Modeling and Analysis of Time Series Data

University of Michigan STATS 531/631 Winter 2026. Instructor: Edward L. Ionides

Course description

This course gives an introduction to time series analysis using time domain methods and frequency domain methods. The goal is to acquire the theoretical and computational skills required to investigate data collected as a time series. The first half of the course will develop classical time series methodology, including auto-regressive moving average (ARMA) models, regression with ARMA errors, and estimation of the spectral density. The second half of the course will focus on state space model techniques for fitting structured dynamic models to time series data. We will progress from fitting linear, Gaussian dynamic models to fitting nonlinear models for which Monte Carlo methods are required. Examples will be drawn from ecology, economics, epidemiology, finance and elsewhere.

Additional information is in the syllabus. A provisional schedule for the topics is posted but deviations from this schedule may occur. Please follow the issues for the course GitHub repository at https://github.com/ionides/531w26. You are more than welcome to contribute issues and/or pull requests to the course repo. The repository is public, so your contributions should be polite and respectful.

631 includes a reading group where we discuss a research paper each week. Students registering for 631 are expected to have taken at least one core PhD-level class such as STATS 600.

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Class notes

1. Introduction

2. Estimating trend and autocovariance

3. Stationarity, white noise, and some basic time series models

4. Linear time series models and the algebra of ARMA models

Homework and participation assignments

• Homework 0. Some course preparation.

• Homework 1, due Sun Jan 18, 11:59pm.

• Homework 2, due Tue Jan 27, 11:59pm.

Midterm exams.

These are drawn from the same problem bank as the daily quizzes. They are done without electronic devices and aim to reinforce the foundational course material.

• Midterm 1. In class on Monday 2/16. Sample questions. With solutions. Sample midterm randomly drawn from the test generator; the actual test will use a different seed.

• Midterm 2. In class on Wednesday 4/15.

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Acknowledgements and License

This course and the code involved are made available with a Creative Commons license. A list of acknowledgments is available.