Business 41914: Multivariate Time Series Analysis

Spring
Quarter of 2015

Instructor: Ruey S. Tsay

Office: HPC 455

Tel: 773-702-6750

Fax: 773-702-0458 (Write my name on the cover page.)

e-mail: ruey.tsay@Chicagobooth.edu

Lecture: Mondays 8:30 am to 11:30 am, HPC 3A

Office hour: (a) Thursdays 11:00 am to
12:00 noon

(b) By appointment

Teaching Assistant: Mr. Yongning Wang

email: ywang1@chicagobooth.edu

You may send questions to TA (and cc me).

Text: Multivariate Time Series Analysis with R and Financial Applications (2014), Ruey S. Tsay, Wiley:

ISNB:978-1118617908

Some
reference books:

(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.

Some
reference articles:

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.

Course Syllabus.

Grading:
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.

Lecture:

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)

Homework assignments:

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]

Solutions
to HW Assignments:

1. HW1 and R-analysis.

2. HW2

3. HW3 and R-analysis

4. HW4

5. HW5, and R-analysis

Final
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.

Computing:

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