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.
Prerequisites
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.
Software
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
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.
Grading
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.
- the autocorrelation function (ACF)
- stationarity
- linear models for time series
- nonstationarity
Assignment 2,
due February 6
Lecture 3, February 6
More on ARMA models.
Seasonal models.
Slides.
Assignment 3, due February 20
from the text, pages 104-106, exercises
2.1,
2.3,
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),
2.11,
2.12
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
Midterm:
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.
library(var)
library(urca)
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.