Nonlinear Times Series
A Second Course in Time Series Analysis
To Be Published November 15th 2013 by Chapman and Hall/CRC – 400 pages
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.
Preliminaries. Markov and Iterative Models: Nonlinear Markovian Models. Stability, Recurrence, Mixing. Ergodicity, Limit Theorems. Parametric Inference. Nonparametric Inference. Hidden Markov Models: Some HMM Models. Filtering and Smoothing in HMM. Parametric Inference for HMM. Nonparametric Inference for HMM. Particle Filtering Basics. Advanced Issues in Particle Filtering. Particle Smoothing Basics. Numerical Methods for Inference.