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Time Series with Mixed Spectra [Kõva köide]

3.00/5 (2 hinnangut Goodreads-ist)
(IBM Watson Research Center, Yorktown Heights, New York, USA)
  • Formaat: Hardback, 680 pages, kõrgus x laius: 234x156 mm, kaal: 1420 g, 19 Tables, black and white; 105 Illustrations, black and white
  • Ilmumisaeg: 18-Jul-2013
  • Kirjastus: Chapman & Hall/CRC
  • ISBN-10: 1584881763
  • ISBN-13: 9781584881766
Teised raamatud teemal:
Time Series with Mixed SpectraSuurem pilt
  • Formaat: Hardback, 680 pages, kõrgus x laius: 234x156 mm, kaal: 1420 g, 19 Tables, black and white; 105 Illustrations, black and white
  • Ilmumisaeg: 18-Jul-2013
  • Kirjastus: Chapman & Hall/CRC
  • ISBN-10: 1584881763
  • ISBN-13: 9781584881766
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781584881766.html
Märksõnad:

Time series with mixed spectra are characterized by hidden periodic components buried in random noise. Despite strong interest in the statistical and signal processing communities, no book offers a comprehensive and up-to-date treatment of the subject. Filling this void, Time Series with Mixed Spectra focuses on the methods and theory for the statistical analysis of time series with mixed spectra. It presents detailed theoretical and empirical analyses of important methods and algorithms.

Using both simulated and real-world data to illustrate the analyses, the book discusses periodogram analysis, autoregression, maximum likelihood, and covariance analysis. It considers real- and complex-valued time series, with and without the Gaussian assumption. The author also includes the most recent results on the Laplace and quantile periodograms as extensions of the traditional periodogram.

Complete in breadth and depth, this book explains how to perform the spectral analysis of time series data to detect and estimate the hidden periodicities represented by the sinusoidal functions. The book not only extends results from the existing literature but also contains original material, including the asymptotic theory for closely spaced frequencies and the proof of asymptotic normality of the nonlinear least-absolute-deviations frequency estimator.

Arvustused

"It masterfully integrates the most significant advances in the literature." Journal of the American Statistical Association

" an excellent introduction and overview of the literature dealing with statistical inference on time-series involving sinusoids. It will be an indispensable reference that research workers and graduate students of allied fields will rely on in the future." Mathematical Reviews, January 2015

"It is extremely thorough in its approach. Every term is carefully defined, and many proofs are given in elaborate detail. The range of problems and methods considered in the book is extensive." Journal of Time Series Analysis, 2015

Preface ix
1 Introduction
1(12)
1.1 Periodicity and Sinusoidal Functions
1(2)
1.2 Sampling and Aliasing
3(1)
1.3 Time Series with Mixed Spectra
4(3)
1.4 Complex Time Series with Mixed Spectra
7(6)
2 Basic Concepts
13(24)
2.1 Parameterization of Sinusoids
13(5)
2.2 Spectral Analysis of Stationary Processes
18(5)
2.3 Gaussian Processes and White Noise
23(5)
2.4 Linear Prediction Theory
28(3)
2.5 Asymptotic Statistical Theory
31(6)
3 Cramer-Rao Lower Bound
37(38)
3.1 Cramer-Rao Inequality
37(3)
3.2 CRLB for Sinusoids in Gaussian Noise
40(7)
3.3 Asymptotic CRLB for Sinusoids in Gaussian Noise
47(11)
3.4 CRLB for Sinusoids in NonGaussian White Noise
58(6)
3.5 Proof of Theorems
64(11)
4 Autocovariance Function
75(36)
4.1 Autocovariances and Autocorrelation Coefficients
75(2)
4.2 Consistency and Asymptotic Unbiasedness
77(3)
4.3 Covariances and Asymptotic Normality
80(10)
4.4 Autocovariances of Filtered Time Series
90(1)
4.5 Proof of Theorems
91(20)
5 Linear Regression Analysis
111(56)
5.1 Least Squares Estimation
111(9)
5.2 Sensitivity to Frequency Offset
120(2)
5.3 Frequency Identification
122(4)
5.4 Frequency Selection
126(10)
5.5 Least Absolute Deviations Estimation
136(11)
5.6 Proof of Theorems
147(20)
6 Fourier Analysis Approach
167(86)
6.1 Periodogram Analysis
167(17)
6.2 Detection of Hidden Sinusoids
184(10)
6.3 Extension of the Periodogram
194(14)
6.3.1 Sinusoids with NonFourier Frequencies
194(3)
6.3.2 Refined Periodogram
197(4)
6.3.3 Secondary Analysis
201(3)
6.3.4 Interpolation Estimators
204(4)
6.4 Continuous Periodogram
208(17)
6.4.1 Statistical Properties
208(2)
6.4.2 Periodogram Maximization
210(13)
6.4.3 Resolution Limit
223(2)
6.5 Time-Frequency Analysis
225(4)
6.6 Proof of Theorems
229(24)
7 Estimation of Noise Spectrum
253(58)
7.1 Estimation in the Absence of Sinusoids
253(23)
7.1.1 Periodogram Smoother
254(4)
7.1.2 Lag-Window Spectral Estimator
258(3)
7.1.3 Autoregressive Spectral Estimator
261(10)
7.1.4 Numerical Examples
271(5)
7.2 Estimation in the Presence of Sinusoids
276(14)
7.2.1 Modified Periodogram Smoother
277(2)
7.2.2 M Spectral Estimator
279(4)
7.2.3 Modified Autoregressive Spectral Estimator
283(4)
7.2.4 A Comparative Example
287(3)
7.3 Detection of Hidden Sinusoids in Colored Noise
290(6)
7.4 Proof of Theorems
296(15)
8 Maximum Likelihood Approach
311(64)
8.1 Maximum Likelihood Estimation
311(2)
8.2 Maximum Likelihood under Gaussian White Noise
313(18)
8.2.1 Multivariate Periodogram
314(8)
8.2.2 Statistical Properties
322(9)
8.3 Maximum Likelihood under Laplace White Noise
331(10)
8.3.1 Multivariate Laplace Periodogram
332(5)
8.3.2 Statistical Properties
337(4)
8.4 The Case of Gaussian Colored Noise
341(10)
8.5 Determining the Number of Sinusoids
351(4)
8.6 Proof of Theorems
355(20)
9 Autoregressive Approach
375(80)
9.1 Linear Prediction Method
375(17)
9.1.1 Linear Prediction Estimators
376(9)
9.1.2 Statistical Properties
385(7)
9.2 Autoregressive Reparameterization
392(4)
9.3 Extended Yule-Walker Method
396(8)
9.3.1 Extended Yule-Walker Estimators
397(2)
9.3.2 Statistical Properties
399(5)
9.4 Iterative Filtering Method
404(20)
9.4.1 Iterative Filtering Estimator: Complex Case
405(8)
9.4.2 Iterative Filtering Estimator: Real Case
413(11)
9.5 Iterative Quasi Gaussian Maximum Likelihood Method
424(20)
9.5.1 Iterative Generalized Least-Squares Algorithm
426(10)
9.5.2 Iterative Least-Eigenvalue Algorithm
436(6)
9.5.3 Self Initialization
442(2)
9.6 Proof of Theorems
444(11)
10 Covariance Analysis Approach
455(74)
10.1 Eigenvalue Decomposition of Covariance Matrix
455(3)
10.2 Principal Component Analysis Method
458(24)
10.2.1 Reduced Rank Autoregressive Estimators
459(13)
10.2.2 Statistical Properties
472(10)
10.3 Subspace Projection Method
482(10)
10.3.1 MUSIC and Minimum-Norm Estimators
482(7)
10.3.2 Statistical Properties
489(3)
10.4 Subspace Rotation Method
492(11)
10.4.1 Matrix-Pencil and ESPRIT Estimators
492(8)
10.4.2 Statistical Properties
500(3)
10.5 Estimating the Number of Sinusoids
503(7)
10.6 Sensitivity to Colored Noise
510(3)
10.7 Proof of Theorems
513(16)
11 Further Topics
529(38)
11.1 Single Complex Sinusoid
529(5)
11.2 Tracking Time-Varying Frequencies
534(6)
11.3 Periodic Functions in Noise
540(5)
11.4 Beyond Single Time Series
545(7)
11.5 Quantile Periodogram
552(15)
12 Appendix
567(44)
12.1 Trigonometric Series
567(6)
12.2 Probability Theory
573(2)
12.3 Numerical Analysis
575(2)
12.4 Matrix Theory
577(8)
12.5 Asymptotic Theory
585(26)
Bibliography 611(26)
Index 637
Ta-Hsin Li is a research statistician at the IBM Watson Research Center. He was previously a faculty member at Texas A&M University and the University of California, Santa Barbara. Dr. Li is a fellow of the American Statistical Association and an elected senior member of the Institute of Electrical and Electronic Engineers. He is an associate editor for the EURASIP Journal on Advances in Signal Processing, the Journal of Statistical Theory and Practice, and Technometrics. He received a Ph.D. in applied mathematics from the University of Maryland.