096425- TIME SERIES AND FORECASTING

Fall semester, 2006/7

• Instructor: Robert J. Adler
  
  
• Teaching Assistant: Anna Levit
  
  
• Times and places:
  Lectures: Tuesdays, 08:30-10:30, Bloomfield Building (IE&M) 310
  Exercise class: Tuesdays, 10:30-11:30, Bloomfield Building (IE&M) 310
  
  
• 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.
  
  

• Grade: The final grade will be made up as follows:

  Component	% of final grade
  Mid term exam (mid January)	40
  Homework exercises	30
  Project	30

• Prerequisites: This course is aimed at graduate and serious undergraduate students with an interest in quantitative methods.
  The appropriate prerequisites are a course 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.
  

  NOTE: Serious graduate students in Statistics and others wanting to a better understanding of the theoretical basis of time series analysis should enrol for the course Seminar in Time Series 098425 rather than this course. The structure of 098425, for this semester, will involve attending the lectures of 096425, doing basically the same homework and the same project, attending one additional lecture at a higher level (also open to registrants in 096425) and doing a slightly different exam.
  For these students 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.
  Note: Due to the significant overlap between the two courses, students will NOT be allowed to enrol in both 096425 and 098425 during this semester.

• Textbook: There are many excellent textbooks in time series analysis, and two of the best were written by Peter Brockwell and Richard Davis. I will be using Introduction to Time Series and Forecasting .
  Material for the additional lectures aimed at the Seminar in Time Series 098425 students will come from the more serious version of this book: Time Series : Theory and Methods .
  
  
• 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.

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COURSE OUTLINE

The following outline is not cast in stone and will probably a little during the semester. But it should give you a good idea of where we are heading, and when.

The chapter references in the third column are to the textbook Introduction to Time Series and Forecasting and in the fourth to Time Series : Theory and Methods

Weeks	Topics	Chapter	Chapter
1	Examples, objectives, general approaches. Removing trend and/or seasonality.	1.1-1.6	1.1,1.2,1.4
2	Stationary random processes: the autocorrelation function; the sample mean and sample autocorrelation function; Bartlett's formula.	2.1-2.4	1.3, 1.5, 7.1, 7.2
3	Stationary processes and best linear mean square prediction.	2.5	2.1-2.3
4	ARMA processes and their autocorrelation and partial autocorrelation functions.	3.1-3.3	3.1-3.4
5-6	Intro to spectral theory and linear filtering. Spectral densities of ARMA processes.	4.1-4.4	4.1-4.4
7	Recursive prediction of ARMA processes.	2.5, 5.4	5.1-5.5
8	Parameter estimation for ARMA processes.	5.1-5.5	8.1-8.9
9	Model-building with ARIMA processes.	6.1-6.6	9.1-9.6
10	Multivariate ARMA processes.	7.1-7.4	11.6-11.8
11	State space models	8.1-8.4	12.1
12	Transfer functions models	10.1	12.2
13-14	Everything else: The models we left out, infinite variance, long term memory, ...

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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.