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Instructor:
Robert J. Adler
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Teaching Assistant:
Anna Levit
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Times and places:
Lectures: Thursday, 13:30-15:30, Bloomfield Building (IE&M) 310.
Exercise class: Wednesday, 09:30-10:30, Bloomfield Building (IE&M) 153. (There will be no exercise class in the first week of the semester.)
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Syllabus: The formal syllabus is
"Stationarity, auto-correlation, auto-regression processes, moving averages, parameter estimation, Yule-Walker equations, maximum
likelihood estimation, prediction, spectral representation,
spectral estimation".
For more details, see the detailed timetable below.
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Grade:
The final grade will be made up as follows:
| Component |
% of final grade |
| Final exam |
50 |
| Homework exercises |
50 |
(The homework exercises will contain a project component.)
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Prerequisites: This is a graduate course open to
serious undergraduates. The appropriate prerequisites are a
course in Stochastic Processes such as
Stochastic Processes 098413 and a course in
Statistics such as Theory of Statistics 098414 or
Applied Statistics 098417. Some background in
Analysis such as in
Elements of Modern Analysis for Electrical Engineering 108324
is also recommended.
A strong undergraduate should be able to get by with courses such as
Stochastic Models in Operations Research 094314 for the Stochastic
Processes background and Data Mining 096411 or another post-introductory
Statistics course for the Statistics
background, as well as being prepared to spend a little extra time during the
semester reading up on background.
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Textbook: There are many excellent textbooks in time series
analysis, and two of the best were written by Peter Brockwell and
Richard Davis. Time Series : Theory and Methods
is the book I will be using, although I will not go into the full details of
all its arguments. There is a much simpler version of this book
Introduction to Time Series and Forecasting which has basically the same
material without the proofs and is often a good place to see a
concept for the first time.
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Computing: The homework (and especially the project) will
require the use of some sort of package for the analysis of time series.
Virtually all the usual statistical packages have such modules, as does
Matlab. The books of Brockwell and Davis mentioned above come with a very
easy to use package that will be more than sufficient for the course. Each
student will be able to make his/her own choice of software.
COURSE OUTLINE
The following outline is not cast in stone: I will probably change it
depending on who takes the course and what we turn out to be
interested in. But it should give you an idea of where we are
heading, and when.
The chapter references in the third column are to the textbook
Time Series : Theory and Methods
| Weeks |
Topics |
Chapter |
| 1 |
Examples, objectives, general approaches.
Removing trend and/or seasonality. | 1.1,1.2,1.4 |
| 2-3 |
Stationary random processes: the autocorrelation function; the sample mean and sample autocorrelation function;
Bartlett's formula. | 1.3, 1.5, 7.1, 7.2 |
| 4 |
Stationary processes and best linear mean square prediction.
|
2.1-2.3 |
| 5 |
ARMA processes and their autocorrelation and partial autocorrelation functions.
| 3.1-3.4 |
| 6-7 |
Introduction to spectral theory and linear filtering. Spectral densities of ARMA processes. |
4.1-4.4 |
| 8 |
Recursive prediction of ARMA processes. | 5.1-5.5 |
| 9-11 |
Parameter estimation for ARMA processes. | 8.1-8.9 |
| 12-14 |
Model-building with ARIMA processes. | 9.1-9.6 |
ADDITIONAL INFORMATION
If you want extra information, you can reach me in the office at
8294503, at home at 8251794 (but not Shabbatot or Hagei Yisrael), or,
most reliably, at
robert@ieadler.technion.ac.il.
If you are reading this in hard copy rather than on the web, go to
the Teaching section of my homepage at ie.technion.ac.il/Adler.phtml
to get the hyperlinks.
Depending on consumer interest, this course may be followed in the second semester by a more advanced continuation, Seminar in Time Series 098425. The syllabus
for the last time I taught that course is