Spectral Analysis for Univariate Time Series 2nd Edition by Donald 1108776175 9781108776172

Spectral Analysis for Univariate Time Series 2nd Edition by Donald Percival – Ebook Instant Download/Delivery ISBN(s): 1108776175, 9781108776172

Product details:

• ISBN 10: 1108776175
• ISBN 13: 9781108776172
• Author: Donald 

Spectral analysis is widely used to interpret time series collected in diverse areas. This book covers the statistical theory behind spectral analysis and provides data analysts with the tools needed to transition theory into practice. Actual time series from oceanography, metrology, atmospheric science and other areas are used in running examples throughout, to allow clear comparison of how the various methods address questions of interest. All major nonparametric and parametric spectral analysis techniques are discussed, with emphasis on the multitaper method, both in its original formulation involving Slepian tapers and in a popular alternative using sinusoidal tapers. The authors take a unified approach to quantifying the bandwidth of different nonparametric spectral estimates. An extensive set of exercises allows readers to test their understanding of theory and practical analysis. The time series used as examples and R language code for recreating the analyses of the series are available from the book’s website.

Table of contents:

1. 1 Introduction to Spectral Analysis
2. 1.0 Introduction
3. 1.1 Some Aspects of Time Series Analysis
4. Comments and Extensions to Section 1.1
5. 1.2 Spectral Analysis for a Simple Time Series Model
6. 1.3 Nonparametric Estimation of the Spectrum from Data
7. 1.4 Parametric Estimation of the Spectrum from Data
8. 1.5 Uses of Spectral Analysis
9. 1.6 Exercises
10. 2 Stationary Stochastic Processes
11. 2.0 Introduction
12. 2.1 Stochastic Processes
13. 2.2 Notation
14. 2.3 Basic Theory for Stochastic Processes
15. Comments and Extensions to Section 2.3
16. 2.4 Real-Valued Stationary Processes
17. 2.5 Complex-Valued Stationary Processes
18. Comments and Extensions to Section 2.5
19. 2.6 Examples of Discrete Parameter Stationary Processes
20. 2.7 Comments on Continuous Parameter Processes
21. 2.8 Use of Stationary Processes as Models for Data
22. 2.9 Exercises
23. 3 Deterministic Spectral Analysis
24. 3.0 Introduction
25. 3.1 Fourier Theory – Continuous Time/Discrete Frequency
26. Comments and Extensions to Section 3.1
27. 3.2 Fourier Theory – Continuous Time and Frequency
28. Comments and Extensions to Section 3.2
29. 3.3 Band-Limited and Time-Limited Functions
30. 3.4 Continuous/Continuous Reciprocity Relationships
31. 3.5 Concentration Problem – Continuous/Continuous Case
32. 3.6 Convolution Theorem – Continuous Time and Frequency
33. 3.7 Autocorrelations andWidths – Continuous Time and Frequency
34. 3.8 Fourier Theory – Discrete Time/Continuous Frequency
35. 3.9 Aliasing Problem – Discrete Time/Continuous Frequency
36. Comments and Extensions to Section 3.9
37. 3.10 Concentration Problem – Discrete/Continuous Case
38. 3.11 Fourier Theory – Discrete Time and Frequency
39. Comments and Extensions to Section 3.11
40. 3.12 Summary of Fourier Theory
41. 3.13 Exercises
42. 4 Foundations for Stochastic Spectral Analysis
43. 4.0 Introduction
44. 4.1 Spectral Representation of Stationary Processes
45. Comments and Extensions to Section 4.1
46. 4.2 Alternative Definitions for the Spectral Density Function
47. 4.3 Basic Properties of the Spectrum
48. Comments and Extensions to Section 4.3
49. 4.4 Classification of Spectra
50. 4.5 Sampling and Aliasing
51. Comments and Extensions to Section 4.5
52. 4.6 Comparison of SDFs and ACVSs as Characterizations
53. 4.7 Summary of Foundations for Stochastic Spectral Analysis
54. 4.8 Exercises
55. 5 Linear Time-Invariant Filters
56. 5.0 Introduction
57. 5.1 Basic Theory of LTI Analog Filters
58. Comments and Extensions to Section 5.1
59. 5.2 Basic Theory of LTI Digital Filters
60. Comments and Extensions to Section 5.2
61. 5.3 Convolution as an LTI Filter
62. 5.4 Determination of SDFs by LTI Digital Filtering
63. 5.5 Some Filter Terminology
64. 5.6 Interpretation of Spectrum via Band-Pass Filtering
65. 5.7 An Example of LTI Digital Filtering
66. Comments and Extensions to Section 5.7
67. 5.8 Least Squares Filter Design
68. 5.9 Use of Slepian Sequences in Low-Pass Filter Design
69. 5.10 Exercises
70. 6 Periodogram and Other Direct Spectral Estimators
71. 6.0 Introduction
72. 6.1 Estimation of the Mean
73. Comments and Extensions to Section 6.1
74. 6.2 Estimation of the Autocovariance Sequence
75. Comments and Extensions to Section 6.2
76. 6.3 A Naive Spectral Estimator – the Periodogram
77. Comments and Extensions to Section 6.3
78. 6.4 Bias Reduction – Tapering
79. Comments and Extensions to Section 6.4
80. 6.5 Bias Reduction – Prewhitening
81. Comments and Extensions to Section 6.5
82. 6.6 Statistical Properties of Direct Spectral Estimators
83. Comments and Extensions to Section 6.6
84. 6.7 Computational Details
85. 6.8 Examples of Periodogram and Other Direct Spectral Estimators
86. Comments and Extensions to Section 6.8
87. 6.9 Comments on Complex-Valued Time Series
88. 6.10 Summary of Periodogram and Other Direct Spectral Estimators
89. 6.11 Exercises
90. 7 Lag Window Spectral Estimators
91. 7.0 Introduction
92. 7.1 Smoothing Direct Spectral Estimators
93. Comments and Extensions to Section 7.1
94. 7.2 First-Moment Properties of Lag Window Estimators
95. Comments and Extensions to Section 7.2
96. 7.3 Second-Moment Properties of LagWindow Estimators
97. Comments and Extensions to Section 7.3
98. 7.4 Asymptotic Distribution of LagWindow Estimators
99. 7.5 Examples of Lag Windows
100. Comments and Extensions to Section 7.5
101. 7.6 Choice of Lag Window
102. Comments and Extensions to Section 7.6
103. 7.7 Choice of LagWindow Parameter
104. Comments and Extensions to Section 7.7
105. 7.8 Estimation of Spectral Bandwidth
106. 7.9 Automatic Smoothing of Log Spectral Estimators
107. Comments and Extensions to Section 7.9
108. 7.10 Bandwidth Selection for Periodogram Smoothing
109. Comments and Extensions to Section 7.10
110. 7.11 Computational Details
111. 7.12 Examples of Lag Window Spectral Estimators
112. Comments and Extensions to Section 7.12
113. 7.13 Summary of Lag Window Spectral Estimators
114. 7.14 Exercises
115. 8 Combining Direct Spectral Estimators
116. 8.0 Introduction
117. 8.1 Multitaper Spectral Estimators – Overview
118. Comments and Extensions to Section 8.1
119. 8.2 Slepian Multitaper Estimators
120. Comments and Extensions to Section 8.2
121. 8.3 Multitapering of Gaussian White Noise
122. 8.4 Quadratic Spectral Estimators and Multitapering
123. Comments and Extensions to Section 8.4
124. 8.5 Regularization and Multitapering
125. Comments and Extensions to Section 8.5
126. 8.6 Sinusoidal Multitaper Estimators
127. Comments and Extensions to Section 8.6
128. 8.7 Improving Periodogram-Based Methodology via Multitapering
129. Comments and Extensions to Section 8.7
130. 8.8 Welch’s Overlapped Segment Averaging (WOSA)
131. Comments and Extensions to Section 8.8
132. 8.9 Examples of Multitaper andWOSA Spectral Estimators
133. 8.10 Summary of Combining Direct Spectral Estimators
134. 8.11 Exercises
135. 9 Parametric Spectral Estimators
136. 9.0 Introduction
137. 9.1 Notation
138. 9.2 The Autoregressive Model
139. Comments and Extensions to Section 9.2
140. 9.3 The Yule–Walker Equations
141. Comments and Extensions to Section 9.3
143. 10 Harmonic Analysis
144. 11 Simulation of Time Series

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