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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).
|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.
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.|
|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.|
|Nov||1||Order Selection and the AIC|
|3||Diagnostic and Residual Checking|
|Nov||7||Examples of ar(). Spectral Density. R Code|
|8||Spectral Representation Theorem, example|
|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|