CSI 779 / STAT 789

Topics in Computational Statistics:

Analysis of Financial Time Series

Spring, 2014

Thursdays 4:30 to 7:10.

Innovation Hall 211

Instructor: James Gentle; email: jgentle@gmu.edu

Time series analysis is one of the most important statistical methods in finance and economics. This course will cover the basic ARMA models; conditional heteroscedastic models, with an emphasis on GARCH models; nonlinear models such as TAR; models of market microstructure; and continuous time models.

The emphasis will be on the mathematical models, the statistical methods, and the computations, rather than on topics in the domain of finance.


While some background in finance would be useful, it will not be necessary. Some knowledge of statistical theory and methods (roughly equivalent to CSI 672 / STAT 652 and STAT 554) is a prerequisite. Knowledge of advanced calculus and differential equations is also required.

Main text

The text is Analysis of Financial Time Series, third edition, by Ruey S. Tsay (2010). ISBN 978-0-470-41435-4
The general flow of the course follows this text. We will cover most of the first 5 chapters, plus assorted material from other chapters, and supplementary material.


The main software used will be R, which can be obtained without cost from the R Project for Statistical Computing.

Students who are familiar with SAS, Matlab, or other statistical packages are encouraged to explore the use of these packages for analysis of financial time series. These other packages may be used for the assignments if the packages provide the required functionality, but examples discussed in class will use R.


Data, of course, are the raw materials of any statistical analyses. There is a wealth of easily accessible financial data. For this course we will generally be interested in daily, weekly, or monthly closing prices and the volume corresponding to the periods. An easy source of the kind of data we will use is Yahoo. Also, we will use data that the author of the text has collected into files at his website.


Performance in the class will be evaluated based on

  • midterm exam (30%)
  • final exam (40%)
  • a number of homework assignments (30%)

    Students may discuss the homework assignments, but what is submitted for grading must be written by the individual students.

    Approximate schedule

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

    Lecture 1, January 23

    Assignment 1, due January 30: Exercises 1.1 through 1.4 in text with the following exceptions. For 1.1, 1.3, and 1.4, use the ending date of December 31, 2013. (Use the same starting date, as given in the text.)

    Lecture 2, January 30

  • Analysis of returns and some simple time series models.
    Assignment 2, due February 6

    Lecture 3, February 6

    More on ARMA models.
    Seasonal models.

    Assignment 3, due February 20 from the text, pages 104-106, exercises
    2.5 but use IBM data from 2008-1-1 to 2013-12-31,
    2.10 (data are in w-Aaa.txt and w-Baa.txt at author's website),

    February 13

    Class canceled because of weather.

    Lecture 4, February 20

    More on volatility.
    Conditional heteroscedasticity.
    ARCH and GARCH models.
    Slides used in lectures 4, 5, and 6 .

    Assignment 4, due February 27.

    Lecture 5, February 27

    More on GARCH models.

    Lecture 6, March 6

    More on GARCH models and variations.

    Assignment 5, due March 27.

    March 13

    Spring break; class does not meet.

    Meeting 7, March 20

    Closed book, closed notes, and closed computers except for one sheet (front and back) of prewritten notes.

    Lecture 7, March 27

    Nonlinear models.
    Threshold models.

    Lecture 8, April 3

    More on nonlinear models.
    A good review article for APARCH and other models is Bollerslev, T., R.F. Engle and D.B. Nelson (1994), ARCH Models, in R.F. Engle and D. McFadden (eds.), Handbook of Econometrics, Volume IV, 2959-3038. Amsterdam: North-Holland.
    A good summary of the various models and their relationships to each other is at http://public.econ.duke.edu/~boller/Papers/glossary_arch.pdf.

    Assignment 6, due April 10: Exercises 4.1, 4.2, 4.4 in text with the following exceptions. For 4.1 use the ending date of December 31, 2013, (and the same starting date as given in the text) for the daily returns of JNJ stock. For 4.2 use the starting date of January 1, 1962, and the ending date of December 31, 2013, for the monthly returns of GE stock.
    The R functions needed for this assignment are in the fGarch package; see the last few slides on the lecture for this week (which we did not get to in class!)

    Lecture 9, April 10

    More on models: local fitting; neural nets.
    Multivariate time series.

    Assignment 7, due April 17: from the text, page 225, exercise 4.5, and page 462, exercises 8.1 and 8.2.

    Lecture 10, April 17

    Multivariate time series.

    Lecture 11, April 24

    More on multivariate time series.

    Assignment 8, due May 1: Exercist 8.7, page 463.
    You may find the following code useful to get started.

    url <- "http://faculty.chicagobooth.edu/ruey.tsay/teaching/fts3/m-gs1n3-5304.txt"
    x <- read.table(url)
    y <- cbind(x$V1,x$V2)
    ps <- VARselect(y)
    ### use BIC (also called SC)
    p <- as.numeric(ps$selection[3])
    fit <- VAR(y, p=p)

    The only function from the urca package is ca.jo.
    You use VARselect, VAR, VECM, etc. from the var package.

    Lecture 12, May 1

    Continuous time models.

    Lecture 13, May 6 (Tuesday)

    Continuous time models. Black-Scholes options pricing.
    Other topics.

    May 10 (Saturday)

    4:30pm - 6:30pm Final Exam.
    Closed books, notes, and computers except for one sheet (front and back) of prewritten notes.