Statistics for Long-Memory Processes

by ;
Edition: 1st
Format: Hardcover
Pub. Date: 1994-10-01
Publisher(s): Chapman & Hall/
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Summary

Statistical Methods for Long Term Memory Processes is covers the diverse statistical methods and applications for data with long-range dependence. Presenting material that has appeared only in journals, the author provides a concise and effective overview of probabilistic foundations, statistical methods, and applications. The material emphasize basic principles and practical applications and provides the reader with an integrated perspective of both theory and practice. This book explores data sets from a wide range of disciplines, such as hydrology, climatology, telecommunications engineering, and high-precision physical measurement. The data sets are conveniently compiled in the index, and this allows the reader to view statistical approaches in a practical context. Statistical Methods for Long Term Memory Processes also supplies S-PLUS programs for the major methods discussed. This feature allows the practitioner to apply long memory processes in daily data analysis. For newcomers to the area, the firstthree chapters provide the basic knowledge necessary for understanding the remainder of the material. To promote selective reading, the author presents the chapters independently. Combining essential methodologies with real-life applications, this outstanding volume is and indispensable reference for statisticians and scientists who analyze data with long-range dependence.

Table of Contents

Preface ix
Introduction
1(40)
An elementary result in statistics
1(10)
Forecasting, an example
11(3)
``Physical'' models with long memory
14(6)
General remarks
14(1)
Aggregation of short-memory models
14(2)
Critical phenomena
16(1)
Hierarchical variation
17(1)
Partial differential equations
18(2)
Some data examples
20(9)
Other data examples, historic overview, discussion
29(12)
Two types of situations
29(3)
The Joseph effect and the Hurst effect
32(2)
Uniformity trials
34(1)
Economic time series
35(1)
Semisystematic errors, unsuspected slowly decaying correlations, the personal equation
36(3)
Why stationary models? Some ``philosophical'' remarks
39(2)
Stationary processes with long memory
41(26)
Introduction
41(4)
Self-similar processes
45(5)
Stationary increments of self-similar processes
50(5)
Fractional Brownian motion and Gaussian noise
55(4)
Fractional ARIMA models
59(8)
Limit theorems
67(14)
Introduction
67(1)
Gaussian and non-gaussian time series with long memory
67(2)
Limit theorems for simple sums
69(4)
Limit theorems for quadratic forms
73(4)
Limit theorems for Fourier transforms
77(4)
Estimation of long memory: heuristic approaches
81(19)
Introduction
81(1)
The R/S statistic
81(6)
The correlogram and partial correlations
87(5)
Variance plot
92(2)
Variogram
94(1)
Least squares regression in the spectral domain
95(5)
Estimation of long memory: time domain MLE
100(16)
Introduction
100(2)
Some definitions and useful results
102(2)
Exact Gaussian MLE
104(4)
Why do we need approximate MLE's?
108(1)
Whittle's approximate MLE
109(4)
An approximate MLE based on the AR representation
113(3)
Definition for stationary processes
113(2)
Generalization to nonstationary processes; a unified approach to Box-Jenkins modelling
115(1)
Estimation of long memory: frequency domain MLE
116(8)
A discrete version of Whittle's estimator
116(4)
Estimation by generalized linear models
120(4)
Robust estimation of long memory
124(24)
Introduction
124(5)
Robustness against additive outliers
129(4)
Robustness in the spectral domain
133(8)
Nonstationarity
141(3)
Long-range phenomena and other processes
144(4)
Estimation of location and scale, forecasting
148(24)
Introduction
148(1)
Efficiency of the sample mean
148(3)
Robust estimation of the location parameter
151(5)
Estimation of the scale parameter
156(1)
Prediction of a future sample mean
157(2)
Confidence intervals for μ and a future mean
159(5)
Tests and confidence intervals for μ with known long-memory and scale parameters
159(1)
Tests and confidence intervals for a future mean, with known long-memory and scale parameters
160(1)
Tests and confidence intervals for μ with unknown long-memory and scale parameters
161(3)
Tests and confidence intervals for a future mean, with unknown long-memory and scale parameters
164(1)
Forecasting
164(8)
Regression
172(25)
Introduction
172(4)
Regression with deterministic design
176(10)
Polynomial trend
176(4)
General regression with deterministic design
180(6)
Regression with random design; ANOVA
186(11)
The ANOVA model
186(1)
Definition of contrasts
187(1)
The conditional variance of contrasts
188(1)
Three standard randomizations
189(2)
Results for complete randomization
191(1)
Restricted randomization
192(2)
Blockwise randomization
194(3)
Goodness of fit tests and related topics
197(14)
Goodness of fit tests for the marginal distribution
197(4)
Goodness of fit tests for the spectral density
201(5)
Changes in the spectral domain
206(5)
Miscellaneous topics
211(7)
Processes with infinite variance
211(2)
Fractional GARMA processes
213(2)
Simulation of long-memory processes
215(3)
Introduction
215(1)
Simulation of fractional Gaussian noise
216(1)
A method based on the fast Fourier transform
216(1)
Simulation by aggregation
217(1)
Simulation of fractional ARIMA processes
217(1)
Programs and data sets
218(44)
Splus programs
218(19)
Simulation of fractional Gaussian noise
218(2)
Simulation of fractional ARIMA (0,d,0)
220(3)
Whittle estimator for fractional Gaussian noise and fractional ARIMA (p, d, q)
223(10)
Approximate MLE for F E X P models
233(4)
Data sets
237(25)
Nile River minima
237(3)
VBR data
240(3)
Ethernet data
243(12)
NBS data
255(2)
Northern hemisphere temperature data
257(5)
Bibliography 262(40)
Author index 302(4)
Subject index 306

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