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.
Class meets Mon/Wed 10:00-11:30 in 1427 Mason Hall
Homework will be graded on completeness. To get these points, the homework must include two statements titled “Sources” and “Please explain”.
The statement of sources must list all books, internet resources or other people consulted while completing the homework. For example, “Sources: notes only,” or, “Sources: collaboration with X and Y; web site Z,” or, “Sources: notes and office hours.” Any material taken from any source, such as the internet, must be properly acknowledged. Directly copied text must be in quotation marks. Directly copied equations must be explicitly referenced to the source. Unattributed copying from any source is plagiarism, and has potentially serious consequences.
The explanation request provides useful feedback for the GSI and instructor. For example, “Please explain: nothing, everything is clear,” or, “Please explain: I’m having difficulties manipulating Taylor series.” or, “Please explain: I had difficulty constructing the prewhitening filter. What is a good way to do that in R?”
Homework will not be graded on correctness, to encourage independent work. The GSI may provide some feedback on correctness, but students are responsible for checking their work against posted solutions.
The midterm and final projects must take care to properly reference all sources. For projects, no specific source and explanation request statements are requested.
Stationarity, white noise, and some basic time series models. (R script)
Linear time series models and the algebra of ARMA models. (R script)
Parameter estimation and model identification for ARMA models. (R script)
Introduction to partially observed Markov process models. (R script)
Statistical methodology for nonlinear partially observed Markov process models. (R script)
Dynamic models and their simulation by Euler’s method. (R script)
Practical likelihood-based inference for POMP models. (R script)
Time series models with covariates, and a case study of polio. (R script)
Case study: POMP modeling to investigate financial volatility. (R script)
There are further POMP case studies, in a similar style, on Ebola modeling, measles transmission, and dynamic variation in the rate of human sexual contacts.
Homework 0, due in class on 1/10. Setting up your computational environment.
Homework 1, due in class on Wednesday 1/17. Solution.
Homework 2, due in class on Monday 1/29. Solution.
Homework 3, due 11:59pm on Monday 2/5. Solution.
Homework 4, to be carried out by Monday 2/12.
Homework 5, due 11:59pm on Monday 2/19. Solution.
Homework 6, due in class on Wednesday 3/14. Solution.
Homework 7, due 11:59pm on Monday 3/26. Solution.
Homework 8, to be carried out by Monday 4/2.
Homework 9, due on Monday 4/16. Solution.
The midterm exam will involve reasoning about a data analysis using the theoretical and computational techniques we have studied in class.
The exam may include techniques covered in homeworks and will assume familiarity with the notes. Reading the textbook is not mandatory for the exam, but may be useful to get a broader perspective.
You should bring to the exam just pens and/or pencils. The exam will be taken without any electronic devices, books or notes.
The best predictor of the style of the exam is the past papers from the Winter 2016 version of this course: