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)

Klappentext

This book presents a number of new techniques that have been discussed in the literature during the last two decades concerning the investigation of stationarity, linearity and Gaussianity of hydrologic and environmental times series. These techniques cover different approaches for assessing nonstationarity, ranging from time domain analysis, to frequency domain analysis, to the combined time-frequency and time-scale analyses, to segmentation analysis, in addition to formal statistical tests of linearity and Gaussianity. It is hoped that this endeavor would facilitate further research into this important area.

Inhalt

Introduction.- 2. Data Used in the Book.- 2.1. Hydrologic and Climatic Data.- 2.2. Synthetic and Observed Environmental Data.- 2.3. Observed Data.- 3. Time Domain Analysis.- 3.1. Introduction.- 3.2. Visual Inspection of Time Series.- 3.3. Statistical Tests of Significance.- 3.4. Testing Autocorrelated Data.- 3.5. Application of Trend Tests to Hydrologic Data.- 3.6. Conclusions.- 4. Frequency Domain Analysis.- 4.1. Introduction.- 4.2. Conventional Spectral Analysis.- 4.3. Multi-Taper Method (MTM) of Spectral Analysis.- 4.4. Maximum Entropy Spectral Analysis.- 4.5. Spectral Analysis of Hydrologic and Climatic Data.- 4.6. Discussion of Results.- 4.7. Conclusions.- 5. Time-Frequency Analysis.- 5.1. Introduction.- 5.2. Evolutionary Spectral Analysis.- 5.3. Evolution of Line Components in Hydrologic and Climatic Data.- 5.4. Evolution of Continuous Spectra in Hydrologic and Climatic Data.- 5.5. Conclusions.- 6. Time-Scale Analysis.- 6.1. Introduction.- 6.2. Wavelet Analysis.- 6.3. Wavelet Trend Analysis.- 6.4. Identification of Dominant Scales.- 6.5. Time-Scale Distribution.- 6.6. Behavior of Hydrologic and Climatic Time Series at Different Scales.- 6.7. Conclusions.- 7. Segmentation of Non-Stationary Time Series.- 7.1. Introduction.- 7.2. Tests based on AR Models.- 7.3. A test based on wavelet analysis.- 7.4. Segmentation algorithm.- 7.5. Variations of test statistics with the AR order p.- 7.6. Sensitivity of test statistics for detecting change points.- 7.7. Performances of algorithms with and without boundary optimization.- 7.8. Conclusions about the segmentation algorithm.- 8. Estimation of Turbulent Kinetic Energy Dissipation.- 8.1. Introduction.- 8.2. Multi-taper Spectral Estimation.- 8.3. Batchelor Curve Fitting.- 8.4. Comparison of Spectral Estimation Methods.- 8.5.Batchelor Curve Fitting to Synthetic Series.- 8.6. Conclusions on Batchelor curve fitting.- 9. Segmentation of Observed Data.- 9.1. Introduction.- 9.2. Temperature Gradient Profiles.- 9.3. Conclusions on Segmentation of Temperature Gradient Profiles.- 9.4. Hydrologic Series.- 9.5. Conclusions on Segmentation of Hydrologic Series.- 10. Linearity and Gaussianity Analysis.- 10.1. Introduction.- 10.2. Tests for Gaussianity and Linearity (Hinich, 1982).- 10.3. Testing for Stationary Segments.- 10.4. Conclusions about Testing the Hydrologic Series.- 11. Bayesian Detection of Shifts in Hydrologic Time Series.- 11.1. Introduction.- 11.2. Data Used in this Chapter.- 11.3. A Bayesian Method to Detect Shifts in Data.- 11.4. Discussion of Results.- 11.5. Conclusions.- 12. References.- 13. Index.