Drought early warning requires both a sound description of past droughts and an honest estimate of how far ahead they can be predicted. This study used 108 years (1900–2007) of monthly climatic water balance (precipitation minus potential evapotranspiration) at eleven locations, from arid Lahore and Kimberley to humid Abashiri and São Paulo. The Standardized Precipitation Evapotranspiration Index (SPEI) was computed at 1-, 3- and 12-month scales with a Python implementation that reproduced the reference R package to within 10⁻¹². Run theory, the modified Mann–Kendall test and the Pettitt test were applied, and one- and three-month-ahead forecasts of SPEI-3 and SPEI-12 from ARIMA, support vector regression (SVR), XGBoost and a long short-term memory (LSTM) network were compared with persistence and climatology benchmarks for 1980–2007, with the SPEI distribution fitted to 1900–1979 only. Annual SPEI-12 decreased significantly at ten of the eleven sites (Sen slopes −0.08 to −0.17 per decade), with change points between 1932 and 1977. The number of SPEI-3 drought events rose from 414 in 1900–1953 to 687 in 1954–2007. Relative to the reference climate, the test period was markedly drier: SPEI-12 was below −1 in 18–67% of months, against 14–19% before 1980. At a one-month lead, SVR forecast SPEI-3 best (mean NSE = 0.65, critical success index 0.55), followed by LSTM (0.62) and ARIMA (0.52), and was significantly better than ARIMA at ten sites. For SPEI-12, the overlap of the accumulation windows made persistence hard to beat (NSE = 0.84 at a one-month lead), and LSTM gave the largest gain at a three-month lead (NSE = 0.59 vs. 0.51; skill score +17%). No model forecast SPEI-3 three months ahead (NSE < 0). Forecast skill at monthly scales therefore comes mainly from the memory built into the index, and ML models add modest but consistent value only when this memory is partial.