference from the identity for the 1- and 5- day forecast. We are mainly interested to understand the capability to predict the global CO 2 signal for the whole network. The forecast from the single series have been combined following the procedure of Liuzzo et al. , (2013) and compared with the observation processed likewise (Fig. 1b). While the RMSE and R 2 values are respectively higher and lower, if compared with the single time series forecast, the t-test on the indicates that the adopted procedure is able to provide sufficiently accurate 1-day forecasts. However, the longer the span, the less reliable become forecasts, even though the first-order features of the signal are well approximated (Fig. 1c). The analysis of the residuals is useful to check whether the predictions have adequately captured the information in the data. A good forecasting method will yield residuals with zero mean and normally distributed. The normal Q-Q residuals plots of the forecast of the single time series indicate a clear departure from the normality which is variously marked depending among the various series (Fig. 2). The observed departure from normality is similar for the three forecasts and could suggest that some information is left over when it should be accounted for in the prediction. Conversely, the normal Q-Q residuals plots of the combined signal shows a good fit of the normality assumption, especially for the 1-step forecast, while slight departures from the normality in the tails is observed for 5- and 10-step forecasts (Fig. 2, bottom row). Fig. 2 - Top row: normal Q-Q plot of the residuals time series at 1-, 5-, and 10-steps for each of the 14 time series. Bottom row: normal Q-Q plot of the residuals time series at 1-, 5-, and 10-steps for the resulting combined signal.