Course: Math 545, Introduction to Time Series, Spring 2020
Prerequisite: MATH 225, MATH 226, and MATH 208. (It is helpful, though not necessary, to have taken graduate versions of these classes such as 507A, 525A, 541A.)
Course Content: Transfer function models; stationary, nonstationary processes; moving average, autoregressive models; spectral analysis; estimation of mean, autocorrelation, spectrum; seasonal time series.
Last update: 23 December 2019

Instructor: Steven Heilman, stevenmheilman(@-symbol)
Office Hours: Mondays, 10AM-12PM, KAP 406G
Lecture Meeting Time/Location: Mondays, Wednesdays, and Fridays, 9AM-950AM, KAP 140
TA: ... (@-symbol)
You are not required to buy a textbook. Free lecture notes are provided below.
Recommended Textbook: Brockwell and Davis, Time Series, Theory and Methods, 2nd edition. The plan is to cover chapters 1-3, 5, and 7-9 of this book.
Other Textbooks: Brockwell and Davis, Introduction to Time Series and Forecasting. A more elementary version of the other book by the same authors.
Copertwait and Metcalfe Introductory Time Series with R. A text focusing on time series in the R programming language.

First Midterm:  Friday, February 14, 9AM-950AM, KAP 140
Second Midterm: Friday, March 27, 9AM-950AM, KAP 140
Final Exam: Take-Home Exam, distributed May 1 at 10AM PST, due May 8, 5PM PST, submitted via email

Email Policy:

Exam Procedures: Students must bring their USCID cards to the midterms and to the final exam. Phones must be turned off. Cheating on an exam results in a score of zero on that exam. Exams can be regraded at most 15 days after the date of the exam. This policy extends to homeworks as well. All students are expected to be familiar with the USC Student Conduct Code. (See also here.)
Disability Services: If you are registered with disability services, I would be happy to discuss this at the beginning of the course. Any student requesting accommodations based on a disability is required to register with Disability Services and Programs (DSP) each semester. A letter of verification for approved accommodations can be obtained from DSP. Please be sure the letter is delivered to me as early in the semester as possible. DSP is located in 301 STU and is open 8:30am-5:00pm, Monday through Friday.
213-740-0776 (phone)
213-740-6948 (TDD only)
213-740-8216 (fax)

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Exam Resources: Here is a page containing old exams for a course similar to ours. The material on these exams might differ from the material on our exams.

Homework Policy:

Grading Policy:

Tentative Schedule: (This schedule may change slightly during the course.)

Week Monday Tuesday Wednesday Thursday Friday
1 Jan 13: Introduction Jan 14 Jan 15: Review of Probability Theory Jan 16: Jan 17: Review of Probability Theory
2 Jan 20: No class   Jan 21 Jan 22: 1.2, Stochastic Processes Jan 23: Jan 24: Homework 1 due. 1.3, Stationarity
3 Jan 27: 1.4, Estimation Jan 28 Jan 29: 1.5, Autocovariance Jan 30: Jan 31: 1.6, Multivariate Normal
4 Feb 3: 2.1, 2.2, Hilbert Spaces Feb 4 Feb 5: 2.3, 2.4, 2.5, Hilbert Space Projections Feb 6 Feb 7: Homework 2 due. 2.6, Linear Regression
5 Feb 10: 2.7, Hilbert Spaces and Linear Regression Feb 11 Feb 12: 2.8, Fourier Series Feb 13 Feb 14: Exam 1
6 Feb 17: No class Feb 18 Feb 19: 2.8, Fourier Series Feb 20 Feb 21: 2.8, Random Fourier Series
7 Feb 24: 3.1, ARMA Processes Feb 25 Feb 26: 3.1, ARMA Processes Feb 27 Feb 28: Homework 3 due. 3.2, ARMA of Infinite Order
8 Mar 2: 3.4, Partial Autocorrelation Mar 3 Mar 4: 3.5, Autocovariance Generating Function Mar 5 Mar 6: 4.1, 4.2, Spectral Representation
9 Mar 9: 4.3, 4.4, Spectral Representation Mar 10 Mar 11: 4.8, 4.9, Spectral Representation Mar 12: Mar 13: Homework 4 due. 5.1, Prediction
10 Mar 16: No class (spring break) Mar 17 Mar 18: No class (spring break) Mar 19 Mar 20: No class (spring break)
11 Mar 23: 5.2, Recursive Methods Mar 24 Mar 25: 5.3, Recursion and ARMA Mar 26 Mar 27: Exam 2
12 Mar 30: 5.4, Gaussian Prediction Mar 31 Apr 1: 5.5, ARMA Prediction Apr 2: Apr 3: 5.6, Frequency Prediction
13 Apr 6: 7.1, Mean Estimation Apr 7 Apr 8: 7.2 Estimation Apr 9 Apr 10: Homework 5 due. 7.2, Estimation
14 Apr 13: 10.1, 10.2, Spectral Inference Apr 14 Apr 15: 10.1, 10.2, Spectral Inference Apr 16 Apr 17: 10.6, Maximum Likelihood ARMA Spectral Estimation
15 Apr 20: 10.6, Maximum Likelihood ARMA Spectral Estimation Apr 21 Apr 22: 11.1, Multivariate Time Series Apr 23 Apr 24: 11.1, Multivariate Time Series
16 Apr 27: Leeway Apr 28 Apr 29: Leeway Apr 30 May 1: Homework 6 due. Review of course

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Homework .tex files

Exam Solutions

Supplementary Notes