Abstract
The Kolmogorov–Wiener theory of extrapolation of stationary random processes (KWT) has been created about 80 years ago. The theory proves that no linear method of extrapolation (prediction, forecasting) can be better than what is possible to achieve through KWT. If the time series is Gaussian (which happens in climatology and geophysics in general), the KWT is the best possible solution for time series forecasting, be it linear or nonlinear. Any method of statistical forecasting must be tested against KWT which is never done in geophysics and solar research because KWT is not known in Earth and solar sciences. This chapter contains a brief description of KWT, a proof of its efficiency, and examples of its application with climatic and meteorological time series having different predictability properties. The examples include the annual global surface temperature, QBO, oceanic and atmospheric components of ENSO, and MJO. The high efficiency of KWT is demonstrated with QBO and MJO, while the extrapolation of global annual temperature may be acceptable for up to 5–7 years if its trend is regarded as a nature-caused factor. The example with the oceanic component of ENSO is successful for at least eight months. Variations of SOI are unpredictable.
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Privalsky, V. (2021). Statistical Forecasting of Geophysical Processes. In: Time Series Analysis in Climatology and Related Sciences. Progress in Geophysics. Springer, Cham. https://doi.org/10.1007/978-3-030-58055-1_6
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