HW No. 1: Redo Figures 1.6, 1.7 and 1.8 from Chapter 1 in P&W book. Also from P&W book,
Chapter 1, Sec. 1.7: Problem 1, 2(a), 3. Due January 30. (problem 2(b) is bonus).
HW No. 2: Chapter 2 in P&W book. page 82, problem 18 and 19 parts (a), (b) and (c). Page 83, problem 21 parts (a),
(b) and (c). Due for February 13.
Class Description
This course will be about modern methods for time series data
that are appropriate to model non-stationary data and to
perform monitoring, intervention and forecasting. Mainly the focus will be the
analysis and application of classes of dynamic linear models (DLMs) from a
Bayesian point of view. We also place some focus on AR, ARMA modeling ideas.
I will consider aspects of spectral analysis/periodogram analysis.
This course is intended to be of wide interest to students that want to
learn more on time series, Bayesian modeling and computation with Markov Chain Monte Carlo (MCMC)
methods.
Prerrequistes
Some background in probability, regression and inference but mainly a desire to learn about Bayesian Time
Series. The course is intended for Masters (second year and above) and/or PhD students in
statistics with a serious interest in
modern time series models beyond the traditional/classical methods.
I will start by covering basic ideas in time series. Read for example sections
1.1-1.4 of the Prado and West textbook (mentioned below) or some of my notes on my Stat 581 page mentioned
below.
Class Development
The lectures will be mainly discussion of the main ideas, overview, perspective and for presentations. Out
of lecture work will involve mastering material from the text and reading related research
articles, homework assignments and development of class presentations. The class presentations could relate
to some of the advanced material in the text. You're also welcome to use your own data project and show how
advanced time series can be applied in such case. Presentations can be individual or in teams of 2
members. Each team (or individual) will lead the discussion of one or two lectures in the semester.
I will lecture for about 20-22 classes (focused on Ch.1-5 of the textbook) and rest will run as a graduate seminar.
A write-up based on your presentations is welcomed but optional. Here is a list of possible topics for
presentations:
Sequential Monte Carlo-Particle Filter Methods (Ch. 6 P&W) Yonghua Wei in charge
Markov Switching Models (Ch. 7)
Univariate Stochastic Volatility (Ch. 7)
Multiprocess Models (Ch. 7)
Vector AR and ARMA models (Ch. 9)
Multivariate DLMs (theory) (Ch. 10)
Time varying covariances (Ch. 10)
Applications to financial Time Series (Ch. 10)
Dynamic graphical models (Ch. 10)
Spatial-temporal models (not in book).
Any topic you suggest in time series that has some serious methodological consideration and that I approve.
ONE PAGE PROPOSAL OF CLASS PROJECT DUE FEBRUARY 20
Computing
Some R code will be provided for some of the class examples. Some of the book material/examples is available
in Matlab.