Math 461 Time Series Analysis

Instructor: Likai Chen (likai.chen[at]

Lectures: 10:00-10:50 a.m on Mondays, Wednesdays, and Fridays in Duncker 101

Office hour: Mon 12:00-1:00 p.m. and Wed 3:00-4:30 p.m. Cupples I Room 107

TA: Yuchen Han (

TA hour: Tue 2:30-3:30 p.m. Cupples I Room 6


Topics covered

Generalities of time series and exploratory data analysis: data types, trend, seasonality,nonstationarity and stationarity; Time-series in the time domain and autocorrelation; autoregressive integrated moving average (ARIMA) models; model selection methods; forecasting; frequency domain and spectral analysis; State-Space Models and Kalman Filter; Nonlineartime series; multivariate time series. More advanced topics if time allows it.


Math 493 (Probability) and 494 (Mathematical Statistics); or permission of the instructor. Some programmingexperience in R is useful but not essential.


Time Series Analysis and Its Applications (with R examples).
R.H. Shumway and D.S.Stoffer, 4th Edition, Springer.
Available for free download on Springer Link through our library website.


There will be one midterm and one comprehensive final. Midterm is(tentatively) set as Wednesday Oct 09. The final is scheduled Dec 16, 10:30-12:30 a.m. All exams are closed book and closed note. No web-enabled devices may be used. One page (letter size and two-sided) note may be brought to exams. All the distribution tables will be provided by the instructor. Calculators are allowed but not required. You should always bring your Washington University Photo ID to exams. Proctor may check student’s IDs.

Make-up exams are strongly discouraged. If you are aware of a conflict, please inform the instructor before the exam. Make-up exam will only be given if (1) within 1 week of the standard exam and (2) suitable documentation is provided within 2 days.


There will be about 7 HWs; Only a few selected problems will be graded and counted towards your HW score. NO LATE HOMEWORK WILL BE ACCEPTED.

Homework collection via crowdmark: Only PDF and JPEG format are accepted.

You will receive a link in email to submit your homework on crowdmark. After you finish homework, you need to upload your work for each homework question separately. Simply drag and drop your files to the upload areas under the questions or browse to locate them. You can drag pages between questions, and add or delete more pages under each questions. Please DO NOT upload your entire file to all homework questions, but only keep the related pages to each question. If you upload pictures of your homework, please make sure your pictures are sharp enough to be graded. Please ensure the uploaded pages are in order and rotated correctly. After your work is graded, you will receive another link in email to review your score and grading comments.


Your grade will be based on homework, midterm and final exam.

Midterms 35%
Final 45%
Homework 20%

The threshold for each grade

A A- B+ B B- C + C C -
88 or above85-88 83-85 77-83 75-77 73-75 65-73 60-65
Only very few top students will get A+.


Open-source software R for statistical computing, and its manual .
Download R from Wustl's software.
Download R Studio from its developer's website.