Syllabus. Statistics 221: Time Series Analysis, Prof. Rick Paik Schoenberg.

Lectures: Tues, Thur 12:30-1:45pm, Boelter 5422.

Text: Time Series Analysis and Its Applications, With R Examples, 2nd edition
by R. Shumway and D. Stoffer. Springer, NY, 2006.
There may also be supplemental readings distributed in class.

Office hours: Tuesdays, 10-11am, MS 8965. Or by email appointment.

email: frederic@stat.ucla.edu

Course webpage: http://www.stat.ucla.edu/~frederic/221/F06

Description: Statistics 221 will explore the methods used in the analysis of numerical time series data. The course will be both theoretical and applied. Students will learn standard concepts in temporal and frequency analysis, followed by some more recent topics such as wavelets and chaos. Examples will be provided throughout the instruction of the course, and students will implement the techniques discussed in class, using real data sets. Dedicated students should come away with an in-depth understanding of statistical concepts related to time series, as well as a thorough comprehension of how and when to implement various techniques in practice.

The course is designed for graduate students in statistics or mathematics, and may also be taken by students from other disciplines provided those students have sufficient mathematical and statistical backgrounds. Some experience in statistical computing is recommended.

Grading:
Midterm exam (40%) -- Thur, Nov 16, in class.
Written project (50%) -- due Thur, Dec 7, in class.
Oral Presentation/participation (10%) -- last week of class.

Attendance in class is generally not mandatory and not counted as part of the grade. However, the last week of class is an exception: all students MUST attend class, on time, for the final week.

There will most likely be no extensions for the project or presentation and no make-up for the exam. Students who are unable to make these dates or otherwise fulfill the course requirements must consult with the instructor in advance, if possible.

A rough, preliminary outline of the class is given below.

1) Introduction (day 1)
a) terminology
b) examples
c) objectives

2) Descriptive techniques (week 1)
a) time plots & transformations
b) curve fitting
c) filtering
d) differences
e) periodic components
f) autocorrelation

3) Basic stochastic models (week 2-3)
a) white noise
b) random walks
c) AR
d) MA
e) ARMA
f) General linear models

4) Time domain analysis (weeks 4-5)
a) correlogram
b) smoothing
c) Box-Jenkins approach
d) significance testing
e) residual analysis
f) nonparametric techniques
g) forecasting & linear prediction

5) Spectral analysis (weeks 6-7)
a) spectral density, spectrum
b) Fourier transform, FFT
c) periodogram
d) smoothing techniques
Written Project:
Find a time-series dataset and analyze it using some of the relevant methods described in class. Your report should contain 4-6 pages of text, followed by as many figures as appropriate. You may include as many figures as you like, but the text itself should not exceed 6 pages, double-spaced.

In selecting your dataset choose something that interests you, and try to have a main, answerable question in mind. Begin your paper with an introduction, a description of your data and how they were obtained, and a summary of the main question(s) to be addressed in your paper. Then summarize your analyses, paying special attention to any assumptions you are making and the plausibility of those assumptions. Conclude by assessing how effective the methods you used were in helping to answer your main question(s).

Oral presentations of project results will take place on the last week of class. These will involve simply presenting a clear and concise 5-minute summary of your dataset and 1 or 2 of your main results. Do not try to show all the results from your paper in your 5-minute oral presentation!!! You should only show around 4 figures in your presentation.