3. Results
3.1 Data analysis
The first step in any time-series analysis and forecasting is to plot the observations against time, to gain an insight into possible trends and/or cycles associated with the temporal evolution of datasets. For our PDSI time series, Fig. 2a shows that the series presents important interannual and decadal variability, with smooth changes in its structure and turning points which help in orienting the choice of the most appropriate forecasting method (after Chatfield, 2000).
The whole of the PDSI time series (214 years of data from 1801 to 2014) was segregated into sub-sets for the purposes of training and validation (Fig. 2a). Forecasts were performed for the 60-year follow-up period (Fig. 2b). Alternative initial conditions were simulated for each run, taking periods with a different start year (in 10-year steps-up from year 1801 to 1900) and periodical cycles (41, 42 and 43) for model training (training datasets).
For 1954-2014 (Fig. 2b), the simulation results for validation testing are quite promising, judging by the closeness of ensemble prediction (red curve) to the observed 11-year Gaussian Filter (black curve) PDSI evolution.