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.

A course outline, course information and grading policies are described in the syllabus.

Class notes and lectures

  1. Introduction

  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 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. Introduction to partially observed Markov process models

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

  12. Simulation of stochastic dynamic models

  13. Likelihood for POMP models: Theory and practice

  14. Likelihood maximization for POMP models

  15. A case study of polio including covariates, seasonality & over-dispersion

  16. A case study of financial volatility and a POMP model with observations driving latent dynamics

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 assignments

Please read the grading policy in the syllabus before submitting homework.

Midterm project

Final project

Using the Great Lakes cluster