Nonlinear time series: theory, methods and applications with R examples
"This text emphasizes nonlinear models for a course in time series analysis. After introducing stochastic processes, Markov chains, Poisson processes, and ARMA models, the authors cover functional autoregressive, ARCH, threshold AR, and discrete time series models as well as several complementa...
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton, Fla [u.a.]
CRC Press
2014
|
| Series: | Texts in statistical science
|
| Subjects: | |
| Online Access: | Cover image Inhaltsverzeichnis |
| Summary: | "This text emphasizes nonlinear models for a course in time series analysis. After introducing stochastic processes, Markov chains, Poisson processes, and ARMA models, the authors cover functional autoregressive, ARCH, threshold AR, and discrete time series models as well as several complementary approaches. They discuss the main limit theorems for Markov chains, useful inequalities, statistical techniques to infer model parameters, and GLMs. Moving on to HMM models, the book examines filtering and smoothing, parametric and nonparametric inference, advanced particle filtering, and numerical methods for inference".. |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XX, 531 S. Ill., graph. Darst. |
| ISBN: | 9781466502253 |
Staff View
MARC
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| 100 | 1 | |a Douc, Randal |d 1971- |e Verfasser |0 (DE-588)105018629X |4 aut | |
| 245 | 1 | 0 | |a Nonlinear time series |b theory, methods and applications with R examples |c Randal Douc ; Eric Moulines ; David S. Stoffer |
| 264 | 1 | |a Boca Raton, Fla [u.a.] |b CRC Press |c 2014 | |
| 300 | |a XX, 531 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Texts in statistical science | |
| 500 | |a Includes bibliographical references and index | ||
| 520 | |a "This text emphasizes nonlinear models for a course in time series analysis. After introducing stochastic processes, Markov chains, Poisson processes, and ARMA models, the authors cover functional autoregressive, ARCH, threshold AR, and discrete time series models as well as several complementary approaches. They discuss the main limit theorems for Markov chains, useful inequalities, statistical techniques to infer model parameters, and GLMs. Moving on to HMM models, the book examines filtering and smoothing, parametric and nonparametric inference, advanced particle filtering, and numerical methods for inference".. | ||
| 650 | 7 | |a MATHEMATICS / Probability & Statistics / General |2 bisacsh | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Time-series analysis |x Mathematical models | |
| 650 | 4 | |a MATHEMATICS / Probability & Statistics / General | |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-027210913 | |
Record in the Search Index
| _version_ | 1826181947379941376 |
|---|---|
| adam_text |
Contents
Preface
xiii
Frequently Used Notation
xvii
I Foundations
1
1
Linear Models
3
1.1
Stochastic processes
3
1.2
The covariance world
5
1.2.1
Second-order stationary processes
5
1.2.2
Spectral representation
9
1.2.3
Wold decomposition
13
1.3
Linear processes
15
1.3.1
What are linear Gaussian processes?
15
1.3.2
ARMA
models
16
1.3.3
Prediction
19
1.3.4
Estimation
21
1.4
The multivariale cases
25
1.4.1
Time domain
25
1.4.2
Frequency domain
27
1.5
Numerical examples
28
Exercises
30
2
Linear Gaussian State Space Models
33
2.1
Model basics
33
2.2
Filtering, smoolhing, and forecasting
36
2.3
Maximum likelihood estimation
42
2.3.1
Newton-Raphson
42
2.3.2
EM algorithm
43
2.4
Smoolhing splines and the
Kalman
smoother
45
2.5
Asymptotic distribution of the MLE
47
2.6
Missing data modulations
49
2.7
Structural component models
50
2.8
Stale-space models with conelated errors
53
2.8.1
ARMAX models
54
VII
viii
CONTENTS
2.8.2 Regression
with
autocorrelated
errors
56
Hxcrcises
56
3
Beyond Linear Models
61
3.1
Nonlinear non-Gaussian data
62
3.2
Volteira
series expansion
68
3.3
Cumulants
and higher-order spectra
69
3.4
Bilinear models
72
3.5
Conditionally heleroseedastie models
73
3.6
Threshold
ARMA
models
77
3.7
Functional auloregrcssive models
78
3.8
Linear processes with infinite variance
79
3.9
Models /or counts
81
3.9.1
Integer valued models
81
3.9.2
Generalized linear models
83
3.10
Numerical examples
84
Exercises
89
4
Stochastic Recurrence Equations
91
4.
1 The Scalar Case
93
4.1.1
Strict
staţionari
ty
93
4.
J.
2
Weak
staţionari
ty
98
4.1.3
GARCHd,
I)
102
4.2
The Veclor Case 1
07
4.2.1
Strict stationarity j09
4.2.2
Weak stationarity
j j
|
4.2.3
GARCH^, q)
*
,14
4.3
Iterated random function I |g
4.3.1
Strict stationarity jjg
4.3.2
Weak stationarity
Exercises
II Markovian Models
131
Markov Models: Construction and Definitions
133
5.1
Markov chains: Past, future, and forgelfulness
133
5.2
Kernels
5.3
Homogeneous Markov chain
5.4
Canonical representation
.
^
5.5
Invariant measures
. Ig
5.6
Observation-driven models
Л«
5.7
Iterated random functions
.
«~
5.8
MCMC methods ,52
5.8.1
Metropolis-Hastings algorithm
5.8.2
Gibbs sampling
CONTENTS ix
Exercises J
57
6
Stability and
Convergence
165
6.1
Uni foi m ergodic
i ty
166
6.1.1
Total variation distance
166
6.1.2
Dobrushin coefficient
167
6.1.3
The Doeblin condition
169
6.1.4
Examples
169
6.2
V-geometric ergodicity
173
6.2.1
V-total variation distance
173
6.2.2
V-Dobrushin coefficient
174
6.2.3
Drift and minorization conditions
175
6.2.4
Examples
180
6.3
Some proofs
6.4 Endnotes
Exercises
7
Sample Paths and Limit Theorems
7.1
Law ofl
arge
numbers
196
7.1.1
Dynamical system and ergodicity
196
7.1.2
Markov chain ergodicity
203
7.2
Central limit theorem
211
7.3
Deviation inequalities for additive functionals
218
7.3.1 Rosenthal
type inequality
218
7.3.2
Concentration inequality
221
7.4
Some proofs
225
Exercises
231
8
Inference for Markovian Models
239
8.1
Likelihood inference
239
8.2
Consistency and asymptotic normality of the MLE
245
8.2.1
Consistency
245
8.2.2
Asymptotic normality
247
8.3
Observation-driven models 2r>4
8.4
Bayesian inference
263
8.5
Some proofs
271
8.6 Endnotes 274
Exercises
275
HI State Space and Hidden Markov Models
285
9
Non-Gaussian and Nonlinear State Space Models
287
9.1
Definitions and basic properties
287
9.1.1
Discrete-valued state space
HMM
287
9.1.2
Continuous-valued state-space models
295
CONTHNTS
9.1.3
Conditionally Gaussian linear slate-space models
297
9.1.4
Switching
processos
willi
Markov regimes
3ÍX)
9.2
Filtering
and smoothing
302
9.2.
1
Di screte-va
I ueil state-space
HMM
303
9.2.2
Continuous-valued state-space
HMM
310
9.3
Kndnotcs
314
Exercises
315
10
Partiele
Filtering
10.1
Importance sampling
321
10.2
Sequential importance sampling
329
10.3
Sampling importance resampling
334
10.3.1
Algorithm description
335
10.3.2
Resampling techniques
336
10.4
Particle filter
337
10.4.1
Sequential importance sampling
337
10.4.2
Auxiliary sampling
339
10.5
Convergence of the particle filter
341
10.5.1
Exponential deviation inequalities
341
10.5.2
Time-uniform bounds
343
10.6 Endnotes 349
Exercises
350
11
Particle Smoothing
361
11.1
Poor man's smoother algorithm
362
11.2
FFBSm algorithm
365
[ .3
FFBSi algorithm
367
1.4
Smoothing functional
369
1
.5
Particle independent Metropolis-Hastings
370
1
.6
Particle Gibbs
376
1
.7
Convergence of the FFBSm and FFBSi algorithms
38
1
11.7.1
Exponential deviation inequality
384
1
1
.7.2
Asymptotic normality
.1,7.3
Time uniform bounds
11.8 Endnotes
Exercises
^д-у
12
Inference for Nonlinear State Space Models 4«5
12.
1 Monte Carlo maximum likelihood estimation 407
12.1.1
Particle approximation of the likelihood function
407
12.1.2
Particle stochastic gradient
12.1.3
Particle Monte Carlo EM a,^,,,,,,,,*
12.1.4
Particle stochastic approximation EM
12.1.3
Particle Monte Carlo EM algorithms
12.1.4
Particle stochastic approximation EM A \,
12.2
Bayesian analysis 415
12.2.1
Gaussian linear state space models 4
'
8
CONTENTS
xi
12.2.2
Gibbs sampling for
NLSS
model
423
12.2.3
Panicle marginal Markov chain Monte Carlo
428
12.2.4
Particle Gibbs algorithm
431
12.3 Endnotes 433
Exercises
435
13
Asymptotic* of the MLE for NLSS
441
13.1
Strong consistency ol the MLE
442
13.1.1
Forgetting the initial distribution
442
13.1.2
Approximation by conditional likelihood
444
13.1.3
Strong consistency
445
13.1.4
Identiliability of mixture densities
452
13.2
Asymptotic normality
453
13.2.
1 Convergence of the observed information
458
13.2.2
Limit distribution of the MLE
460
13.3
Endnotes
461
Exercises
462
IV Appendices
467
Appendix A Some Mathematical Background
469
A.
1
Some measure theory
469
A.2 Some probability theory
471
Appendix
В
Martingales
475
B.I Definitions and elementary properties
475
B.2 Limits theorems
477
Appendix
С
Stochastic Approximation
483
C.I Robbins-Monro algorithm: Elementary results
484
C.2 Stochastic gradient
487
C.3 Slepsize selection and averaging
488
C.4 The
Kiefer-Wolfowitz
procedure
488
Appendix
D
Data Augmentation
491
D. I The EM algorithm in the incomplete data model
492
D.2 The Fisher and Louis identities
494
D.3 Monte
Cřrlo EM
algorithm
495
D.3.
1
Stochastic approximation EM
496
D.4 Convergence of the EM algorithm
498
D.5 Convergence of the MCEM algorithm
500
D.5.1 Convergence of perturbed dynamical systems
500
D.5.2 Convergence of the MCEM algorithm
502
xii
CONTKNTS
References
505
Index
527 |
| any_adam_object | 1 |
| author | Douc, Randal 1971- Moulines, Eric 1963- Stoffer, David S. |
| author_GND | (DE-588)105018629X (DE-588)1050741625 (DE-588)1050751000 |
| author_facet | Douc, Randal 1971- Moulines, Eric 1963- Stoffer, David S. |
| author_role | aut aut aut |
| author_sort | Douc, Randal 1971- |
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| ctrlnum | (OCoLC)880942799 (DE-599)BVBBV041764793 |
| dewey-full | 519.5/5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5/5 |
| dewey-search | 519.5/5 |
| dewey-sort | 3519.5 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV041764793 |
| illustrated | Illustrated |
| indexdate | 2025-03-10T05:00:20Z |
| institution | BVB |
| isbn | 9781466502253 |
| language | English |
| lccn | 013045980 |
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| physical | XX, 531 S. Ill., graph. Darst. |
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| publisher | CRC Press |
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| spelling | Douc, Randal 1971- Verfasser (DE-588)105018629X aut Nonlinear time series theory, methods and applications with R examples Randal Douc ; Eric Moulines ; David S. Stoffer Boca Raton, Fla [u.a.] CRC Press 2014 XX, 531 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Texts in statistical science Includes bibliographical references and index "This text emphasizes nonlinear models for a course in time series analysis. After introducing stochastic processes, Markov chains, Poisson processes, and ARMA models, the authors cover functional autoregressive, ARCH, threshold AR, and discrete time series models as well as several complementary approaches. They discuss the main limit theorems for Markov chains, useful inequalities, statistical techniques to infer model parameters, and GLMs. Moving on to HMM models, the book examines filtering and smoothing, parametric and nonparametric inference, advanced particle filtering, and numerical methods for inference".. MATHEMATICS / Probability & Statistics / General bisacsh Mathematisches Modell Time-series analysis Mathematical models MATHEMATICS / Probability & Statistics / General Nichtlineare Zeitreihenanalyse (DE-588)4276267-4 gnd rswk-swf Nichtlineare Zeitreihenanalyse (DE-588)4276267-4 s DE-604 Moulines, Eric 1963- Verfasser (DE-588)1050741625 aut Stoffer, David S. Verfasser (DE-588)1050751000 aut http://images.tandf.co.uk/common/jackets/websmall/978146650/9781466502253.jpg Cover image Digitalisierung UB Bamberg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027210913&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Douc, Randal 1971- Moulines, Eric 1963- Stoffer, David S. Nonlinear time series theory, methods and applications with R examples MATHEMATICS / Probability & Statistics / General bisacsh Mathematisches Modell Time-series analysis Mathematical models MATHEMATICS / Probability & Statistics / General Nichtlineare Zeitreihenanalyse (DE-588)4276267-4 gnd |
| subject_GND | (DE-588)4276267-4 |
| title | Nonlinear time series theory, methods and applications with R examples |
| title_auth | Nonlinear time series theory, methods and applications with R examples |
| title_exact_search | Nonlinear time series theory, methods and applications with R examples |
| title_full | Nonlinear time series theory, methods and applications with R examples Randal Douc ; Eric Moulines ; David S. Stoffer |
| title_fullStr | Nonlinear time series theory, methods and applications with R examples Randal Douc ; Eric Moulines ; David S. Stoffer |
| title_full_unstemmed | Nonlinear time series theory, methods and applications with R examples Randal Douc ; Eric Moulines ; David S. Stoffer |
| title_short | Nonlinear time series |
| title_sort | nonlinear time series theory methods and applications with r examples |
| title_sub | theory, methods and applications with R examples |
| topic | MATHEMATICS / Probability & Statistics / General bisacsh Mathematisches Modell Time-series analysis Mathematical models MATHEMATICS / Probability & Statistics / General Nichtlineare Zeitreihenanalyse (DE-588)4276267-4 gnd |
| topic_facet | MATHEMATICS / Probability & Statistics / General Mathematisches Modell Time-series analysis Mathematical models Nichtlineare Zeitreihenanalyse |
| url | http://images.tandf.co.uk/common/jackets/websmall/978146650/9781466502253.jpg http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027210913&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT doucrandal nonlineartimeseriestheorymethodsandapplicationswithrexamples AT moulineseric nonlineartimeseriestheorymethodsandapplicationswithrexamples AT stofferdavids nonlineartimeseriestheorymethodsandapplicationswithrexamples |