Course information


Course outline

  1. Introduction to time series analysis.

  2. Time series models, trend and autocovariance.

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

  4. Linear time series models and the algebra of autoregressive moving average (ARMA) models.

  5. Parameter estimation and model identification for ARMA models.

  6. Extending the ARMA model: Seasonality and trend.

  7. Introduction to the frequency domain.

  8. Smoothing in the time and frequency domains.

  9. Introduction to partially observed Markov process models.

  10. Statistical methodology for nonlinear partially observed Markov process (POMP) models.

  11. Dynamic models and their simulation by Euler’s method.

  12. Practical likelihood-based inference for POMP models.

  13. POMP models with covariates, and a case study of polio transmission.

  14. A case study using POMP modeling to study financial volatility.


Grading

Each homework will have a question asking about sources. You will be asked to explain which parts of your responses above made use of a source, meaning anything or anyone you consulted (including classmates or office hours) to help you write or check your answers. All sources are permitted, but failure to attribute material from a source is plagiarism, which is unethical and may have serious consequences. Directly copied text must be in quotation marks. Directly copied equations must be explicitly referenced to the source. The reader should not have to carry out detective work to figure out correctly which parts of the homework are attributable to a source. Careful attribution of sources is fundamental to good scholarship, and it also facilitates meaningful grading given the reality of abundant sources.

The graders will look for an honest effort applied to the homework, with contributions that go beyond the sources. It is your responsibility to demonstrate to the reader that you have engaged in careful thought related to the questions. If you use sources, you are welcome to comment on what you learned from the sources as a way to show engagement with the questions.

The midterm and final project will also have a substantial grading component allocated to clear and scholarly assignment of credit to sources.


Student Mental Health and Wellbeing

University of Michigan is committed to advancing the mental health and wellbeing of its students. If you or someone you know is feeling overwhelmed, depressed, and/or in need of support, services are available. For help, contact Counseling and Psychological Services (CAPS) at 734.764.8312 and https://caps.umich.edu during and after hours, on weekends and holidays. You may also consult University Health Service (UHS) at 734.764.8320 and https://www.uhs.umich.edu/mentalhealthsvcs. For a listing of other mental health resources available on and off campus, visit http://umich.edu/~mhealth/