A forecast based on a systematic statistical
examination of data representing past observed behavior of the system to be forecast, including observations of useful predictors outside the system.
In short-term climate
forecasting, CCA (canonical correlation
analysis), as described by Barnston (1994), is a good example of a statistical forecast. Depending on method and scope, the limitations of statistical forecasts are related to shortness of record, danger of overfitting, assumptions of linearity
(often), absence (often) of physical considerations, etc. Purely statistical forecasts in weather forecasting have become rare; however, a combination of dynamical model
output and statistics
is very common in weather forecasting. Some statistical methods are guided by physical principles to such an extent that they resemble dynamical models. An example of the latter is empirical wave propagation
described by Qin and van den Dool (1996). See perfect prognosis method
Barnston, A. 1994. Linear statistical short-term climate predictive skill in the Northern Hemisphere. J. Climate. 7. 1513–1564.
Qin, J., and H. M. van den Dool 1996. Simple extensions of an NWP model. Mon. Wea. Rev.. 124. 277–287.
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