MA641 Time Series Analysis I

Course Catalog Description


Scope and applications of time series analysis: process control, data analysis and forecasting, and signal processing. Exploratory data analysis: graphical analysis, trend and seasonality detection and removal, and moving-average fi ltering. Review of basic statistical concepts related to the characterization of stationary processes. ARMA models and prediction of stationary processes. Estimation of ARMA models and model building and forecasting with ARMA models. Spectral analysis: periodogram testing for seasonality and periodicities and the maximum entropy and maximum-likelihood estimators. Asymptotic convergence. Selected topics, such as multivariate time series, nonlinear models, Kalman filtering, econometric forecasting, and long-memory processes. Selected applications, such as the unit-root problem in economics, forecasting and testing for market efficiency in financial time series, process control, and quality control.


MA 611 Probability and MA 612 Mathematical Statistics

Campus Fall Spring Summer
On Campus
Web Campus


Professor Email Office
Pawel Polak

More Information

Course Outcomes

Course Resources


(SL) Slides from the lectures.

(TSAIA) Time Series Analysis and Its Applications: With R Examples 4th ed. 2017 Edition by Robert H. Shumway , David S. Sto er (the book is available from the authors website:

Additional Readings:

(ITSF) Introduction to Time Series and Forecasting by Peter J. Brockwell and Richard A. Davis

(TSTM) Time Series: Theory and Methods by Peter J. Brockwell and Richard A. Davis

(AFTS) Analysis of Financial Time Series 3rd Edition by Ruey S. Tsay

(MTSA) Multivariate Time Series Analysis: With R and Financial Applications by Ruey S. Tsay


Grading Policies

Homework Assignments 30%, Midterm Exam 30%, Final Project 40%.

Homework (30%)
  1. There will be 4 HW assignments.
  2. Collaboration is allowed in solving the problems, but each student has to hand in her or his own independently written solutions.
  3. You will submit your answers on Canvas
  4. No late homework, under any circumstances, will be accepted.
  5. Please note that mathematics/statistics questions by email will not be answered due to the lack of an appropriate interface. You are encouraged to ask your technical questions during oce hours.
Midterm Exam (30%)
  1. Open-book.
  2. Students are not allowed to work with or talk to other students during the exam period.
Final Project (40%)
  1. Final project counts for 40% of your nal grade.
  2. You will form groups of up to three students for this project (equal contribution of group members will be assumed). Please contact me if you are looking for people to join your group or if you are looking for a group which you can join.
  3. You can help other groups and discuss with them your analysis. However, ask them to give you credit (with the description of your contribution) at the last slide of their presentation. You will get extra points for this credit.
  4. Projects consists of the code which we can run using the original data, and the presentation slides.
  5. No late project, under any circumstances, will be accepted.
  6. During the Final Exam week, you will present your projects in class. Depending on the number of groups, you will have around 20 minutes for the presentation.
Conversion of Numerical Grades to Final Letter Grades

The conversion of numerical grades (0-100) to Final Letter Grades (A-F) will be made according to the following tentative scale:

A 100-85 A- 84-81

B+ 80-77 B 76-73 B- 72-69

C 68-60

F ≤ 59

Lecture Outline

Topic Reading
Week 1 Nature of Time Series Data with Examples, Stochastic Process, Stationarity
Week 2 Autocorrelation Function (ACF), Partial Autocorrelation Function (PACF), and Statistical Tests for Stationarity, White Noise, and Normality, Examples
Week 3 Spectral Analysis, Discrete Fourier Transform, and Periodogram, Empirical Examples
Week 4 Time Series Regression with Examples, STL Decomposition, Local Regression, and Smoothing
Week 5 Linear Filters, and Linear Processes
Week 6 Backshift Operator and AR(1) Process with Examples
Week 7 ARMA Model and ACF and PACF for ARMA Models with Examples
Week 8 No Classes - Spring Break
Week 9 Take-Home Midterm Exam (deadline before Spring Break), ARIMA Models with Examples using Box-Jenkins Method
Week 10 SARIMA Models, ACF and PACF for SARIMA Models with Examples
Week 11 Forecasting: Time Series Forecasting with Examples
Week 12 Forecasting: Prediction Error, Prediction for ARMA Models, Prediction Uncertainty and Bootstrap
Week 13 Introduction to Multivariate Time Series Models: VAR Models, Large Dimensional Time Series Modeling, LASSO-VAR with Examples
Week 14 Volatility Modeling via GARCH and AR(p)-GARCH Models
Week 15 Examples of Long Memory Time Series and Fractional Di erencing; State Space Models, Linear Gaussian Model and the Kalman Filter with Examples
Week 16 Final Project Presentations