S8602027X: Computational Finance
Instructor:James
Gentle
email: jgentle@gmu.edu
Lectures: Tuesdays and Thursdays 13:30  16:55, E206
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 threshold
models; and, as time permits, 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
Some knowledge of statistical theory and methods is a
prerequisite.
Knowledge of advanced calculus and differential equations is
also required.
Some general background in finance will be useful.
Main text
The text is Analysis of Financial Time Series,
third edition, by Ruey S. Tsay (2010).
ISBN 9780470414354
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. Another important data source is the US Federal Reserve
Economic Data (FRED) provided by the
Federal Reserve Bank of
St. Louis.
Approximate schedule
May 19
May 21
 Review statistical tests of distributions.
(beginning on slide 5 of revised previous lecture)

Analysis of returns and some simple time series models.
 the autocorrelation function (ACF)
 stationarity
 linear models for time series
 nonstationarity
 Exercises (due May 31)
I had an error in 4(a). It would also affect 4(b).
I said "prices" and I meant "log returns".
This was my error, so I will accept an analysis of prices, as originally
stated. (Of course I will also accept an analysis of log returns, or even
simple returns.)
The important thing is that you understand the tests, and they are done the
same way for prices or returns or just any time series. (Of course the conclusions
will be different.)
Thanks to Zhenhua for catching this error!
May 26
 More on ARMA models (beginning with slide 27 of previous lecture)

Forecasting, choosing models, and simulation.
 Forecasting origins and horizons; forecast errors.
 Data sources. US Federal Reserve Economic Data (FRED), provided by
Federal Reserve Bank of St. Louis
This site provides US economic data of many types; interest rates, GDP,
unemployment, and so on. Also, a limited amount of international economic
data. The data are available in text files or raw csv files or as graphs.
 Exercises (due June 9)
May 28
 Corrections, comments: slide 22 of "Returns, distributions,..." (May 19)
pvalue = pt(abs(tc),T1)+(1pt(abs(tc),T1))
 More on forecasting and simulation (beginning with slide 4 of previous lecture)
 Volatility.

Not constant.

Measuring volatility.

Exercises (due June 9)
June 2
June 4

More on GARCH models and variations (begin around slide 14 from previous lecture).
June 9
 R: review; questions?
 Comments on implied volatility exercises. (Last slide from lecture of May 28.)

More on variations of GARCH models and fitting the models (begin on slide 69 from
lecture of June 2).

Nonlinear models.

Exercises. (Due June 16 but will not be graded for credit)
June 11
June 16
June 17
15:0017:00 Twohour exam on material covered through June 16.
Closed book and notes, except for one sheet (front and back) of
prewritten notes.
Approximately half of the exam will involve programming in R.
Solutions.

Sample exam (Think of this as a study guide; it is longer than the real thing! Also,
since this is just an example, answers to some of the questions might be found in the
statements of other questions. Do not expect this on the real thing.)
 Sample R usage exam (There is no real R ``programming'' in this, but it does
involve basic R functions and operations.)
June 18