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: Wednesdays, 3:00–4:00 p.m.

Teaching Assistants

Arunsoumya Basu (arunsoumya.basu@duke.edu)
Office Hours: Tuesdays, 10:30–11:30 a.m.

Semu Serunjogi (semu.serunjogi@duke.edu)
Office Hours: Thursdays, 2:00–3:00 p.m.

Office-hour locations will be posted on Canvas.

Additional meetings with course staff are available by appointment; email the relevant staff member to arrange one.

TA office hours are the main setting for working through workbook exercises and homework problems. Questions about homework administration, including requests for deadline extensions, should also be directed to the teaching assistants. The teaching assistants administer homework deadlines and decide whether to grant extensions.

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.

Grading

Assessment is based on four components:

  • Final examination: weight 5.
  • Midterm examination: weight 3.
  • Handwritten homework: weight 2.
  • Pop quizzes: weight 1.

The course percentage is the maximum of:

  1. Final only: Final (100%)
  2. Final and midterm: Final (62.5%) + Midterm (37.5%)
  3. All four components: Final (5/11) + Midterm (3/11) + Homework (2/11) + Pop Quizzes (1/11)
  4. Final, homework, and pop quizzes: Final (5/8) + Homework (2/8) + Pop Quizzes (1/8)

The most favorable scheme is applied automatically. Homework and pop quizzes can therefore improve the course percentage, but they cannot lower it. Homework is ordinarily submitted in hard copy at the start of Wednesday’s lecture. The best seven of nine homework scores and the best six of eight pop-quiz scores count. No homework is due during the midterm and fall-break period. See the syllabus for the full assessment policies and deadline calendar.

Schedule

Week Date Topic Slides Homework
1 Mon Aug 24 Workbook 1 — What Is a Time Series? (Quarto source) Lecture 1  
  Wed Aug 26 Workbook 2 — Solutions of Generating Equations (Quarto source) Lecture 2  
2 Mon Aug 31 Workbook 3 — Forecasting When the Process Law Is Known (Quarto source) Lecture 3  
  Wed Sep 2 Workbook 4 — Bayesian Forecasting Under Parameter Uncertainty (Quarto source) Lecture 4  
3 Mon Sep 7 Labor Day — no class    
  Wed Sep 9 Workbook 5 — Learning Covariances from One Path (Quarto source) Lecture 5 HW 1 due
4 Mon Sep 14 Workbook 6 — Estimating Uncertainty from One Path (Quarto source) Lecture 6  
  Wed Sep 16 Workbook 7 — From Dependence to a Central Limit Theorem (Quarto source) Lecture 7 HW 2 due
5 Mon Sep 21 Workbook 8 — Choosing a Transformation (Quarto source) Lecture 8  
  Wed Sep 23 Workbook 9 — Assessing a Stationary Approximation (Quarto source) Lecture 9 HW 3 due (data)
6 Mon Sep 28 Workbook 10 — Stationary Relationships Between Nonstationary Series    
  Wed Sep 30 Integration and midterm review: Workbooks 1–10   HW 4 due (workbook, Quarto + data)
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.