Nonstationarities in Hydrologic and Environmental Time Series

Conventionally, time series have been studied either in the time domain or the frequency domain. The representation of a signal in the time domain is localized in time, i.e . the value of the signal at each instant in time is well defined . However, the time representation of a signal is poorly localized in frequency , i.e. little information about the frequency content of the signal at a certain frequency can be known by looking at the signal in the time domain . On the other hand, the representation of a signal in the frequency domain is well localized in frequency, but is poorly localized in time, and as a consequence it is impossible to tell when certain events occurred in time. In studying stationary or conditionally stationary processes with mixed spectra , the separate use of time domain and frequency domain analyses is sufficient to reveal the structure of the process . Results discussed in the previous chapters suggest that the time series analyzed in this book are conditionally stationary processes with mixed spectra. Additionally, there is some indication of nonstationarity, especially in longer time series.

From the reviews:

"The authors consider a number of modern statistical tests of nonstationarity, including trend analysis, multitaper method and maximum entropy spectral analysis, evolutionary spectral analysis, wavelet analysis, and series segmentation through change point detection. ... this book is well organized and easy to read ... . A clear distinction is made between processes with discrete, continuous, and mixed spectra ... . Nonstationarities in Hydrologic and Environmental Time Series addresses a number of important issues and ideas ... ." (Adam Monahan, Bulletin of the American Meteorological Society, March, 2005)