STA 542: Introduction to Time Series Analysis
Syllabus for STA 542 - Introduction to Time Series Analysis
Course Description
Time series data arrive in order along one observed path. Dependence changes what that path can reveal about a process, how uncertainty accumulates, and how a forecasting procedure should be evaluated. This course develops the probability models and statistical methods needed to answer those questions.
Topics include process specification, learning under dependence, forecasting, model criticism, multivariate series, and changing-state models, illustrated by examples from climate, finance, environmental science, and sensing. Both frequentist and Bayesian reasoning are used. Mathematical arguments establish what a method targets and when it can work; simulation and real-data analysis in R show how it behaves in practice.
Prerequisites
- One of Statistical Science 521L, 532, or 732, or an equivalent course in mathematical statistics.
- Familiarity with probability, conditional expectation, likelihood, regression, elementary asymptotics, linear algebra, and basic Bayesian analysis, including prior, posterior, and posterior predictive distributions.
- Working familiarity with R.
Instructor
Lasse Vuursteen (lasse.vuursteen@duke.edu)
Office Hours: Fridays at 1:00 p.m.; the location will be posted on Canvas. Other meetings are available by request over email.
Teaching Assistants
Arunsoumya Basu (arunsoumya.basu@duke.edu)
Semu Serunjogi (semu.serunjogi@duke.edu)
Office Hours: Posted on Canvas.
All homework questions, including requests for deadline extensions, should be directed to the teaching assistants.
Course Information
| Dates | August 24 – November 23, 2026 |
| Lectures | Mondays/Wednesdays 10:05–11:20 a.m. |
| Location | Old Chemistry 001 |
Find the detailed syllabus here. It contains the complete policies for course materials, Quarto and R, grading, homework, pop quizzes, examinations, collaboration, extensions, and accommodations.
Course Materials
The workbooks and lecture slides are the primary course materials. Workbook and homework links will be added as materials are released.
Grading
The four components are the final examination, midterm examination, handwritten homework, and pop quizzes. The course percentage is the maximum of:
- Final only: Final (100%)
- Final and midterm: Final (62.5%) + Midterm (37.5%)
- All four components: Final (50%) + Midterm (30%) + Homework (10%) + Pop Quizzes (10%)
- Final, homework, and pop quizzes: Final (5/7) + Homework (1/7) + Pop Quizzes (1/7)
The best eight of ten homework scores and the best six of eight pop-quiz scores count. See the syllabus for the full assessment policies.
Schedule
| Week | Date | Topic |
|---|---|---|
| 1 | Mon Aug 24 | Workbook 1 — What Is a Time Series? |
| Wed Aug 26 | Workbook 2 — Solutions of Generating Equations | |
| 2 | Mon Aug 31 | Workbook 3 — Forecasting When the Process Law Is Known |
| Wed Sep 2 | Workbook 4 — Bayesian Forecasting Under Parameter Uncertainty | |
| 3 | Mon Sep 7 | Labor Day — no class |
| Wed Sep 9 | Workbook 5 — What Can One Path Reveal? | |
| 4 | Mon Sep 14 | Workbook 6 — When Does the Law Determine the Model? |
| Wed Sep 16 | Workbook 7 — How Much Information Is in a Dependent Sample? | |
| 5 | Mon Sep 21 | Workbook 8 — Transforming a Time Series |
| Wed Sep 23 | Workbook 9 — Flexible Prediction From One Path | |
| 6 | Mon Sep 28 | Workbook 10 — Dependence by Frequency |
| Wed Sep 30 | Integration and midterm review: Workbooks 1–10 | |
| 7 | Mon Oct 5 | Midterm problem clinic and flex meeting |
| Wed Oct 7 | Midterm examination: Workbooks 1–10 | |
| 8 | Mon Oct 12 | Fall break — no class |
| Wed Oct 14 | Workbook 11 — Fitting from Moment Restrictions | |
| 9 | Mon Oct 19 | Workbook 12 — Fitting by Prediction Errors |
| Wed Oct 21 | Workbook 13 — Likelihood and Misspecification | |
| 10 | Mon Oct 26 | Workbook 14 — Choosing and Checking a Fitted Model |
| Wed Oct 28 | Workbook 15 — Forecasting After Fitting | |
| 11 | Mon Nov 2 | Workbook 16 — Evaluating Forecasts in Time |
| Wed Nov 4 | Workbook 17 — When the Observation Is a Vector | |
| 12 | Mon Nov 9 | Workbook 18 — Does Another Series Improve the Forecast? |
| Wed Nov 11 | Workbook 19 — What If the Mechanism Changes Over Time? | |
| 13 | Mon Nov 16 | Workbook 20 — How Do We Learn a Changing State? |
| Wed Nov 18 | Workbook 21 — Did the System Change Abruptly? | |
| 14 | Mon Nov 23 | Course integration, final-exam preparation, and flex |
| — | Wed Dec 9 | Cumulative final examination, 9:00 a.m.–12:00 p.m. |
The topic schedule is tentative and may change with the pace of the class. Examination dates and university holidays are fixed.