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Nonlinear times series : theory, methods and applications with R examples / Randal Douc, Eric Moulines and David S. Stoffer.

By: Contributor(s): Material type: TextTextSeries: Chapman & Hall/CRC texts in statistical science seriesPublication details: Boca Raton : CRC Press, c2014.Description: xx, 531 p. ; 25 cmISBN:
  • 9781466502253 (hardback)
Subject(s): DDC classification:
  • 000SA.3 23 D728
Contents:
I. Foundations 1. Linear models-- 2. Linear Gaussian state space models-- 3. Beyond linear models-- 4. Stochastic recurrence equations-- II. Markovian models 5. Markov models: construction and definitions-- 6. Stability and convergence-- 7. Sample paths and limit theorems-- 8. Inference for Markovian models-- III State space and hidden Markov models 9. Non-Gaussian and nonlinear state space models-- 10. Particle filtering-- 11. Particle smoothing-- 12. Inference for nonlinear state space models-- 13. Asymptotics of the MLE for NLSS-- IV. Appendics-- References-- Index.
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"--
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Includes bibliographical references and index.

I. Foundations
1. Linear models--
2. Linear Gaussian state space models--
3. Beyond linear models--
4. Stochastic recurrence equations--

II. Markovian models
5. Markov models: construction and definitions--
6. Stability and convergence--
7. Sample paths and limit theorems--
8. Inference for Markovian models--

III State space and hidden Markov models
9. Non-Gaussian and nonlinear state space models--
10. Particle filtering--
11. Particle smoothing--
12. Inference for nonlinear state space models--
13. Asymptotics of the MLE for NLSS--

IV. Appendics--
References--
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"--

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