Outline.  
Statistics 221:  Time Series Analysis, Prof. Schoenberg. <br><br>

Lectures:  MWF 12-12:50pm, Math-Science 5217.<br><br>

Text:  The Analysis of Time Series:  an Introduction, 5th edition<br>
by C. Chatfield; Chapman & Hall: London, NY, 1996.<br>
There will also be supplemental readings distributed in class.<br><br>

Office hours:  Tuedays, 12-1pm, and Tuesdays 1:40-2:30pm, MS 6167.<br><br>

email:  frederic@stat.ucla.edu<br><br>

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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.<br><br>
   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.  Statistics M100abc (or equivalent) is a prerequisite and
some experience in statistical computing is strongly recommended.<br><br><br>
A rough, preliminary outline of the class is given below.<br><br><br>

1) Introduction (day 1)<br>
    a) terminology<br>
    b) examples<br>
    c) objectives<br><br>

2) Descriptive techniques (week 1)<br>
    a) time plots & transformations<br>
    b) curve fitting<br>
    c) filtering<br>
    d) differences<br>
    e) periodic components<br>
    f) autocorrelation<br>
    g) moments, cumulants<br><br>

3) Basic stochastic models (week 2-3)<br>
    a) white noise<br>
    b) random walks<br>
    c) ARMA<br>
    d) mixed models<br>
    e) GLM<br><br>

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

5)  Spectral analysis (weeks 6-7)<br>
    a) spectral density, spectrum<br>
    b) Fourier transform, FFT<br>
    c) periodogram<br>
    d) smoothing techniques<br>
    e) consistent estimation<br>
    f) confidence intervals<br><br>

6)  Other topics (weeks 8-10)<br>
a) spectral modelling<br>
b) linear systems<br>    
c) GARCH<br>
d) wavelets<br>
e) chaos <br>
f) computational methods <br>    
g) applications in finance, 
signal processing, image analysis, neuroscience, and other areas.<br>
<br><br><br>

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