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:

  1. Final only: Final (100%)
  2. Final and midterm: Final (62.5%) + Midterm (37.5%)
  3. All four components: Final (50%) + Midterm (30%) + Homework (10%) + Pop Quizzes (10%)
  4. 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.