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Spectral Analysis and Its Applications, by Gwilym M. Jenkins, Donald G. Watts
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- Sales Rank: #1677126 in Books
- Published on: 1968-06
- Ingredients: Example Ingredients
- Original language: English
- Number of items: 1
- Binding: Hardcover
- 541 pages
Most helpful customer reviews
0 of 0 people found the following review helpful.
One of the two best texts on spectral theory
By Ross S. Bowden
After seven years of study in the area, I have concluded that Jenkins and Watts text , together with Priestley's book, is the best available reference on spectral theory and its applications. J&W is clear in its explanations and provides a thorough background in the subject. In both the discrete and continuous domain, it covers time series models, their associated spectral theory and the estimation of spectra. It is not an introductory text and would be best suited for post-graduate study. I have no hesitation in recommending both J&W and P as outstanding guides to frequency-based time series analysis. As time series researchers we are fortunate to have such outstanding books available for studying such a difficult area of statistics.
4 of 4 people found the following review helpful.
The best resource for spectral analysis, 44 years and counting
By Harmon
Even though this book was published in 1968, it is still the authority on spectral analysis.
Written primarily as a post-grad text, this is the most complete resource I have found that deals with how to actually connect theory and practice. Though it is a difficult read, it is complete, well organized, builds from first principles, and is consistent in notation. The text is fairly accessible if you have a strong background in elementary statistics and Fourier theory. (If not, these items are reviewed in chapters 2-4)
To illustrate the practicality of spectral analysis in engineering problems, Jenkins writes, "...Weiner theory of prediction and control shows that an optimum filter or control system can be designed if various spectra associated with the signal and the noise in the system are known. However, little attention is paid in books on control theory to the very important practical question of how to estimate these spectra from finite lengths of record. It is with such problems that we shall be concerned in this book."
An abbreviated TOC includes:
Ch 1 > Aims and means in Time Series Analysis
Ch 2 > Fourier Analysis (in great detail for continuous, discrete, periodic, and aperiodic data)
Ch 3 > Probability Theory (Distributions, moments, random variables)
Ch 4 > Introduction to Statistical Inference (Confidence intervals, maximum likelihood, least squares theory)
Ch 5 > Introduction to Time Series Analysis
- Stationarity, ergodicity
- Autocorrelation, autocovariance
- Estimation of autocovariance functions
- Parametric modeling
Ch 6 > The Spectrum
- The sample spectrum
- Spectrum from sample autocovariance function
- Spectra from white noise process and linear process
- Smoothing spectral estimates
- Confidence intervals for spectral estimates
- Data windows
- Bandwidth of a spectral window
Ch 7 > Examples of Univariate Spectral Analysis
- Effect of bandwidth on smoothing
- Effect of data window on smoothing
- Optimal smoothing
- Digital filtering
- Model building
- Frequency response studies
Ch 8 > The Cross Correlation Function and Cross Spectrum
- Cross-covariance function
- Bivariate linear process
- The sample cross-covariance function
- The sample cross spectrum
- Quadrature spectra
- Cospectra
- Squared coherency spectrum
Ch 9 > Estimation of Cross Spectra
- Properties of smoothed estimators
- Confidence intervals
- Discrete formulation
- Practical aspects of sample cross-spectra
Ch 10 > Estimation of Frequency Response Functions
- Impulse response functions
- Direct and parametric methods
- Gain and phase estimators
- Least squares in the frequency domain
- Smoothing estimates
- Confidence Intervals
- Practical procedure for estimating FRF's
Ch 11 > Multivariate Spectral Analysis
- The Covariance matrix
- The Spectral matrix
- Multivariate linear systems
- Multiple regression
- Multiple correlation
- Partial correlation
- Partial cross, squared coherency, and phase spectra
- Multivariate frequency response
- Discrete estimation formulae
10 of 11 people found the following review helpful.
Wish I'd bought it sooner
By jim humphries
Spectral Analysis and Its Applications is an excellent source for professionals with intermediate time-series statistics skills. It clearly outlines and demonstrates the methods necessary to carry out sound spectral analysis of time-series data and how to use this data for modelling purposes. It is also a great aid and reference for anyone who needs the means to triumph over inexperience and under-education in time-series debates. Four years out of graduate school, I need this book again; I wish I'd bought it sooner.
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