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:

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

Homework 9

Due Wednesday, November 18, at the start of class. Assignment sheet (PDF).

Homework 8

Due Wednesday, November 11, at the start of class. Assignment sheet (PDF).

Homework 7

Due Wednesday, November 4, at the start of class. Assignment sheet (PDF).

Homework 6

Due Wednesday, October 28, at the start of class. Assignment sheet (PDF).

Read workbook online Download all files (ZIP)

The ZIP contains the assignment PDF, the workbook, and the data files. Extract it, then open climate-workbook.html inside the homework-06 folder. The workbook can be read offline.

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
	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 10 — Multivariate Stationarity and Cointegration (Quarto source)	Lecture 10
9	Mon Oct 19	Workbook 11 — Vector Autoregression (Quarto source)	Lecture 11
	Wed Oct 21	Workbook 11 — Vector Autoregression (continued) (Quarto source)	Lecture 11	HW 5 due (workbook, all files (ZIP))
10	Mon Oct 26	Workbook 12 — Matrix Filters and VARMA (Quarto source)	Lecture 12
	Wed Oct 28	Workbook 13 — Fitting Time Series Models (Quarto source)	Lecture 13	HW 6 due (workbook, all files (ZIP))
11	Mon Nov 2	Workbook 14 — Assessing Fitted Vector Models (Quarto source, all files (ZIP))	Lecture 14
	Wed Nov 4	Workbook 15 — Modeling What Is Hidden (Quarto source, all files (ZIP))	Lecture 15	HW 7 due
12	Mon Nov 9	Workbook 16 — Evaluating Forecasts in Time
	Wed Nov 11	Workbook 17 — When the Observation Is a Vector		HW 8 due
13	Mon Nov 16	Workbook 18 — Does Another Series Improve the Forecast?
	Wed Nov 18	Workbook 19 — What If the Mechanism Changes Over Time?		HW 9 due
14	Mon Nov 23	Workbook 20 — How Do We Learn a Changing State?
—	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.