Nonlinear Models in Time Series Analysis

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.

Limit Theorems and Statistical Techniques

They discuss the main limit theorems for Markov chains, useful inequalities, statistical techniques to infer model parameters, and GLMs.

Hidden Markov Models (HMM) and Inference

Moving on to HMM models, the book examines filtering and smoothing, parametric and nonparametric inference, advanced particle filtering, and numerical methods for inference.