DS-GA 1018: Probabilistic Time Series Analysis Fall 2025

Erin Grant • New York University

General Information

Instructor:

Erin Grant (eringrant@)

Office Hours: Mondays & Wednesdays 2:30-3:30pm, CDS 765

Teaching Assistants:

Ansh Kumar Sharma (as20482@)

Office Hours: Mondays 12:30-1:30pm, CDS 765

Yilun Kuang (yk2516@)

Office Hours: Mondays 12:30-1:30pm, CDS 765

Course website:

https://eringrant.github.io/ptsa

Lectures:

Wednesdays 12:30pm-2:30pm, GCASL 275

Lab Sections:

Mondays 1:30pm-2:20pm, CDS C10

Mondays 4:55pm-5:45pm, CDS C10

Prerequisites:

Introductory statistics, linear algebra, and familiarity with Python

Grading:

Homeworks (10%), Midterm I & II (50%), Project (25%), Labs (10%), Participation (5%).

Important links:

Gradescope for lab and homework submission

Course Description

The goal of this course is to give students an understanding of the fundamental probabilistic models used to analyze time-dependent data. Time series analysis has applications ranging from econometrics, to sociology, to astrophysics. The methods used can vary wildly by application and, as the rapid advances of the last few years have shown us, can quickly become outdated.

The goal of this class is not to provide you with a laundry list of models or to have you memorize a series of facts. Instead, the class will explore the key principles of probabilistic inference and use them to derive and understand several popular methods. The lectures and homeworks will focus on this theoretical understanding, with the labs and projects providing opportunities to apply the topics learned in class.

This course is a graduate course intended for MS and PhD students. That means that the pace of learning will be quick and that the homeworks and midterms will go beyond rote applications of the material learned in class. It also means that students are expected to engage actively in their learning. Students will have to develop and execute a novel final project that will require extensions beyond the material provided in lectures.

The class is open to undergraduate students with permission from the instructor.

Learning objectives

On completing this course, students should be able to:

Course policies

Grading

Grades for the course will be calculated as follows:

  • Homeworks (10%): There are 5 homeworks distributed across the semester. You are given at least 2 weeks to solve each homework. The exercises are meant to build off the material covered in lecture, with the difficulty ranging from direct applications of the lecture material to more challenging extensions. The homeworks may take some time to complete, but students who actively attend lectures, lab sections, and office hours should be able to complete all the problems. Homeworks are due Wednesdays at 5pm.
  • Midterm I & II (50%): There are two midterms that will contribute 50% to your final grade. Each student's composite midterm grade will weight either midterm between 25% to 75% to maximize the composite grade (i.e., max_α [α (midterm I) + (1-α) (midterm II)] where α is chosen from the range [0.25, 0.75]).
  • Project (25%): Projects will be completed in groups of 2-3 students. Students are welcome to select their own groups, but the course staff will form groups for students that do not already have one. Individual projects are not permitted without approval, and are likely only to be approved for PhD students. There is a great deal of flexibility in the project topic so long as it touches on material relevant to the class. Examples of past projects will be listed on the course page. Expectations for the project will be discussed in class.
  • Labs (10%): When you registered for the course, you should have selected one of the two lab sections on Mondays. During the lab section, the section leader will provide you with a physical lab worksheet that you can fill in during the lab. For lab participation credit, you can submit a picture or scan of your worksheet on Gradescope by 9 AM the Monday of the next lab. (You can use the Gradescope mobile app for this! Or a regular scanner.) Lab worksheets are graded pass/fail (*i.e.*, for completeness, not correctness); the section leader will review answers to the lab at the beginning of the next week's lab.
  • Participation (5%): Participation will be graded based off engagement and attendance during lectures, labs, and office hours. Students who attend class and lab sections and engage with the material should expect full credit. The instructor will update this section to provide specific opportunities for participation as the semester progresses.

Late policy

Students will be given 5 late days to distribute among the homeworks. Late days may not be used for the labs or the final project. To not overburden the grading staff, a maximum of two late days can be used for any individual homework. After all late days are exhausted, each day of delay will result in a 10% deduction in the grade for the homework.

Attendance policy

Attendance in lecture is expected, with the understanding that you may need to miss one or two lectures (see participation section of grading). Lecture notes will be provided, but recording of the lecture will only be made available for students with extenuating circumstances. The lectures and lab sections will not be streamed over zoom.

Attendance in lab section is mandatory. If there is a week where you cannot attend lab section, please reach out to the course staff (instructor and section leader) with as much anticipation as possible.

Collaboration policy

Students are actively encouraged to discuss the assignments with other students working in the class, but every assignment that is submitted must be written in your own words. Students should try to solve the problem on their own before collaborating with their peers. If you collaborate with other students while completing the assignment, write their names on the assignment. If you use code found online to solve a lab assignment, cite your source. So long as you are open about your sources of collaboration and do not copy solutions, you will not be penalized for collaboration.

If you have completed a problem before your peers, you are welcome and encouraged to give them guidance. However, you should not allow students to copy your solutions nor post solutions to any of the problems in this course online. Lastly, do not solicit help from people outside of the class (beyond classmates and course staff).

Admissible resources

The work you submit should represent your own work. Do not submit solutions that you do not understand. In particular, you should be able to explain your solution, in your own words (without referencing your write-up). You are encouraged to only reference course materials in developing your solutions. If you choose to consult written sources beyond the course material and textbook (including generative AI), you must list each of these sources in your submission. Note: Exams will be closed book, closed Internet, and closed generative AI. As such, the staff recommends you use these tools sparingly, as a resource for learning, not as an integral part of solving homeworks. This policy is adapted from CS 4820 at Cornell University.

Acknowledgments

The materials for the majority of this course are due to prior year instructors Professor Cristina Savin and Sebastian Wagner-Carena. The present instructor will develop one lecture (non-linear and/or non-Gaussian SSM) and the second midterm.

The present instructor did and will *not* use generative AI to produce *course content* (text and images in lecture, assignment, and midterm materials). Website, slide and handout *styling* was coded with the aid of Node.js, Pandoc, Reveal.js, and Claude Code and will be open-sourced.

Course Schedule

Date
Lecture
Assignments Out
Assignments In (Deadlines)
September 3, 2025
Lecture 1
Introduction, logistics, review
September 8, 2025
Lab 1
Introduction, logistics, review
Lab 1
September 10, 2025
Lecture 2
Introduction to ARMA models
Homework 1
*minor erratum fixed in 2(v)
September 15, 2025
Lab 2
Building intuition with Gaussians
Lab 2
September 17, 2025
Lecture 3
Estimation and prediction in ARMA models
September 22, 2025
Lab 3
LDS inference
Lab 3
Lab 1 & Lab 2 (9 AM)
email L1 to instructor
September 24, 2025
Lecture 4
State space models
Homework 2
Homework 1 (Friday 5 PM)
September 29, 2025
Lab 4
LDS learning
Lab 4
Lab 3 (9 AM)
October 1, 2025
Lecture 5
Inference and prediction in state space models
October 6, 2025
Lab 5
Particle filtering
Lab 5
Lab 4 (9 AM)
October 8, 2025
Lecture 6
Filtering and smoothing in state space models
Homework 3
Homework 2 (Friday 5 PM)
October 14, 2025
Midterm review
Midterm I Review Lab
Lab 5 (9 AM)
October 15, 2025
Midterm I
First 5 weeks of material (Lecture 1 (Review) + Lectures 2-5)
In-class exam
October 20, 2025
Lab 6
Links between models and their generalizations
Lab 6
October 22, 2025
Lecture 7
Hidden markov models
Homework 4
Homework 3 (Friday 5 PM)
October 27, 2025
Lab 7
Hidden Markov models
Lab 7
Lab 6 (9 AM)
October 29, 2025
Lecture 8
Gaussian processes
November 3, 2025
Lab 8
Gaussian processes
Lab 8
Lab 7 (9 AM)
November 5, 2025
Lecture 9
Non-linear and/or non-Gaussian SSMs
Homework 5
Homework 4 (Friday 5 PM)
November 10, 2025
Lab 9
Non-linear and/or non-Gaussian SSMs
Lab 9
Lab 8 (9 AM)
November 12, 2025
Lecture 10
Deep learning for time series (**Likely guest lecture**)
November 17, 2025
Midterm review
Midterm II review
Lab 9 (9 AM)
November 19, 2025
Midterm II
Lectures 6-9
In-class exam
November 24, 2025
Project work lab
Get feedback on your project from the instructors.
November 26, 2025
No Class
Legislative Friday
Homework 5 (Friday 5 PM)
December 1, 2025
Lab 10
Spectral analysis
Lab 10
December 3, 2025
Lecture 11
Spectral analysis
December 10, 2025
Project Presentations
Project presentations for all groups.
Student presentations
Project writeup

References

Recommended Textbooks

[shumw]
Shumway, Robert H. and Stoffer, David S. (2017). Time Series Analysis and Its Applications: With R Examples. Springer, 4 edition.
[bisho]
Bishop, Christopher (n.d.). Pattern Recognition and Machine Learning. Springer.
[rasmu]
Rasmussen, Carl Edward and Williams, Christopher K. I. (n.d.). Gaussian Processes for Machine Learning. MIT Press, 3. print edition.