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.
The course outline, course information and grading policies are described in the syllabus.
Stationarity, white noise, and some basic time series models
Parameter estimation and model identification for ARMA models
Extending the ARMA model: Seasonality, integration and trend
Introduction to time series analysis in the frequency domain
Case study: An association between unemployment and mortality?
Introduction to simulation-based inference for epidemiological dynamics via the pomp R package
A case study of polio including covariates, seasonality & over-dispersion
A case study of financial volatility and a POMP model with observations driving latent dynamics
A case study of measles: Dynamics revealed in long time series
Please read the grading policy in the syllabus before submitting homework.
Homework 0. Setting up your computational environment. Nothing to submit.
Homework 1, due Mon Jan 17, 11:59pm. This included Participation 1. Solution.
Homework 2, due Mon Jan 24, 11:59pm. Solution.
Participation 2, due Mon Jan 31, 11:59pm.
Homework 3, due Mon Feb 7, 11:59pm. Solution.
Participation 3, due Mon Feb 14, 11:59pm.
Homework 4, due Mon Feb 14, 11:59pm. Solution.
Participation 4, due Mon Mar 7, 11:59pm.
Homework 5, due Mon Mar 14, 11:59pm. Solution.
Participation 5, due Mon Mar 21, 11:59pm.
Homework 6, due Mon Mar 21, 11:59pm. Solution.
Homework 7, due Mon Mar 28, 11:59pm. Solution.
Participation 6, due Mon Apr 4, 11:59pm.
Homework 8, due Mon Apr 4, 11:59pm. Solution.
Participation 7, due Mon Apr 18, 11:59pm.
There is no assigned homework for the last two weeks of the semester. You should work on your final project. The remaining lectures contain material that will be useful for your final projects.
You are welcome to browse previous midterm projects. The 2021 midterm projects have a posted summary of peer review comments. Earlier projects from 2016, 2018, 2020 and 2021
You’re welcome to browse previous final projects. The 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. The changes from pomp 2.0 to the current pomp 4.x are smaller.
Great Lakes access will be set up after the midterm project and used for the second half of the course.
Introductory notes for using our class account on the greatlakes cluster. This is optional but may be helpful for your final project.
If you are already familiar with using R on Great Lakes, all you need to know is the class account: stats531w22_class.
You are expected to use our class account only for computations related to STATS/DATASCI 531.
Please share knowledge about cluster computing between group members, and/or on piazza, to help everyone who wants to learn these skills.
Cluster-related questions can also be emailed to hpc-support@umich.edu.
This course and the code involved are made available with an MIT license. Some components follow a Creative Commons Attribution non-commercial license. A longer list of acknowledgments is available.