index.md

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DATASCI/STATS 531/631 (Winter 2025) <br>'Modeling and Analysis of Time Series Data'	Instructor: Edward L. Ionides	html_document toc true

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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. Online discussion is on piazza.

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

5. Parameter estimation and model identification for ARMA models

6. Extending the ARMA model: Seasonality, integration and trend

7. Introduction to time series analysis in the frequency domain

8. Smoothing in the time and frequency domains

9. Case study: An association between unemployment and mortality?

10. Forecasting

11. Introduction to partially observed Markov process models

12. Introduction to simulation-based inference for epidemiological dynamics via the pomp R package

13. Simulation of stochastic dynamic models

Homework and participation assignments

• Homework 0. Some course preparation. Nothing to submit.

• Homework 1, due Sun Jan 19, 11:59pm. Solution.

• Homework 2, due Tue Jan 28, 11:59pm. Solution.

• Piazza participation 1, due Tue Jan 28, 11:59pm.

• Homework 3, due Sun Feb 9, 11:59pm. Solution.

• Homework 4, due Sun Feb 16, 11:59pm. Solution.

• Piazza participation 2, due Sun Feb 16, 11:59pm.

• Homework 5, due Sun Mar 16, 11:59pm.

Quizzes

• Quiz 1. In class on Monday 2/17. Sample questions. With solutions. Sample quiz randomly drawn from the quiz generator; the actual quiz will use a different seed.

• Quiz 2. In class on Wednesday 4/16. Sample questions. With solutions. Note: this quiz is still in development.

Midterm project

• Information.

• Midterm peer review report instructions

• 2025 midterm projects

• You are welcome to browse previous midterm projects. The course websites from 2021, 2022 and 2024 have a posted summary of peer review comments. Earlier projects are also available, from 2016, 2018 and 2020.

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Final project

• Information

• Final peer review report instructions

• You're welcome to browse previous final projects. The 2024, 2022 and 2021 final projects have a posted summary of peer review comments. Earlier projects from 2016, 2018, 2020 may also be useful.

If building on old source code, note that there are some differences between versions of the software package pomp. The pomp version 2 upgrade guide can be helpful. There are various smaller changes between pomp 2.0 and the current pomp 5.6.

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Acknowledgements and License

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