Nonstationarities in Hydrologic and Environmental Time Series

ISBN-13: 9789401039796 / Angielski / Miękka / 2012 / 365 str.

A.R. Rao;K.H. Hamed;Huey-Long Chen

Opis

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.

Recenzje

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)

Spis treści

1. Introduction.- 2. Data Used in the Book.- 2.1. Hydrologic and Climatic Data.- 2.2. Synthetic and Observed Environmental Data.- 2.2.1. Synthetic Data Sampling from Batchelor Spectrum.- 2.2.2. Details of Data Generated by Sampling from the Batchelor Spectrum.- 2.2.3. Synthetic Data from AR Model.- 2.3. Observed Data.- 2.3.1. Measured Temperature Gradient Profiles.- 3. Time Domain Analysis.- 3.1. Introduction.- 3.2. Visual Inspection of Time Series.- 3.3. Statistical Tests of Significance.- 3.3.1. Parametric Tests.- 3.3.2. Non-parametric Tests.- 3.4. Testing Autocorrelated Data.- 3.5. Application of Trend Tests to Hydrologic Data.- 3.5.1. Visual Inspection of Data.- 3.5.2. Statistical Trend Tests.- 3.5.3. Sub-period Trend Analysis.- 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.- 4.5.1. Results from MEM Analysis.- 4.5.2. Results from MTM Analysis.- 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.- 7.2.1. Test 1 (de Souza and Thomson, 1982).- 7.2.2. Test 2 (Imberger and Ivey, 1991).- 7.2.3. Test 3 (Davis, Huang and Yao, 1995).- 7.2.4. Test 4 (Tsay, 1988).- 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.- 7.6.1. Detection results for synthetic series from model 2.1.2.- 7.6.2. Detection results for synthetic series from model 2.1.3.- 7.6.3. Detection results for synthetic series from model 2.1.4.- 7.6.4. Detection results for synthetic series from model 2.1.5.- 7.6.5. Conclusions on performances of tests 1–5.- 7.7. Performances of algorithms with and without boundary optimization.- 7.7.1. Detection of non-stationary segment.- 7.7.2. Detection of multi-segment series.- 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.- 8.5.1. Batchelor curve fitting using the first error function.- 8.5.2. Batchelor curve fitting using the second error function.- 8.5.3. Batchelor curve fitting using the third error function.- 8.6. Conclusions on Batchelor curve fitting.- 9. Segmentation of Observed Data.- 9.1. Introduction.- 9.2. Temperature Gradient Profiles.- 9.2.1. Ratios of Unresolved, Bad-Fit and Good-Fit Segments.- 9.2.2. Estimated Values of ? and XT from Resolved Spectra.- 9.2.3. Estimated Values of ? and XT from Profiles in the Same Lake.- 9.2.4. Estimated Values of ? and XT from Different Lakes.- 9.3. Conclusions on Segmentation of Temperature Gradient Profiles.- 9.4. Hydrologic Series.- 9.4.1. Stationary Segments from Hydrologic Series.- 9.4.2. Change Points in 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.- 10.3.1. Testing Temperature Gradient Profiles.- 10.3.2. Testing Hydrologic Series.- 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.- 11.3.1. Theory.- 11.3.1.1. Parameters of the distribution and the change point n1.- 11.3.1.2. The Unconditional Posterior Distributions of ?, ? and ?.- 11.3.1.3. The Conditional Posterior Distributions of ?i, ?21 and ?i.- 11.3.2. Computation Sequences.- 11.4. Discussion of Results.- 11.4.1. The Posterior Distribution of the Change point n1.- 11.4.2. The Unconditional Posterior Distributions of ?, ? and ?.- 11.4.3. The Conditional Posterior Distributions of ?i,?2i and ?i.- 11.5. Conclusions.- 12. References.- 13. Index.