Welcome to CSI 678 / STAT 658

Time Series Analysis and Forecasting

Fall, 2010

Instructor: James Gentle

Lectures: Thursdays 4:30pm - 7:10pm, Innovation Hall 207

If you send email to the instructor, please put "CSI 678" or "STAT 658" in the subject line.

Course Description

Time series analysis is used for diverse applications in economics, the social sciences, the physical and environmental sciences, medicine, and signal processing. This course presents the fundamental principles of time series analysis including mathematical modeling of time series data and methods for statistical inference. Models in both the time domain and the frequency domain will be developed and explored.

An integral part of the course is the use of R for simulation, calculation, and implementation of time series analysis techniques. Students may use other software for assignments if they are familiar with the software.


The prerequisites for this course include STAT 544 or ECE 528 or equivalent multivariable calculus-based graduate course in Applied Probability or Random Processes.

Text and other reading materials

The text is R. H. Shumway and D. S. Stoffer, Time Series Analysis and Its Applications With R Examples, second edition, Springer-Verlag, 2006. ISBN 978-0-387-29317-2. The website for the text is http://www.stat.pitt.edu/stoffer/tsa2/.

The software used in this course is R, which is a freeware package that can be downloaded from the Comprehensive R Archive Network (CRAN). It is also available on various GMU computers in student labs.

The text provides examples in R and the associated website provides data files and R scripts that can be downloaded. If students are familiar with other software, they may find it instructive to translate the R scripts into the other language. Students may use other software for assignments, but use of other software will not be covered in the course.

No prior experience in R is assumed for this course. A good site for getting started with R, especially for people who are somewhat familiar with SAS or SPSS, is Quick R.


Student work in the course (and the relative weighting of this work in the overall grade) will consist of

  • homework assignments (30)
  • two midterm exams (40)
  • final exam (30)


    Each homework will be graded based on 100 points, and 5 points will be deducted for each day that the homework is late. Start each problem on a new sheet of paper and label it clearly. Homework will not be accepted as computer files (and certainly not as faxes!); it must be submitted on paper.

    Academic honor

    Each student enrolled in this course must assume the responsibilities of an active participant in GMU's scholarly community in which everyone's academic work and behavior are held to the highest standards of honesty. The GMU policy on academic conduct will be followed in this course.

    Collaborative work

    Students are free to discuss homework problems or other topics with each other or anyone else, and are free to use any reference sources. Group work and discussion outside of class is encouraged, but of course explicit copying of homework solutions should not be done.

    The details of the schedule will evolve as the semester progresses. Basically, the plan is to cover Chapters 1 through 4 of the text fairly thoroughly, plus selected topics from Chapters 5 through 7 if time permits.

    Week 1, September 2

    Course overview; notation; etc.
    The R program.
    Nature of time series data.
    Means, autocovariance, autocorrelation, cross-covariance, cross-correlation.
    Simulation in R.
    Assignment 1, due September 9: In Shumway and Stoffer: problems 1.1, 1.2, 1.3, 1.4, 1.6.

    Week 2, September 9

    Estimation of time series parameters.
    Vector-valued time series.
    Convergence of sequences of random variables (estimators).
    Exploratory data analysis and comparison of statistical models.
    Regression and time series.
    Assignment 2, due September 16: In Shumway and Stoffer: problems 1.8, 1.13, 1.19, 1.22, 1.25, 2.1.

    Week 3, September 16

    R functions for data-handling.
    Smoothing time series.
    Assignment 3, due September 23: In Shumway and Stoffer: problems 2.6, 2.9, 2.11. Also try problem 2.4 if you know what the "Gaussian regression model" is. It does not seem to be defined in the text, and I have not discussed it yet.

    Week 4, September 23

    More on exploratory data analysis, regression, and smoothing.
    Assignment 4, due October 7: In Shumway and Stoffer: problems 1.27, 1.30, 2.2, 2.8, 2.10.
    (Problems 1.27 and 1.30 address material that will not be on the exam; the other problems are for review, and you should work them first.)

    Week 5, September 30

    Inclass midterm exam.
    Closed book and closed notes. One hour and a half.
    Covers material in Shumway and Stoffer through approximately the end of Chapter 2. (Will not cover asymptotic properties.)
    Assignment 5, due October 14: In Shumway and Stoffer: problem 1.20 with the addition:
    use your estimated value of the ACF to set a 95% two-sided confidence interval for the ACF, using Property P1.1 on page 30.

    Week 6, October 7

    Sample ACF, CCF, and their large-sample properties.
    ARMA models; basic setup and notation.
    Difference equations.
    Assignment 6, due October 14: In Shumway and Stoffer: problems 3.1, 3.2, 3.3, 3.5, 3.6. (In 3.3, you do not have to address causality or invertibility, because I did not have time to discuss those properties.)

    Week 7, October 14

    ARMA models; causal and invertible.
    ACF and PACF.
    Forecasting using ARMA models.
    Assignment 7, due October 21: In Shumway and Stoffer: problems 3.8, 3.9, 3.13, 3.14.

    Week 8, October 21

    Estimation in ARMA models.
    Nonstationary series; integration; ARIMA models
    Fitting models.
    Seasonal ARIMA.
    Assignment 8, due October 28: In Shumway and Stoffer: problems 3.17, 3.19, 3.26, 3.29, 3.36.

    Week 9, October 28

    More on ARIMA models.
    No assignment to turn in

    Week 10, November 4

    Lecture (approx 1 hour)
    Inclass midterm exam.
    Closed book and closed notes.
    Covers material in Shumway and Stoffer through approximately the end of Chapter 3.
    Assignment 9, due November 11: In Shumway and Stoffer: problems 3.28, 3.30, 3.33.

    Week 11, November 11

    Review midterm; summary of ARIMA modeling.
    The periodogram and spectral density.
    Assignment 10, due November 18: In Shumway and Stoffer: problems 4.1, 4.4, 4.5, 4.6.

    Week 12, November 18

    The periodogram and the discrete Fourier transform.
    Nonparametric spectral estimation.
    Cross spectra.
    Assignment 11, due December 2: In Shumway and Stoffer: problems 4.8, 4.9, 4.12, 4.13.

    November 25: No class.

    Week 13, December 2

    Linear filters.
    Parametric spectral estimation.
    Assignment 12, due December 9: In Shumway and Stoffer: problems 4.18, 4.19, 4.27, 4.30.

    Week 14, December 9

    Lagged regression.
    Optimal signal extraction.

    December 16

    4:30pm - 7:15pm Final Exam.
    Closed book and closed notes.