STAT 464/864 | Time Series Analysis and Spectrum Estimation

The description of the course given in the curriculum manual states:

Autocorrelation and autocovariance, stationarity; ARIMA models; model identification and forecasting; spectral analysis. Applications to biological, physical and economic data.

The emphasis in the course will be on understanding ideas rather than speeding through the material. The following outline of topics is therefore subject to change as course progresses.

Expectations for undergraduate students and graduate students will be different, although both groups should expect to complete regular homeworks. In addition, some familiarity with coding will be required by the conclusion of the course (and tutorials will be offered to aid students in their skill development).

Course Reference Materials

Textbook Introduction to Time Series and Forecasting, Brockwell and Davis, 2nd Edition. Available at Campus Bookstore ($85.41 used) or as a (free) e-book in pdf from the Queen's Library subscription to SpringerLink. You will need to use the Queen's WebProxy service to access the e-book from off-campus.
(additional readings on course reserve) Time Series: Theory and Methods, P.J. Brockwell and R.A. Davis. Graduate-level version of our textbook, more detail on theory. Also available via SpringerLink
Spectral Analysis for Physical Applications, D.B. Percival and A.T. Walden. Arguably the best text available for the second half of the course, and definitely the best for actual algorithm implementation.
(additional readings, e-book) Time Series Analysis and Its Applications (with R Examples), R.H. Shumway and D.S. Stoffer. Well-written text with good R examples to help in learning to do practical data analysis.

Additional Materials

Syllabus   Syllabus for course.
Data   Data Sets for assignments and from in-class examples.
Project   Description and Marking Scheme


Introduction to Time Series
Sept 12 Introduction, examples of time series
13 Simple models, the autocorrelation function. Trends.
15 Estimation of trend without seasonality. Slides
19 Estimation of trend without seasonality, SES and differencing. R Code
20 Estimation of trend with seasonality. Sample autocorrelation.
Stationary Processes
Sept 22 Autocovariance function, bias, examples.
26 Properties of ACVF, stationarity.
27 Proof that stationarity and zero-mean implies existence of MA.
29 The AR(1) and ARMA(1,1) Models, definition of Causal and Invertible processes
Oct 3 The ARMA(p,q) Model
4 Existence of stationary solutions, recap of models
6 Examples. R Code
10 Class cancelled, Thanksgiving holiday
11 Examples and the Partial autocorrelation function (PACF)
13 PACF Example, Introduction to Model Fitting
Prediction and Model Fitting
Oct 17 Best Linear Predictor, Durbin-Levinson Algorithm
18 The Innovations Algorithm, Example
20 Prediction of ARMA process
24 Finish prediction. Yule-Walker.
25 Yule-Walker and the PACF. Significance test for order p model-fit. R Code
27 Innovations algorithm for fitting MA models.
31 Maximum-Likelihood Estimation
Nov 1 Order Selection and the AIC
3 Diagnostic and Residual Checking
Spectrum Estimation
Nov 7 Examples of ar(). Spectral Density. R Code
8 Spectral Representation Theorem, example
10 Class cancelled
14 Examples, Introduction to the Periodogram
15 Properties of the Periodogram, Smoothing
17 Statistical Properties, Examples R Code
21 More on the Bias/Variance Problem
22 Direct Spectral Estimators R Code
24 Zeropadding, the FFT, and other Details R Code
Nov 28 Presentations: Day 1
29 Presentations: Day 2
Dec 1 Presentations: Day 3