Summary and Recommendations

Abstract

Climatology and related geophysical and solar sciences have been going for decades through a crisis in research involving mathematical statistics and time series analysis. Mathematical statistics is improperly applied in studies that require the use of time series analysis (exploring multivariate time series in time and frequency domains) and not applied where it is necessary (probability density functions, confidence bounds for estimated statistical characteristics with account for correlation structure of the time series). Time series are erroneously treated as random vectors though random vectors do not have correlation functions and spectra, PDFs are rarely analyzed, reliability of estimates is assessed without taking into account serial correlation within the time series, estimates of statistics are given without confidence bounds, an incorrect test is applied to assess significance of spectral peaks. Studies of teleconnections are based upon improper estimates of cross-correlation coefficients while time series reconstructions, first of all, reconstructions of climate, use the cross-correlation coefficients and regression equations which are not applicable to time series. The classical theory of extrapolation by Kolmogorov and Wiener is not known. This book provides many examples, and this chapter sums up practical recommendations helping to properly analyze and forecast scalar and multivariate time series.