STAT/MATH 4540/5540 Introduction to Time Series. University of Colorado Boulder, Spring 2022.
More class info (grades, discrimination policies, secret zoom link, piazza link, etc.) are on our Canvas page (sign in via the CU SSO)
Catalog description: Studies basic properties, trend-based models, seasonal models modeling and forecasting with ARIMA models, spectral analysis and frequency filtration.
Requires prerequisite course of APPM/STAT/MATH 4520/5520 "Introduction to Mathematical Statistics" (minimum grade C-).
This class is expected to meet in person most of the time, though this may change due to the COVID-19 situation. The semester is starting remotely due to the Marshall Fire from December 2021.
- The instructor is Stephen Becker, Associate Professor of Applied Mathematics
- Contact him at [email protected]
- Office: 338 ECOT (engineering center, office tower)
- There is one teaching assistant (TAs) for this course (Kesler O'Connor)
Meeting time: MWF 10:10 AM - 11:00 AM
Location: ECCR 150 (Engineering Center)
During times when the class is remote, we will meet via zoom (link is on Canvas)
3 hours per week, held in a hybrid fashion: attend the physical office (338 ECOT) or via zoom (link is posted in Canvas)
Times:
- Wed 4-5:30 PM
- Thu 3-4:30 PM
The TA Kesler O'Connor also has office hours
In weeks when homework is due, Kesler's office hours are:
- Mon 1-2 PM
- Tue 1-2:30 PM
- Wed 1-2:30 PM
- Thu 1-2 PM
In weeks when no homework is due, Kesler's office hours are:
- Tue 1-2 PM
- Wed 1-2 PM
- Thu 1-2 PM
This is intended to have a solid workload. This is a three credit course (the standard kind of course).
There will be homeworks due every two weeks. Turn the homework in via Gradescope (which will be linked to via the Canvas assignment page).
- 40% Bi-weekly homeworks.
- Late homework is not accepted
- 20% Midterm 1 (in class)
- 20% Midterm 2 (take-home)
- 20% Final Project (guided, not open-ended)
There is no in-class final exam.
The overall grade may be curved as appropriate (not guaranteed), but note that there is no set "quota" of A's, B's, etc., so you are not directly competing with your classmates.
Graduate students or anyone enrolled in 5540 (instead of 4540) will be given extra homework and/or exam problems, and must do the final project on their own. Students enrolled in 4440 may form groups of two for the final project.
In general, late homework assignments are not accepted. Under exceptional circumstances (such as serious illness, including COVID-19, or serious family issues), homework can be turned in late. If the reason is foreseeable (e.g., planned travel), you must contact the instructor in advance.
Examples:
- Your sister is getting married and you have to travel out-of-state. That's great, but you can turn the homework in early. This is foreseeable, and not an "emergency", so it does not count as an exceptional circumstance.
- A close family member becomes infected with COVID-19 and you have to return to your home country to take care of family. This does count as an exceptional circumstance. Please email the instructor to discuss arrangements.
Cheating is not acceptable. Take-home exams and homeworks are easy to cheat on if you really want to, but as this is an upper-division course, I am relying on the fact that students are here to learn (and paying the university to do so), and thus cheating does not make sense. Cheating does not hurt the instructor, it hurts the student (and hurts the grades of honest classmates).
If a student is caught cheating, on the first occurrence, the penalty ranges from losing points on the item in question (like one test problem; this is for very minor infractions) to losing all points for the assignment (i.e., the entire homework or entire exam). Students may be referred to the honor council. On the second occurrence of cheating, similar penalties may apply, and additionally the student may fail the class, at the instructor's discretion.
"Minor infractions" include not following the instructions during an exam (in person or remote). For example, if the instructions on a remote test are to keep your microphone on and your hands in sight of your webcam, then failing to follow these instructions construes a minor infraction, and (even though cheating may not be proven) you are subject to losing points.
On homeworks, you are free to collaborate with other students, and to use resources like the internet appropriately. However, you must do your own work. There is a gray area between collaboration and cheating, and we rely on the students' and instructors discretion. Copying code verbatim is never permissible. You should be writing up your own work, and explaining answers in your own words. Snippets of code are allowed to be similar (sometimes there is only one good way to do it), but longer chunks of code should never be identical. If not expressly forbidden by the assignment, you may use the internet, but you may never post for help on online forums. (Regarding forums, please use our Piazza website if you want a Q&A forum).
Cheating is not usually an issue in this class, and I have faith that students will continue to act appropriately.
About 5% of students in this class are in the STAT 5540-001B distance learning section. These students are allowed to attend in person, but may also view via zoom (all in-person lectures will be live-streamed) either synchronously or asychronously.
These students must come to campus for in-person exams, unless they live farther than 50 miles away. In that case, students should talk with the instructor about finding an approved testing center.
We will use github for public content (notes, demos, syllabus), and use CU's default LMT Canvas for private content like grades and homework solutions. Canvas will also be used to organize things, like any recorded lectures, comments made via Gradescope, and Q&A forums via piazza.
The class is intended to be in person most of the time, but we will use zoom for the first two weeks and may need to switch to zoom later as well depending on COVID-19.
On zoom, please have your webcam on if at all possible
- Valid reasons for not having the camera on: to protect the privacy of your family or roommate, if you cannot have a virtual background
- Invalid reason: you don't feel like it, or you didn't wash your hair.
We have the same standards of behavior as we would in a classroom: appropriate attire, appropriate and not distracting virtual backgrounds, verbal and chat remarks should be respectful, etc. Real-world backgrounds should be appropriate and professional (please, no drugs or alcohol behind you).
It's always important to have respectful remarks, and even more so in an online setting, since it is easier to get carried away with chat comments since you cannot see the effect on other people.
If we enable private chat on zoom, remember that the zoom host can later see even "private" chats. Inappropriate or inconsiderate remarks, even on private chats, are not allowed.
Advice from your department advisor is recommended before dropping any course. After 11:59 PM Wed Jan. 26, dropping a course results in a "W" on your transcript and you’ll be billed for tuition. After 11:59 PM Fri March. 18, dropping the course is possible only with a petition approved by the Dean’s office.
(The last day to add a class is Wed Jan. 19)
For classroom behavior, requirements for COVID-19, accommodation for disabilities, preferred student names and pronouns, honor code, sexual misconduct/discrimination/harassment/retaliation and religious holidays, please refer to the policies document posted on Canvas.
Studies basic properties, trend-based models, seasonal models modeling and forecasting with ARIMA models, spectral analysis and frequency filtration.
- ECEN 3300 Linear Systems. ECEN 3300 has more emphasis on continuous time systems, and discrete time systems with lots of data and/or periodic. Focus on Nyquist and sampling theorems, spectral analysis. Might cover parametric models for frequency estimation (e.g., MUSIC) but generally does not cover parametric models like ARMA models. Less focus on forecasting.
- MATH 6550 Introduction to Stochastic Processes, as well as APPM 6560 Measure-Theoretic Probability. Mostly covers types of Markov chains and Markov processes, Brownian motion. Less focus on forecasting, more focus on convergence of random variables and rigorous treatment of the math.
- The economics department and the Leeds school of Business may also have related classes that overlap, likely having more emphasis on financial models.
- "Introduction to Time Series and Forecasting", 3rd ed. 2016, by Brockwell and Davis. ISBN-10: 9783319298528
- The electronic version is free to anyone on CU campus via springerlink
- The 2nd edition is mostly the same, but doesn't have the chapter on financial data
- This is the book that's been used for this class consistently, but it uses the authors' own package ITSM, which we will not use
- We'll refer to this book as "Brockwell & Davis"
As a supplement, especially because it includes examples in the R programming language, we may occasionally use the following:
- "Time Series Analysis and Its Applications", 4th ed. 2017, by Shumway and Stoffer.
- This is also free on springerlink
- We'll refer to this book as "Shumway & Stoffer"
The class roughly follows chapters 1--6 of Brockwell and Davis. Main topics are stationarity, trend and seasonality removal, model fitting, overfitting, and forecasting. The heart of the course is on autoregressive-moving-average (ARMA) models, analyzing these models as well as fitting and prediction, but also includes a small amount of spectral analysis.
More specific topics:
- Exploratory data analysis and data cleaning and plotting; trend and seasonality removal
- Overfitting, information criterions.
- Data transformations and variance-stabilizing transformations.
- Residual tests.
- Autocorrelation and autocovariance functions, partial ACF.
- Stationarity (strictly and weakly/wide-sense)
- Durbin-Levinson algorithm, Wold decomposition
- Yule-Walker estimators
- Burg's algorithm and the Innovations algorithm
- Maximum Likelihood Estimation (MLE)
- ARIMA Models
- Regression with correlated errors
- Spectral analysis: periodogram and consistent estimators for spectral density, windowing and averaging
Depending on time and instructor discretion, additional topics may be taught (e.g., chapters 7, 8, 9 of Brockwell and Davis). More specifically, additional topics may include:
- special forecasting models (ARAR/ARARMA, Holt-Winters); multivariate time series
- state-space models and Kalman filtering
- financial data and continuous time series (GARCH Models and Levy Processes), Black-Scholes model, Karhunen–Loève expansion
- Transfer function models, Granger causality.
After taking this course, students should be able to preprocess and explore time series data, apply transformations as needed, then remove trends and seasonality, then fit parametric models appropriate for stationary time series data and/or forecast stationary time series data. Students will be able to identify whether chosen models are appropriate by applying residual tests, as well as use information criterion to prevent overfitting.
Homeworks, projects and take-home exams may involve both mathematical analysis and programming.
Students are expected to already know how to program. While Python is heavily used for data science, we will use the other mainstream free alternative, R. Many (or all) of the calculations could be done in Julia and commercial software like Matlab, ITSM (the textbook authors' own package), SAS, SPSS and STATA, but we focus on R because (1) it is free, (2) it has great packages via the CRAN network, and (3) it is the academic standard for statistical software (and the industry standard, for some industries).
Most of our demonstrations will be using github in conjunction with R via colab (you can use the alias https://colab.to/r).
For more involved coding projects, we recommend use of an IDE that supports R. The standard choice is R Studio which is excellent, but you can also use multi-purpose IDEs like VS Code. When installing these IDEs, you still need to install R itself.
There is a curated list of time series topics in R.
For tips and tricks with R, see our Rresources webpage