Syllabus

General Description:  This is a graduate level course on time series analysis. Frequency and time domain approaches for the analysis of time series will be considered, with emphasis on the later.  Some of the topics that will be covered include: descriptive time series methods; basic theory of stationary processes; ARIMA models; Bayesian learning, forecasting and smoothing; Bayesian Dynamic Linear Models (DLMs); time-varying autoregressions, time series regression models, spectral analysis, MCMC and sequential Monte Carlo for general dynamic models, mixture models and selected topics on multivariate time series (if time permits). 

Books: 

  • Textbook: Prado and West (2010). Time Series: Modeling, Computation, and Inference. Chapman & Hall CRC Press. 

  • West M. and Harrison J. (1997). Bayesian Forecasting and Dynamic Models. Springer-Verlag. Second Edition. Highly recommended and available online at the UCSC Library.

  • Shumway R. and Stoffer D. (2011). Time Series Analysis and Its Applications with R examples. Springer Texts in Statistics. Recommended and available at the UCSC Library.

  • Petris G., Petrone S. and Campagnoli P. (2009) Dynamic Linear Models with R. Springer-Verlag. Recommended and available at the UCSC Library. 

Pre-requisites: AMS-205, AMS-205B, AMS-206, AMS-206B, AMS-207 or similar courses. Students are expected to be familiar with R, Matlab or some programming language for solving some of the homework problems and/or class projects. No formal R/Matlab instruction will be provided.

Evaluation: There will be HW assignments roughly every other week. The homework will not be graded, however, students will present selected problems from the homework assignments in class. The assignment of the selected problems to be presented in class will be done ahead of the presentation date. More information about this will be available during the first week of classes. There will be three in-class exams. One or both exams may also have additional take home parts. Grade distribution: Class Presentations (20%), Exam 1 (25%), Exam 2 (25%) and Exam 3 (30%). Please check the schedule for the dates of the exams. 

NOTE: If you qualify for classroom accommodations because of a disability, please get an Accommodation Authorization from the Disability Resource Center (DRC) and submit it to me in person outside of class (e.g., office hours) within the first two weeks of the quarter. Contact DRC at 459-2089 (voice), 459-4806 (TTY), or http://drc.ucsc.edu for more information on the requirements and/or process.

Tentative Schedule

WEEK
DATES
TOPICS
1
01/09 
01/11

Introduction to time series analysis. Motivating examples.

Exploratory analysis, smoothing methods. Review of likelihood-based and Bayesian inference.

2
01/16
01/18

ARMA models.

ARMA models.

3
01/23 
01/25

ARMA models. 

Frequency domain approaches. Harmonic regression, spectral density estimation.

4
01/30
02/01        

Frequency domain approaches

 

Exam 1

 
02/06
02/08

Frequency domain approaches. Introduction to DLMs.

DLMs.

6
02/13
02/15

DLMs: Inference 

DLMs: Inference, Canonical Models, Similar and Equivalent Models 

7
02/20

 

02/22

DLMs: Canonical Models, Forecast Functions and Superposition 

DLMs: Polynomial Models, Seasonal Models 

8
02/27
03/01

EXAM 2

DLMs: Seasonal Models 

9
03/06
03/08

DLMs: Observational variance discounting. TVAR models. 

Regression Models. Conditionally Gaussian dynamic linear models. 

10
03/13
03/15

TBD

TBD 

Finals
03/22

EXAM 3: 8-11am