Some Notes

• Here is a short introduction on Recursive online estimation of parameters of time-varying AR processes [ps file]. The notes are very heuristic, summarising what time-varying AR processes are and how one can estimate the parameters of a time-varying AR process using an recursive online algorithm.

  For more information on applications see the group of Prof. Witte at the The Institute of Medical Statistics and Computer Science, University of Jena, where they have modelled EEG data with time-varing vector AR processes and have used a recursive online algorithm to estimate the time-varying parameters.

• A Dummies Guide to the Kalman filter and Sequential Monte Carlo methods (aka particle filters) [ps file] is a simple explanation of the Kalman filter for nonlinear, non-Gaussian models and sequential Monte Carlo (aka Monte Carlo filters). It is written as a talk, but with several long explanations. It is mainly based on the informative book "Smoothness Priors Analysis of Time Series" by Kitagawa and Gersch (1996) and some of the chapters in the book "Sequential Monte Carlo in Practice" (2001), in particular "Approximation and maximising the likelihood for general state-space models"' by Huerzler and Kuensch and "Monte Carlo smoothing and self-organising state-space model" by Kitagawa and Sato. Here [ps file] is a more comprehensive list of references on the subject.
• Strong Consistency and the martingale central limit theorem for AR processes (with extension to ARCH)

Here is a scanned version of Tata Subba Rao's book: An Introduction to Bispectral Analysis and Bilinear Time Series Models By Tata Subba Rao and M. M. Gabr.