ABSTRACT

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.

part I|130 pages

Foundations

chapter Chapter 1|30 pages

Linear Models

chapter Chapter 2|28 pages

Linear Gaussian State Space Models

chapter Chapter 3|30 pages

Beyond Linear Models

chapter Chapter 4|40 pages

Stochastic Recurrence Equations

part II|154 pages

Markov Models

chapter Chapter 5|32 pages

Markov Models: Construction and Definitions

chapter Chapter 6|30 pages

Stability and Convergence

chapter Chapter 7|44 pages

Sample Paths and Limit Theorems

chapter Chapter 8|46 pages

Inference for Markovian Models

part III|182 pages

State Space and Hidden Markov Models

chapter Chapter 9|34 pages

Non-Gaussian and Nonlinear State Space Models

chapter Chapter 10|40 pages

Particle Filtering

chapter Chapter 11|44 pages

Particle Smoothing

chapter Chapter 12|36 pages

Inference for Nonlinear State Space Models