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) ebook in pdf from the Queen's Library subscription to SpringerLink. You will need to use the Queen's WebProxy service to access the ebook from offcampus.  
(additional readings on course reserve)  Time Series: Theory and Methods, P.J. Brockwell and R.A. Davis. Graduatelevel
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, ebook) 
Time Series Analysis and Its Applications (with R Examples), R.H. Shumway and D.S. Stoffer. Wellwritten text with good R examples to help in learning to do practical data analysis. 
Syllabus 
Syllabus for course. 

Data  Data Sets for assignments and from inclass 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 zeromean 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, DurbinLevinson Algorithm 
18  The Innovations Algorithm, Example  
20  Prediction of ARMA process  
24  Finish prediction. YuleWalker.  
25  YuleWalker and the PACF. Significance test for order p modelfit. R Code  
27  Innovations algorithm for fitting MA models.  
31  MaximumLikelihood 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  
Presentations  
Nov  28  Presentations: Day 1 
29  Presentations: Day 2  
Dec  1  Presentations: Day 3 