Overview

Most of the time series analysis methods applied today rely heavily on the key assumptions of linearity, Gaussianity and stationarity. Natural time series, including hydrologic, climatic and environmental time series, which satisfy these assumptions seem to be the exception rather than the rule. Nevertheless, most time series analysis is performed using standard methods after relaxing the required conditions one way or another, in the hope that the departure from these assumptions is not large enough to affect the result of the analysis. A large amount of data is available today after almost a century of intensive data collection of various natural time series. In addition to a few older data series such as sunspot numbers, sea surface temperatures, and so on, data obtained through dating techniques (tree-ring data, ice core data, geological and marine deposits) are available. With the advent of powerful computers, the use of simplified methods can no longer be justified, especially with the limited success of those methods in explaining the inherent variability in natural time series. This study presents a number of techniques that have been discussed in the literature during the 1980s and 1990s 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.

Full Product Details

Author:   A.R. Rao ,  K.H. Hamed ,  Huey-Long Chen
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   2003 ed.
Volume:   45
Dimensions:   Width: 15.50cm , Height: 2.20cm , Length: 23.50cm
Weight:   0.834kg
ISBN:  

9781402012976

ISBN 10:   1402012977
Pages:   365
Publication Date:   31 July 2003
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   Awaiting stock  
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Table of Contents

1. 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.

Reviews

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)

From the reviews: <p> 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. a ] this book is well organized and easy to read a ] . A clear distinction is made between processes with discrete, continuous, and mixed spectra a ] . Nonstationarities in Hydrologic and Environmental Time Series addresses a number of important issues and ideas a ] . (Adam Monahan, Bulletin of the American Meteorological Society, March, 2005)

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)

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