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)

Autorentext

I. GENERAL INFORMATION Name: A. Ramachandra Rao Date of Birth: 23 October 1939 Academic Record School Attended Degree Date University of Illinois 1964-68 Ph.D. 1968 University of Minnesota 1962-64 M.S.C.E. 1964 University of Mysore (India) 1956-60 B.E. 1960 1. Professional Experience: Employer Position Date University of Mysore Lecturer in Civil 1960-62 (India) Engineering University of Minnesota Research Assistant 1962-64 University of Illinois Research Assistant 1964-68 Purdue University Visiting Assistant 1968-70 Professor Purdue University Assistant Professor 1970-73 Govt. of New Zealand NRAC Senior Research Fellow 1977-78 Purdue University Associate Professor 1973-80 Purdue University Professor 1980- Construction Engineering Visiting Faculty May-July, 1983 Research Laboratory Member 1983 Purdue University Acting Head, Hydraulics 1983-84 and Systems Engineering Area Indian Institute of Science, Visiting Professor of Jan-July, Bangalore, India Civil Engineering 1989 University of Illinois, Visiting Professor of Jan-May Urbana, IL Civil Engineering 1998 2. Awards, Honors, Citations Awarded a Senior Research Fellowship by the National Research Advisory Council, Government of New Zealand, for research in hydrology with the Ministry of Works and Development during 1977-78. Awarded (but not accepted) a "Senior Scientist Fellowship" by the Alexander Von Humboldt Foundation, West Germany (1977). Awarded (but not accepted) the "C.H. Munro Fellowship" of the Water Research Foundation of Australia, for research in Hydrology, at Monash University, Clayton, Victoria, Australia (1977). Honorary Societies Member, Chi Epsilon, Sigma Xi Citations American Men and Women of Science Who's Who inthe Midwest Who's Who in Frontier Science and Technology Who's Who in Science and Engineering Who's Who, Environmental Registry Who's Who in the World Who's Who in American Education Invited Activities and Lectures Invited by UNESCO to attend the "International Symposium on Hydrologic Aspects of Droughts", New Delhi, 3-8 December 1979. Member, American Delegation to the XVIII General Assembly, IUGG, Hamburg, Federal Republic of Germany, August 15-27, 1983. Invited Specialist, IAWPRC Seminar on "Rainfall as the Basis for Urban Runoff Design and Analysis", Technical University of Denmark, Lyngby, Denmark, August 24-26, 1983. Invited lecture, "Detection of Climatic Changes in Hydrologic Time Series". Eighth IHD Endowment Lecture, Anna University, Madras, India, April 13, 1989. Keynote lecture, "Bayesian Unit Hydrographs" International Conference on Hydrology and Water Resources, Delhi, India, December, 1993. Member, Editorial Board of "Water Science and Technology Library", Kluwer Academic Publishers B.V. Dordrecht, The Netherlands, (1993-99). Editor, "Journal of Irrigation and Drainage Engineering", ASCE, 1992 - 1998. Keynote lecture, "Bayesian Unit Hydrographs" International Conference on Hydrology and Water Resources, Delhi, India, December, 1993. Founder/honorary member, "Center of Resource Management and Eco-development Studies", I.I.T., Delhi, 1994. Fellow, Indian Association of Hydrologists. "Edmund M. Burke Outstanding Civil Engineering Professor", School of Civil Engineering, Purdue University, April 1995. Invited paper, "Principal Component Analysis of Hydrologic Data", A.R. Rao and T.T. Burke, Jr., NATO Advanced Research Workshop on "Integrated Approach to Environmental Data Systems", Izmir, Turkey, Sept. 16-20, 1996. Invited to deliver a keynote paper in the International Symposium on "Emerging Trends inHydrology", Department of Hydrology, University of Roorkee, India, Sept. 25-27, 1997. tßp, Dean Marion B. Scott 1997 Exemplary Character Award, Purdue University. Invited speaker, Int. Conference on Water, Environment, Ecology, Socio-Economics and Health Engineering, Seoul National University, Seoul, Korea, Oct. 18-21, 1999. Invited speaker, Int. Conference on Integrated Water Resources

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

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. Est…