Stat 579: Topics in Statistics. Advanced Time Series

Department of Mathematics and Statistics.
University of New Mexico.


Spring Semester 2014




Instructor: Gabriel Huerta Office: 314 SMLC
email: ghuerta "at" stat.unm.edu
Class Time: T R. 2:00-3:15pm Classroom: Dane Smith Hall (DSH) 234
Office hours: TR. 12:30-1:45pm
Webpage: http://www.stat.unm.edu/~ghuerta/tseries/stat582.htm


Homeworks
  • 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.
    Books
  • Prado, R. and West, M. (2010) Time Series. Modeling, Computation and Inference. CRC Press.
  • (main text).
  • Petris, G., Petrone, S. and Campagnoli, P. (2009) Dynamic Linear Models in R Springer Verlag.
  • West, M. and Harrison, P.J. (1997), Bayesian Forecasting and Dynamic Models , Springer-Verlag, (2nd Edition).

  • Other Class Material
    Some will be provided through our UNM learn page Here are some links that will be used too,
  • Handouts and class notes
  • Support Duke Univ. Webpage .
  • Data sets
  • Research papers
  • Stat 581: page
  • The R-DLM package

  • Grading
  • Homeworks and class presentations. Good portions of this class will run as a graduate seminar.

  • Schedule
  • Introduction to Time Series. Premier on Bayes inference. (Chapter 1 P&W book, Week 1 and 3 notes Stat 581 webpage.)
  • Bayes AR estimation. Model order selection. AR stuctured priors (Chapter 2 P&W book. Stat 581, Week 8-9 notes) .
  • Here is a summary for Chapters 1 and 2 , file
  • Frequency analysis (Chapter 3, P&W book, Stat 581 notes weeks 13-14)
  • Dynamic Linear models. (Chapter 4, P&W book. Notes and code on DLMs from this page. Giovanni Petris' R-DLM package and Notes by Prado).
  • Time varying AR models (Chapter 5, P&W book).