Business 41914: Multivariate Time Series Analysis
Quarter of 2015
Instructor: Ruey S. Tsay
Office: HPC 455
Fax: 773-702-0458 (Write my name on the cover page.)
Lecture: Mondays 8:30 am to 11:30 am, HPC 3A
Office hour: (a) Thursdays 11:00 am to
(b) By appointment
Teaching Assistant: Mr. Yongning Wang
You may send questions to TA (and cc me).
Text: Multivariate Time Series Analysis with R and Financial Applications (2014), Ruey S. Tsay, Wiley:
(a) New Introduction to Multiple Time Series Analysis: Lutkepohl, Springer-Verlag, ISBN 3-540-26239-3.
(b) Time Series Analysis: Forecasting and Control. Box, Jenkins and Reinsel (2008)
4th Ed. Wiley. Chapters 10 and 11.
(c) A Course in Time Series Analysis: Pena, Tiao and Tsay (2001) Wiley
Chapters 14 and 15.
(d) Time Series Analysis by State Space Methods: Durbin and Koopman (2001)
Oxford University Press, for Kalman Filtering and Smoothing.
(e) Time Series Analysis: Hamilton (1994) Princeton University Press.
Chapters 11, 18, 19 & 20.
(f) Analysis of Financial Time Series, 3rd Ed., Tsay (2010), Wiley.
Chapters 8, 9, 10, & 11.
(g) Additional reference books given in the syllabus.
1. Tiao, G. C. and Tsay, R. S. (1989). Model specification in multivariate time series (with discussion).
Journal of Royal Statistical Society, Series B, 51, 157-213.
2. Tsay, R. S. (1991). Two canonical forms for vector ARMA processes. Statistica Sinica, 1, 247-269.
Midterm 40% + Final project 40% + Homework 20%
where scores of each component are normalized to be out of 100.
Final project: An empirical project or a research article. [Sudents should discuss with me before finalizing the topic.]
Software: An R package MTS will be heavily used.
Midterm: May 4 (Lecture: 8:30-9:30 am, Exam 9:30-11:30 am): exam
Open books and notes. A calculator or PC is needed.
Week1: Transfer function models or distributed-lag models. Chapters 10 & 11
of Box, Jenkins and Reinsel (2008).
Multivariate linear time series. Chapter 1 of Tsay (2014)
Data set used: m-un3states.txt, q-gdpunemp.txt, m-housnsa.txt, m-hsn1fnsa.txt
Handout: lec0 and lec1 and lec2
Week2: Vector AR (VAR) Models. lec3 (quarterly GDP data available in the MTS package)
Chapters 2 of Tsay (2014)
Week3: Vector AR (VAR) Models continued: Estimation (including Bayesian method), impulse response function
Prediction, Chapter 2 of Tsay (2014) [Lecture note has been updated.]
Week4: Vector ARMA (VARMA) Models: lec4
Chapter 3 of the textbook. [Note: lec4 will be used in week 5 too.]
Week5: Unit-root nonsationarity and Co-integration: Chapter 5 of the textbook.
Handout: lec5 , data set used: q-gdpun.txt
Week6: Co-integration continued. Error-correction forms. Additional note: lec5a and data used: m-bnd.txt
Will complete co-integration and ECM model in Week 7. (May 10, 2015)
Week7: Structural specification of VARMA process. Chapter 4 of the textbook: lec6, lec7 and data set: flourc.txt
Week8: Factor models, High-dimensional time series analysis, and discussions: lec8 and data sets are available from
Chapter 6 of the textbook
Week9: Multivariate volatility models and examples: lec9, data set used: m-ibmsp-6111.txt, m-ibmspko-6111.txt; see also Chapter 7 of the textbook
Week 10: State-Space Models: lec10 & Factor Models (brief discussions in class)
HW1: Data set: bjserm.txt, w-oilgas-9710.txt [*** New due date: April 13, 2015 ***]
HW2: Data sets: m-cpitb3m.txt, q-gpsavedi.txt, m-ip4comp.txt [Due on April 20, 2015]
HW3: Data sets: hw3p1.txt, m-dec125.txt, q-fdebt2.txt [Due on May 4, 2015]
HW4: Data sets: d-bhpvale-0206.txt, m-ip3comp.txt [Due on May 18, 2015]
HW5: Data sets: m-houst-nsa.txt, m-unippmitcu-6712.txt [Due on June 1, 2015]
to HW Assignments:
1. HW1 and R-analysis.
3. HW3 and R-analysis
5. HW5, and R-analysis
Project: Due on Exam Week (Friday 5:00 pm) [Students should talk to me about their topics.]
(a) Individual project or a team of two students
(b) Theoretical project: journal article critique or empirical project: real data
of vector time series (at least 2-dimensional).
(c) Students can also use empirical data to test any theory relevant to the course.
R is used exclusively in the lecture. I am developing a multivariate time series package for R.
You can use it throughout the course.
Other packages can also be used. We shall give some demonstrations in class.
Students may use other packages that are not discussed in class.
Some R scripts: (a) Corner method for tfm: Corner.R (b) Corner method from a given impulse response function: CornerFun.R (c) Forecasting of seasonal VARMA model: sVARMApred.R
Old Midterm exam: exam13 & Solutions
Midterm exam: EXAM15 & Solutions