**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)gmail.com

**Office Hours:** Mondays, 10AM-12PM, KAP 406G

**Lecture Meeting Time/Location:** Mondays, Wednesdays, and Fridays, 9AM-950AM, KAP 140

**TA: **... (@-symbol)usc.edu

**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:** Friday, May 8, 8AM-10AM, Location TBD

**Email Policy:**

- My email address for this course is stevenmheilman@gmail.com
- It is your responsibility to make sure you are receiving emails from stevenmheilman@gmail.com , and they are not being sent to your spam folder.
- Do NOT email me with questions that can be answered from the syllabus.

**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.

https://dsp.usc.edu/

213-740-0776 (phone)

213-740-6948 (TDD only)

213-740-8216 (fax)

ability@usc.edu

Discrimination, sexual assault, and harassment are not tolerated by the university. You are encouraged to report any incidents to the *Office of Equity and Diversity* http://equity.usc.edu/ or to the *Department of Public Safety* http://capsnet.usc.edu/department/department-public-safety/online-forms/contact-us. This is important for the safety whole USC community. Another member of the university community - such as a friend, classmate, advisor, or faculty member - can help initiate the report, or can initiate the report on behalf of another person. *The Center for Women and Men* http://www.usc.edu/student-affairs/cwm/ provides 24/7 confidential support, and the sexual assault resource center webpage sarc@usc.edu describes reporting options and other resources.

**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**:

- Homeworks are due on Fridays, at the
**beginning**of class. - Late homework is
**not accepted**. - If you still want to turn in your homework late, then the number of minutes late divided by ten will be deducted from the homework score. The exact deduction and rounding procedure is not guaranteed to be accurate.
- The
**lowest one**homework score will be dropped. This policy is meant to account for illnesses, emergencies, etc. - You may use whatever resources you want to do the homework, including computers, textbooks, friends, the TA, etc. However, I would discourage any over-reliance on search technology such as Google, since its overuse could degrade your learning experience. By the end of the quarter, you should be able to do the entire homework on your own, without any external help.
- Do not submit homework via email.
- Collaboration on homeworks is allowed and encouraged.
- All homework assignments must be written by you, i.e. you cannot copy someone else`s solution verbatim.

**Grading Policy:**

- The final course grade is weighted as the larger of the following two schemes.
- Scheme 1: homework (20%), the first midterm (20%), the second midterm (25%), and the final (35%).
- Scheme 2: homework (20%), the largest midterm grade (30%), and the final (50%)

- If you cannot attend one of the exams, you must notify me within the first two weeks of the start of the quarter. Later requests for rescheduling will most likely be denied.
- You must attend the final exam to pass the course.

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 |

**Advice on succeeding in a math class:**

- Review the relevant course material
**before**you come to lecture. Consider reviewing course material a week or two before the semester starts. - When reading mathematics, use a pencil and paper to sketch the calculations that are performed by the author.
- Come to class with questions, so you can get more out of the lecture. Also, finish your homework at least
**two days**before it is due, to alleviate deadline stress. - Write a rough draft and a separate final draft for your homework. This procedure will help you catch mistakes. Also, I would very much recommend typesetting your homework. Learning LaTeX is a very important skill to have for doing mathematics. Here is a template .tex file if you want to get started typesetting.
- If you are having difficulty with the material or a particular homework problem, review Polya's Problem Solving Strategies, and come to office hours.

**Homework**

**Homework .tex files**

**Exam Solutions**

**Supplementary Notes**