Statistical analysis of stationary time series
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| Hauptverfasser: | , |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York
Wiley
1966
Stockholm Almqvist & Wiksell |
| Ausgabe: | 2. print. |
| Schriftenreihe: | Wiley series in probability and mathematical statistics
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
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Datensatz im Suchindex
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| adam_text | Titel: Statistical analysis of stationary time series
Autor: Grenander, Ulf
Jahr: 1966
CONTENTS Chapter 1. Stationary Stochastic Processes and Their Representations 1.0 Introduction....................21 1.1 What Is a Stochastic Process?.............21 1.2 Continuity in the Mean................24 1.3 Stochastic Set Functions of Orthogonal Increments. ... 25 1.4 Orthogonal Representations of Stochastic Processes ... 27 1.5 Stationary Processes.................29 1.6 Representations of Stationary Processes........33 1.7 Time and Ensemble Averages.............42 1.8 Vector Processes...................44 1.9 Operations on Stationary Processes...........49 1.10 Harmonizable Stochastic Processes...........59 Chapter 2. Statistical Questions when the Spectrum is Known (Least Squares Theory) 2.0 Introduction.................... 61 2.1 Preliminaries....................61 2.2 Prediction.....................65 2.3 Interpolation.................... 82 2.4 Filtering of Stationary Processes............85 2.5 Treatment of Linear Hypotheses with Specified Spectrum. 86 Chapter 3. Statistical Analysis of Parametric Models 3.0 Introduction.................... 91 3.1 Periodogram Analysis................91 3.2 The Variate Difference Method............94 3.3 Effect of Smoothing of Time Series (Slutzky’s Theorem) . 95 3.4 Serial Correlation Coefficients for Normal White Noise . . 97 3.5 Approximate Distributions of Quadratic Forms.....101 3.6 Testing Autoregressive Schemes and Moving Averages . . 106 3.7 Estimation and the Asymptotic Distribution of the Coefficients of an Autoregressive Scheme..........Ill 3.8 Discussion of the Methods Described in this Chapter . . . 115 17
Chapter 4. Estimation of the Spectrum 4.0 Introduction....................117 4.1 A General Class of Estimates.............117 4.2 An Optimum Property of Spectrograph Estimates .... 123 4.3 A Remark on the Bias of Spectrograph Estimates .... 129 4.4 The Asymptotic Variance of Spectrograph Estimates . . . 131 4.5 Another Class of Estimates..............137 4.6 Special Estimates of the Spectral Density........145 4.7 The Mean Square Error of Estimates..........153 4.8 An Example from Statistical Optics..........155 Chapter 5. Applications 5.0 Introduction....................158 5.1 Derivations of Spectra of Random Noise........158 5.2 Measuring Noise Spectra...............160 5.3 Turbulence.....................163 5.4 Measuring Turbulence Spectra.............171 5.5 Basic Ideas in a Statistical Theory of Ocean Waves . . . 174 5.6 Other Applications..................177 Chapter 6. Distribution of Spectral Estimates 6.0 Introduction....................179 6.1 Preliminary Remarks.................179 6.2 A Heuristic Derivation of a Limit Theorem.......182 6.3 Preliminary Considerations..............185 6.4 Treatment of Pure White Noise............188 6.5 The General Theorem................190 6.6 The Normal Case..................195 6.7 Remarks on the Nonnormal Case...........198 6.8 Spectral Analysis with a Regression Present.......202 6.9 Alternative Estimates of the Spectral Distribution Function 204 6.10 Alternative Statistics and the Corresponding Limit Theorems 207 6.11 Confidence Band for the Spectral Density........208 6.12 Spectral Analysis of Some Artificially Generated Time Series 214 Chapter 7. Problems in Linear Estimation 7.0 Preliminary Discussion................226 7.1 Estimating Regression Coefficients...........231 7.2 The Regression Spectrum...............233 7.3 Asymptotic Expression for the Covariance Matrices . . . 235 18
7.4 Elements of the Spectrum...............241 7.5 Polynomial and Trigonometric Regression........245 7.6 More General Trigonometric and Polynomial Regression . 248 7.7 Some Other Types of Regression............254 7.8 Detection of Signals in Noise.............255 7.9 Confidence Intervals and Tests............257 Chapter 8. Assorted Problems 8.0 Introduction....................260 8.1 Prediction when the Conjectured Spectrum is not the True One 260 8.2 Uniform Convergence of the Estimated Spectral Density to the True Spectral Density...............262 8.3 The Asymptotic Distribution of an Integral of a Spectrograph Estimate...................263 8.4 The Mean Square Error of Prediction when the Spectrum is Estimated.....................267 8.5 Other Types of Estimates of the Spectrum.......270 8.6 The Zeros and Maxima of Stationary Stochastic Processes 271 8.7 Prefiltering of a Time Series............. 273 8.8 Comments on Tests of Normality...........275 Problems ..........................278 Appendix on Complex Variable Theory ............288 Bibliography ........................294 Index ............................299 19
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| any_adam_object | 1 |
| author | Grenander, Ulf 1923-2016 Rosenblatt, Murray 1926-2019 |
| author_GND | (DE-588)1112557946 (DE-588)1072191784 |
| author_facet | Grenander, Ulf 1923-2016 Rosenblatt, Murray 1926-2019 |
| author_role | aut aut |
| author_sort | Grenander, Ulf 1923-2016 |
| author_variant | u g ug m r mr |
| building | Verbundindex |
| bvnumber | BV011861748 |
| classification_rvk | SK 845 |
| ctrlnum | (OCoLC)258606692 (DE-599)BVBBV011861748 |
| discipline | Mathematik |
| edition | 2. print. |
| format | Book |
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| indexdate | 2025-02-03T16:44:36Z |
| institution | BVB |
| language | English |
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| publishDate | 1966 |
| publishDateSearch | 1966 |
| publishDateSort | 1966 |
| publisher | Wiley Almqvist & Wiksell |
| record_format | marc |
| series2 | Wiley series in probability and mathematical statistics |
| spellingShingle | Grenander, Ulf 1923-2016 Rosenblatt, Murray 1926-2019 Statistical analysis of stationary time series Datenanalyse (DE-588)4123037-1 gnd Zeitreihenanalyse (DE-588)4067486-1 gnd Statistische Analyse (DE-588)4116599-8 gnd Stationärer Prozess (DE-588)4056989-5 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4123037-1 (DE-588)4067486-1 (DE-588)4116599-8 (DE-588)4056989-5 (DE-588)4057630-9 |
| title | Statistical analysis of stationary time series |
| title_auth | Statistical analysis of stationary time series |
| title_exact_search | Statistical analysis of stationary time series |
| title_full | Statistical analysis of stationary time series by Ulf Grenander and Murray Rosenblatt |
| title_fullStr | Statistical analysis of stationary time series by Ulf Grenander and Murray Rosenblatt |
| title_full_unstemmed | Statistical analysis of stationary time series by Ulf Grenander and Murray Rosenblatt |
| title_short | Statistical analysis of stationary time series |
| title_sort | statistical analysis of stationary time series |
| topic | Datenanalyse (DE-588)4123037-1 gnd Zeitreihenanalyse (DE-588)4067486-1 gnd Statistische Analyse (DE-588)4116599-8 gnd Stationärer Prozess (DE-588)4056989-5 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Datenanalyse Zeitreihenanalyse Statistische Analyse Stationärer Prozess Stochastischer Prozess |
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