In the validation stage, RMSE and MASE were equal to 1.0 and 0.68, respectively, which indicate a satisfactory performance and that the forecast model is superior to a random walk \((MASE<1)\)
With the R/S method, the Hurst exponent (H )  was found to be greater than 0.6 in both the whole series (0.611) and the sub-set 1901-2014 (0.743), which is around the threshold of 0.65 used by \citet*{k2004} to identify series than can be predicted accurately. In the case of variance of residuals, we have a situation in which obtained results are hard for interpretation. For the whole of the series, the result \((H<0.380)\) is contradictory to our finding that the Hurst exponent is \(>0.5\) with R/S method and variance of residuals method in the sub-set 1901-2014 (0.611 and 0.550, respectively). With an increase of the number of series terms (amount of observations), the Hurst exponent is expected to get closer to 0 \citep*{Kaklauskas2013}, i.e. the memory effect decreases. However, with the variance residuals method, the estimated Hurst exponent moves away from 0.5 \((H=0.38)\) with the whole of the time series. These contradictory results can be reconciled by considering that a complex concept such PDSI is hardly captured by one metric, the Hurst exponent, which (depending on the estimation method used) may not reflect the changes of heading direction \citep{Dotov2016}. Indeed, the whole of the series (Fig. \ref{div-677474}a) shows frequent and sudden pulses of drought, with a change-point in 1917, as identified by the Buishand test \citep{Buishand1982}, observed in coincidence with the early 20th century pluvial centered on 1915\citep{Cook2007}, which has received much attention in the western U.S. \citep{Woodhouse2005}. By combining these results, it can be stated that the California’s PDSI series is related with either a short-range \((H<0.5)\) or a long-range \((H>0.5)\) memory (in turn reflecting influences on the occurrence of droughts of both large-scale and small-scale climate systems), which assumes that some dependence structure exists that advocates the foreseeability of the series. We thus performed our forecasting analysis on the original time series of PDSI data.