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STAD57H3 Time Series Analysis

Fall 2021

Department of Computer & Mathematical Sciences

Course Description and Learning Outcomes

Welcome to STAD57; this course will introduce you to the analysis of time series, i.e. sequences of data ordered through time, or another dimension. This type of data is ubiquitous in areas such as Economics, Business, Finance, Physical and Environmental Sciences. Since time series do not follow the typical statistical assumptions, we will look at different ways of thinking about and analyzing such data. The course will cover both theoretical and practical aspects of time series analysis, making extensive use of the R statistical software. Upon completion of the course, you will be able to:

● Understand and reason with the basic time series concepts

● Interpret and compare different time series models

● Identify and model different types of time series data

● Perform time series modelling/forecasting and present the results

● Implement time series methods in the R statistical software

Prerequisites

The course prerequisites are STAC62H3 & STAC67H3 (or equivalents) covering stochastic processes and regression. In particular, we will make extensive use of:

● Probability Theory: multivariate distributions (esp. Normal), joint/marginal/conditional dis-tributions, independence, moments (means, variances, covariances), conditional expectations.

● Linear Models: simple & multiple linear regression, parameter estimation (least squares, maximum likelihood), relevant linear algebra calculations

● R programming: basic objects (vectors, arrays), control structures (for/if statements), basic plotting, generating random variates, fitting linear models.

You are expected to have good command of these topics; if not, you should brush up your knowledge.

Textbooks

The main textbook for the course is:

Time Series Analysis and Its Applications, with R examples, 4th Ed., by R.H. Shumway and D.S. Stoffer

Another textbook we will occasionally use is:

Forecasting: Principles and Practice, by R.J. Hyndman and G. Athanasopoulos

Both are available online, and come their own R packages and other useful resources.

Course Structure

● The course material is divided into modules, corresponding to different weeks. For details on the topics covered, see the schedule at the end.

● Lectures will be held live in class, with Zoom recordings becoming available afterwards.

● There will be three assignments involving theoretical and practical questions (R programming required).

● There will be a midterm and final assessment for the course. The midterm will cover the first 3 weeks (6 lectures), and the final will be cumulative.

● All course materials will be posted on Quercus, and are for the sole use of students currently enrolled in the course (sharing materials with anyone outside of the course is unauthorized use).

Evaluation

Assessment	Details	Weight
3 Assignments	due Oct 9, Nov 13, & Dec 6	21% (7% each)
Midterm	Nov 2, instead of class	34%
Final	(TBA, Dec exam period)	45%

Assessments will combine theoretical (paper-&-pencil) problems, critical thinking questions, R pro-gramming, and data analysis write-up & explanation of results.

Late/Missed Work Policy

There will be no extensions for assignments: you will lose 2% of total possible marks for each hour your assignment is late after the deadline. There will be no late exams allowed. If you miss the midterm, the weight will be shifted to the final.

Communication

Questions about course content should be asked during lectures and tutorials, or directed to the course discussion board. We will be using Piazza as our primary discussion board for the course, which is available through Quercus. Questions regarding personal matters should be directly ad-dressed to the instructor by email; make sure to include the course code and your student ID, and allow at least two days for a response.

Accessibility

The University of Toronto is committed to accessibility. If you require accommodations for a disability, or have any accessibility concerns about the course, the classroom, or course materials, please contact AccessAbility Services as soon as possible.

Wellness

University life and academic studies can be stressful, so I encourage you to take good care of yourself. Do your best to maintain a healthy lifestyle throughout the semester by eating well, exercising, socializing, getting enough sleep and taking time to relax. This will help you achieve your goals and cope with stress.

If you, or anyone you know, experiences severe academic stress, difficult life events, or feelings of anxiety or depression, I strongly encourage you to seek support. Consider reaching out to a friend, family, or faculty member that you trust, sooner rather than later. Do not hesitate, because learning to ask for help is an important lesson in itself. And keep in mind that the University’s Health & Wellness Centre is always available for counseling and support.

Academic Integrity

In papers and assignments:

● Using someone else’s ideas or words without appropriate acknowledgement.

● Submitting your own work in more than one course without the permission of the instructor in all relevant courses.

● Obtaining or providing unauthorized assistance on any assignment.

On quizzes and tests:

● Using cell phones or other devices to communicate about the questions.

● Obtaining or providing assistance on any quizzes or tests.

● Posting or sharing quiz or test questions.

● Misrepresenting your identity.

● Submitting an altered test for re-grading.

Misrepresentation:

● Falsifying or altering any documentation required by the University, including doctor’s notes.

● Falsifying institutional documents or grades.

Tentative Lecture Schedule

#	Title	Topics
1	TS Fundamentals	Strict/week stationarity, auto-correlation function (ACF), estimating autocorrelation
2	TS Decomposition	Trend, seasonality, smoothing, differencing, transformations
3	Basic TS Models	linear time series models, auto-regression, moving averages
4	ARMA Models	characteristic polynomials, causality, invertibility
5	ARMA Prediction	best-linear predictors, prediction intervals, long-range be-havior
6	ARMA Estimation	maximum likelihood, conditional least squares, model diag-nostics
7	ARMA Extensions	integrated and/or seasonal models, unit root tests, model selection
8	Midterm	Review
9	TS Regression	ARMA with exogenous variables (ARMAX), TS cross-validation
10	Multivariate TS Models	cross-correlation, vector autoregressive (VAR) models
11	Multivariate topics	impulse response functions, Granger causality, vector-error correction models (VECM)
12	Volatility models	generalized autoregressive conditional heteroskedasticity (ARCH/GARCH) models