Extrapolation suffers when a time series is subject to shocks or discontinuities. Few extrapolation methods account for discontinuities (Collopy and Armstrong, 1992). Instead, when discontinuities occur, extrapolation may lead to large forecast errors. For example, ENSO and Pacifical Decadal Oscillation can lead to experience a strong upward or downward trend of drought (Colet et al., 2002). According with Sheffield and Wood (2008), it is plausible that thermal impacts on drought frequency at in the long term are likely to dominate precipitation changes. We could thus expect a monotonic and positive temperature change with increasing drought frequency across a range of drought metrics by the late 21st century. However, the future direction of PDSI series remains uncertain, because uncertain is the direction of its causal forces (temperature and precipitation). This is a challenge in PDSI future extrapolation.
Our empirical forecasts are in agreement with \citet*{Esfahani2014}, whose forecasts suggest the likelihood for the current moderate drought in California to shift to a mid-range condition in 2020 and a constant level of PDSI towards 2060. These authors advocate that California might have reached its equilibrium, the end of a long-memory process, which would be an exception in southwestern U.S., where PDSI would increase.