Welcome to CSI 678 / STAT 658

Time Series Analysis and Forecasting

Fall, 2012

Instructor: James Gentle

Lectures: Thursdays 4:30pm - 7:10pm, Innovation Hall 133

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. The emphasis, however, will be on the time domain.

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 an equivalent multivariable calculus-based graduate course in Applied Probability or Random Processes.

Text and Software

The text is Time Series Analysis and Its Applications: With R Examples third edition, 2010, by Robert H. Shumway and David S. Stoffer. ISBN # 978-1441978646
Authors' website for text.

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.

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.

The text provides examples in R, and the associated website provides data files and R scripts that can be downloaded. The authors have also provided an R package, astsa. In many assignments, the R function library(astsa) will be used to load the package, along with its built-in datasets.

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, and the data used in the text will have to be obtained from portable files, rather than as R datasets, which are available directly from the authors' package.


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

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


    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.

    Note that other courses at GMU may have different restrictions on discussions among students relating to course content.


    The details of the schedule will evolve as the semester progresses.

    Week 1, August 30

    Assignment: Read Shumway and Stoffer, Sections 1.1 through 1.6. Look over Appendix R.
    Assignment 1a, due September 6: In Shumway and Stoffer: problems 1.1.
    Assignment 1b, due September 13: In Shumway and Stoffer: problems 1.2, 1.3, 1.4, 1.6.

    Week 2, September 6

    Assignment: Read Shumway and Stoffer, Sections 1.7 through 2.1. Assignment 2, due September 13: In Shumway and Stoffer: problems 1.8, 1.13, 1.19, 1.22, 1.25, 2.1.

    Week 3, September 13

    R functions for data-handling.
    Smoothing time series.
    Gaussian regression models.
    Modified Assignment 3, due September 20: In Shumway and Stoffer Third Edition: problems 2.6, 2.11(a),(b),(c).

    All problem numbers henceforth will refer to the problems in the Third Edition of the text.

    Week 4, September 20

    Differencing, detrending, etc.
    More on exploratory data analysis, regression, smoothing, and comparison of statistical models.
    Discuss problems from the text.
    Modified Assignment 4, due October 11: In Shumway and Stoffer: problems 2.2, 2.8, 2.9.

    Week 5, September 27

    Discuss homework and any miscellaneous questions.
    Use of sample ACF and CCF for statistical inference.
    Example 2.9: a quick introduction to the frequency domain.
    Assignment 5, due October 11: In Shumway and Stoffer: problem 1.21 with the addition:
    use your estimated value of the ACF to set a 95% two-sided confidence interval for the ACF, using Property 1.1 on page 29.

    Week 6, October 4

    Inclass midterm exam.
    Closed book and closed notes.
    Covers material in Shumway and Stoffer through approximately the end of Chapter 2, except for the properties of matrices in least squares analysis, the periodogram, and the asymptotic properties of sample statistics.

    Week 7, October 11

    Sample ACF, CCF, and their large-sample properties.
    ARMA models; basic setup and notation.
    Difference equations.
    Causality and invertibility
    Assignment 6, due October 18: In Shumway and Stoffer: problems 3.1, 3.2(a) (b) (c) (d) (e), 3.4(a) (b), 3.5, 3.7(a) (b).

    Week 8, October 18

    More on ARMA models (Sections 3.4, 3.5, 3.6).
    ACF and PACF.
    Assignment 7, due November 1: In Shumway and Stoffer: problems 3.8, 3.9, 3.10, 3.11, 3.16.

    Week 9, October 25

    Interesting and useful sources of data:
  • General data assembled by the St. Louis Fed: research.stlouisfed.org/fred2/.
  • Other data from the Fed Board of Governors: www.federalreserve.gov/econresdata/statisticsdata.htm.
  • Interest rate data from the Fed Board of Governors: www.federalreserve.gov/econresdata/statisticsdata.htm.
  • Other data from the Fed Board of Governors: www.federalreserve.gov/releases/h15/update/.
  • Data from the World Bank: data.worldbank.org/.
  • Stock price data: finance.yahoo.com/.
    Get data as .csv file; read in R by read.csv.
    Can read data directly from web.
    There is a useful R program written by John Nolan that is especially useful for reading and manipulating stock prices from Yahoo.

    Forecasting using ARMA models.
    More on ARMA models and ARIMA models (Sections 3.6, 3.7, 3.8, 3.9).

    Assignment 8, due November 1: Download the quarterly US GDP in chained billions of dollars (to 1 decimal place) from 1947-01-01 to 2012-07-01. (You can obtain it from the St. Louis Fed's FRED site.)
    (a) Make an R ts object to contain the data. (Frequency =?).
    (b) Plot the raw data and comment on any obvious trends or seasonalities.
    (c) Attempt to remove any trend by differencing. Plot and comment.
    (d) As with much economic data, diff log may be a useful transformation. Make this transformation and plot the transformed data.
    (e) Compute the sample ACF and PACF.
    (f) Fit an AR(p) to the diff logs (what p did you choose, and why?). Obtain the residuals and make a QQ plot against a normal distribution (use qqnorm). Comment.
    (g) Fit an MA(q) to the diff logs (what q did you choose, and why?). Obtain the residuals and make a QQ plot against a normal distribution. Comment.
    (h) Fit an ARIMA(p,d,q) model, and discuss.
    (This assignment is similar to Example 3.38 in Shumway and Stoffer.)

    Week 10, November 1

    More on forecasting.
    Seasonal models.
    General review of ARIMA models.
    Assignment 9, due November 8: In Shumway and Stoffer: problems 3.19, 3.28, 3.33, 3.35, 3.36.

    Week 11, November 8

    The periodogram and spectral density.
    Assignment 10, due November 15: In Shumway and Stoffer: problems 4.1, 4.4, 4.5, 4.6.

    Week 12, November 15

    The periodogram and the discrete Fourier transform.
    Nonparametric spectral estimation.
    Cross spectra.
    Assignment 11, due November 29: In Shumway and Stoffer: problems 4.8, 4.9, 4.12, 4.13.

    November 22: No class.

    Week 13, November 29

    More on the periodogram and nonparametric spectral estimation.
    Linear filters.

    Assignment 12, due December 6 (but will not be collected).
    In Shumway and Stoffer: problems 4.18, 4.19, 4.27, 4.29.

    Week 14, December 6

    Additional topics (slide 23 and following, from the leture notes for week 13.)
    Parametric spectral estimation.
    Lagged regression.
    Optimal signal extraction.
    General review.

    December 13

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