Statistics for long-memory processes:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton [u.a.]
Chapman & Hall
1998
|
| Ausgabe: | Reprint |
| Schriftenreihe: | Monographs on statistics and applied probability
61 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 315 S. Ill., graph. Darst. |
| ISBN: | 0412049015 |
Internformat
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| 264 | 1 | |a Boca Raton [u.a.] |b Chapman & Hall |c 1998 | |
| 300 | |a X, 315 S. |b Ill., graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1804138101583380480 |
|---|---|
| adam_text | Contents
Preface
ix
1
Introduction
1
1.1
An
elementary result in statistics
1
1.2
Forecasting, an example
11
1.3
Physical models with long memory
14
1.3.1
General remarks
14
1.3.2
Aggregation of short-memory models
14
1.3.3
Critical phenomena
16
1.3.4
Hierarchical variation
17
1.3.5
Partial differential equations
18
1.4
Some data examples
20
1.5
Other data examples, historic overview, discussion
29
1.5.1
Two types of situations
29
1.5.2
The Joseph effect and the Hurst effect
32
1.5.3
Uniformity trials
34
1.5.4
Economic time series
35
1.5.5
Semisystematic errors, unsuspected slowly
decaying correlations, the personal equation
36
1.5.6
Why stationary models? Some philosophi¬
cal remarks
39
2
Stationary processes with long memory
41
2.1
Introduction
41
2.2
Self-similar processes
45
2.3
Stationary increments of self-similar processes
50
2.4
Fractional Brownian motion and Gaussian noise
55
2.5
Fractional ARIMA models
59
3
Limit theorems
67
CONTENTS
3.1
Introduction
67
3.2
Gaussian and
non-gaussian
time series with long
memory
67
3.3
Limit theorems for simple sums
69
3.4
Limit theorems for quadratic forms
73
3.5
Limit theorems for Fourier transforms
77
Estimation of long memory: heuristic approaches
81
4.1
Introduction
81
4.2
The R/S statistic
81
4.3
The correlogram and partial correlations
87
4.4
Variance plot
92
4.5
Variogram
94
4.6
Least squares regression in the spectral domain
95
Estimation of long memory: time domain MLE
100
5.1
Introduction
100
5.2
Some definitions and useful results
102
5.3
Exact Gaussian MLE
104
5.4
Why do we need approximate MLE s?
108
5.5
Whittle s approximate MLE
109
5.6
An approximate MLE based on the
AR
representation
113
5.6.1
Definition for stationary processes
113
5.6.2
Generalization to nonstationary processes; a
unified approach to Box-Jenkins modelling
115
Estimation of long memory: frequency domain
MLE
116
6.1
A discrete version of Whittle s estimator
116
6.2
Estimation by generalized linear models
120
Robust estimation of long memory
124
7.1
Introduction
124
7.2
Robustness against additive outliers
129
7.3
Robustness in the spectral domain
133
7.4
Nonstationarity
141
7.5
Long-range phenomena and other processes
144
Estimation of location and scale, forecasting
148
8.1
Introduction
148
8.2
Efficiency of the sample mean
148
8.3
Robust estimation of the location parameter
151
CONTENTS
vii
8.4
Estimation
of the scale parameter
156
8.5
Prediction of a future sample mean
157
8.6
Confidence intervals for
μ
and a future mean
159
8.6.1
Tests and confidence intervals for
μ
with
known long-memory and scale parameters
159
8.6.2
Tests and confidence intervals for a future
mean, with known long-memory and scale
parameters
160
8.6.3
Tests and confidence intervals for
μ
with
unknown long-memory and scale parameters
161
8.6.4
Tests and confidence intervals for a future
mean, with unknown long-memory and scale
parameters
164
8.7
Forecasting
164
9
Regression
172
9.1
Introduction
172
9.2
Regression with deterministic design
176
9.2.1
Polynomial trend
176
9.2.2
General regression with deterministic design
180
9.3
Regression with random design; ANOVA
186
9.3.1
The ANOVA model
186
9.3.2
Definition of contrasts
187
9.3.3
The conditional variance of contrasts
188
9.3.4
Three standard randomizations
189
9.3.5
Results for complete randomization
191
9.3.6
Restricted randomization
192
9.3.7
Blockwise randomization
194
10
Goodness of fit tests and related topics
197
10.1
Goodness of fit tests for the marginal distribution
197
10.2
Goodness of fit tests for the spectral density
201
10.3
Changes in the spectral domain
206
11
Miscellaneous topics
211
11.1
Processes with infinite variance
211
11.2
Fractional GARMA processes
213
11.3
Simulation of long-memory processes
215
11.3.1
Introduction
215
11.3.2
Simulation of fractional Gaussian noise
216
11.3.3
A method based on the fast Fourier transform
216
11.3.4
Simulation by aggregation
217
viii CONTENTS
11.3.5 Simulation
of fractional ARIMA processes
217
12
Programs and data sets
218
12.1
Splus programs
218
12.1.1
Simulation of fractional Gaussian noise
218
12.1.2
Simulation of fractional ARIMA(0, d,
0) 220
12.1.3
Whittle estimator for fractional Gaussian
noise and fractional ARIMA(jj, d, q)
223
12.1.4
Approximate MLE for FEXP models
233
12.2
Data sets
237
12.2.1
Nile River minima
237
12.2.2
VBR data
240
12.2.3
Ethernet data
243
12.2.4
NBS
data
255
12.2.5
Northern hemisphere temperature data
257
Bibliography
262
Author index
302
Subject index
306
|
| adam_txt |
Contents
Preface
ix
1
Introduction
1
1.1
An
elementary result in statistics
1
1.2
Forecasting, an example
11
1.3
"Physical" models with long memory
14
1.3.1
General remarks
14
1.3.2
Aggregation of short-memory models
14
1.3.3
Critical phenomena
16
1.3.4
Hierarchical variation
17
1.3.5
Partial differential equations
18
1.4
Some data examples
20
1.5
Other data examples, historic overview, discussion
29
1.5.1
Two types of situations
29
1.5.2
The Joseph effect and the Hurst effect
32
1.5.3
Uniformity trials
34
1.5.4
Economic time series
35
1.5.5
Semisystematic errors, unsuspected slowly
decaying correlations, the personal equation
36
1.5.6
Why stationary models? Some "philosophi¬
cal" remarks
39
2
Stationary processes with long memory
41
2.1
Introduction
41
2.2
Self-similar processes
45
2.3
Stationary increments of self-similar processes
50
2.4
Fractional Brownian motion and Gaussian noise
55
2.5
Fractional ARIMA models
59
3
Limit theorems
67
CONTENTS
3.1
Introduction
67
3.2
Gaussian and
non-gaussian
time series with long
memory
67
3.3
Limit theorems for simple sums
69
3.4
Limit theorems for quadratic forms
73
3.5
Limit theorems for Fourier transforms
77
Estimation of long memory: heuristic approaches
81
4.1
Introduction
81
4.2
The R/S statistic
81
4.3
The correlogram and partial correlations
87
4.4
Variance plot
92
4.5
Variogram
94
4.6
Least squares regression in the spectral domain
95
Estimation of long memory: time domain MLE
100
5.1
Introduction
100
5.2
Some definitions and useful results
102
5.3
Exact Gaussian MLE
104
5.4
Why do we need approximate MLE's?
108
5.5
Whittle's approximate MLE
109
5.6
An approximate MLE based on the
AR
representation
113
5.6.1
Definition for stationary processes
113
5.6.2
Generalization to nonstationary processes; a
unified approach to Box-Jenkins modelling
115
Estimation of long memory: frequency domain
MLE
116
6.1
A discrete version of Whittle's estimator
116
6.2
Estimation by generalized linear models
120
Robust estimation of long memory
124
7.1
Introduction
124
7.2
Robustness against additive outliers
129
7.3
Robustness in the spectral domain
133
7.4
Nonstationarity
141
7.5
Long-range phenomena and other processes
144
Estimation of location and scale, forecasting
148
8.1
Introduction
148
8.2
Efficiency of the sample mean
148
8.3
Robust estimation of the location parameter
151
CONTENTS
vii
8.4
Estimation
of the scale parameter
156
8.5
Prediction of a future sample mean
157
8.6
Confidence intervals for
μ
and a future mean
159
8.6.1
Tests and confidence intervals for
μ
with
known long-memory and scale parameters
159
8.6.2
Tests and confidence intervals for a future
mean, with known long-memory and scale
parameters
160
8.6.3
Tests and confidence intervals for
μ
with
unknown long-memory and scale parameters
161
8.6.4
Tests and confidence intervals for a future
mean, with unknown long-memory and scale
parameters
164
8.7
Forecasting
164
9
Regression
172
9.1
Introduction
172
9.2
Regression with deterministic design
176
9.2.1
Polynomial trend
176
9.2.2
General regression with deterministic design
180
9.3
Regression with random design; ANOVA
186
9.3.1
The ANOVA model
186
9.3.2
Definition of contrasts
187
9.3.3
The conditional variance of contrasts
188
9.3.4
Three standard randomizations
189
9.3.5
Results for complete randomization
191
9.3.6
Restricted randomization
192
9.3.7
Blockwise randomization
194
10
Goodness of fit tests and related topics
197
10.1
Goodness of fit tests for the marginal distribution
197
10.2
Goodness of fit tests for the spectral density
201
10.3
Changes in the spectral domain
206
11
Miscellaneous topics
211
11.1
Processes with infinite variance
211
11.2
Fractional GARMA processes
213
11.3
Simulation of long-memory processes
215
11.3.1
Introduction
215
11.3.2
Simulation of fractional Gaussian noise
216
11.3.3
A method based on the fast Fourier transform
216
11.3.4
Simulation by aggregation
217
viii CONTENTS
11.3.5 Simulation
of fractional ARIMA processes
217
12
Programs and data sets
218
12.1
Splus programs
218
12.1.1
Simulation of fractional Gaussian noise
218
12.1.2
Simulation of fractional ARIMA(0, d,
0) 220
12.1.3
Whittle estimator for fractional Gaussian
noise and fractional ARIMA(jj, d, q)
223
12.1.4
Approximate MLE for FEXP models
233
12.2
Data sets
237
12.2.1
Nile River minima
237
12.2.2
VBR data
240
12.2.3
Ethernet data
243
12.2.4
NBS
data
255
12.2.5
Northern hemisphere temperature data
257
Bibliography
262
Author index
302
Subject index
306 |
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| author | Beran, Jan 1959- |
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| dewey-sort | 3519.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Mathematik Wirtschaftswissenschaften |
| edition | Reprint |
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| id | DE-604.BV035123028 |
| illustrated | Illustrated |
| index_date | 2024-07-02T22:21:51Z |
| indexdate | 2024-07-09T21:22:50Z |
| institution | BVB |
| isbn | 0412049015 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016790655 |
| oclc_num | 255508700 |
| open_access_boolean | |
| owner | DE-739 DE-634 DE-83 DE-19 DE-BY-UBM DE-20 |
| owner_facet | DE-739 DE-634 DE-83 DE-19 DE-BY-UBM DE-20 |
| physical | X, 315 S. Ill., graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Chapman & Hall |
| record_format | marc |
| series | Monographs on statistics and applied probability |
| series2 | Monographs on statistics and applied probability |
| spelling | Beran, Jan 1959- Verfasser (DE-588)141540060 aut Statistics for long-memory processes Jan Beran Statistics for long memory processes Reprint Boca Raton [u.a.] Chapman & Hall 1998 X, 315 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Monographs on statistics and applied probability 61 Mathematical statistics Stochastic processes Statistik (DE-588)4056995-0 gnd rswk-swf Long-memory-Prozess (DE-588)4345167-6 gnd rswk-swf Langzeitverhalten (DE-588)4120653-8 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Langzeit (DE-588)4418319-7 gnd rswk-swf Stochastische Abhängigkeit (DE-588)4220425-2 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 s Stochastische Abhängigkeit (DE-588)4220425-2 s Langzeit (DE-588)4418319-7 s DE-604 Langzeitverhalten (DE-588)4120653-8 s Statistik (DE-588)4056995-0 s 1\p DE-604 Long-memory-Prozess (DE-588)4345167-6 s 2\p DE-604 Monographs on statistics and applied probability 61 (DE-604)BV002494005 61 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016790655&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Beran, Jan 1959- Statistics for long-memory processes Monographs on statistics and applied probability Mathematical statistics Stochastic processes Statistik (DE-588)4056995-0 gnd Long-memory-Prozess (DE-588)4345167-6 gnd Langzeitverhalten (DE-588)4120653-8 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Langzeit (DE-588)4418319-7 gnd Stochastische Abhängigkeit (DE-588)4220425-2 gnd |
| subject_GND | (DE-588)4056995-0 (DE-588)4345167-6 (DE-588)4120653-8 (DE-588)4057630-9 (DE-588)4418319-7 (DE-588)4220425-2 |
| title | Statistics for long-memory processes |
| title_alt | Statistics for long memory processes |
| title_auth | Statistics for long-memory processes |
| title_exact_search | Statistics for long-memory processes |
| title_exact_search_txtP | Statistics for long-memory processes |
| title_full | Statistics for long-memory processes Jan Beran |
| title_fullStr | Statistics for long-memory processes Jan Beran |
| title_full_unstemmed | Statistics for long-memory processes Jan Beran |
| title_short | Statistics for long-memory processes |
| title_sort | statistics for long memory processes |
| topic | Mathematical statistics Stochastic processes Statistik (DE-588)4056995-0 gnd Long-memory-Prozess (DE-588)4345167-6 gnd Langzeitverhalten (DE-588)4120653-8 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Langzeit (DE-588)4418319-7 gnd Stochastische Abhängigkeit (DE-588)4220425-2 gnd |
| topic_facet | Mathematical statistics Stochastic processes Statistik Long-memory-Prozess Langzeitverhalten Stochastischer Prozess Langzeit Stochastische Abhängigkeit |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016790655&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002494005 |
| work_keys_str_mv | AT beranjan statisticsforlongmemoryprocesses |