Business 41914: Multivariate Time Series Analysis

Spring Quarter of 2009

Instructor: Ruey S. Tsay

Office: HPC 455
Tel:      773-702-6750
Fax:     773-702-0458

Lecture: Tuesdays 8:30 am to 11:30 am, HPC 24

Office hour: (a) Thursdays 10:30 am to 11:30 am
                    (b) By appointment
You may e-mail me questions. E-mail is the easiest way
to make contact with me. I try to check the e-mail at least
once a day.

Teaching Assistant:
Mr. Paco Vazquez-Grande, his e-mail:

Text:  No textbook is used

Recommend book: New Introduction to Multiple Time Series Analysis by Lutkepohl, Springer-Verlag 2005.
ISBN 3-540-26239-3.

Some reference books:
(a) Time Series Analysis: Forecasting and Control. Box, Jenkins and Reinsel (1994)
      3rd Ed. Prentice Hall.  Chapters 10 and 11.
(b) A Course in Time Series Analysis: Pena, Tiao and Tsay (2001) Wiley
      Chapters 14 and 15.
(c) Time Series Analysis by State Space Methods: Durbin and Koopman (2001)
      Oxford University Press, for Kalman Filtering and Smoothing.
(d) Time Series Analysis: Hamilton (1994) Princeton University Press.
      Chapters 11, 18,  19 & 20.
(e) Analysis of Financial Time Series, 2nd Ed., Tsay (2005), Wiley.
      Chapters 8, 9, 10, & 11.
(f) 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

Midterm: May 5 (Lecture: 8:30-9:30 am, Exam 9:30-11:30 am)
Open books and notes. A calculator or PC is needed.

Week1:  Transfer function model or distributed-lag model.  Chapters 10 & 11
                of Box, Jenkins and Reinsel (1994).
                Data set used: gas-furnace
                Handout: lec1, R commands used: Rcommands-1.txt
Week2:  Vector ARMA Models. Chapter 14 of Pena, Tiao and Tsay (2002)
                Data sets used: clsar1.dat, clsma1.dat
                Handout:  lec2, R commands used: Rcommands-2.txt
Week 3: Vector ARMA Models (continued).
               Data sets used: gas-furnace (see Lecture 1),  CGK series 
               Handout: lec3, R commands used: Rcommands-3.txt
Week 4: Unit-Root Nonstationarity and Co-integration
               Handout: lec4,
               Data set used: q-gdpun.txt (year, mm, dd, gdp, unemp-rate).
Week 5:  Diffusion index and Factor Models
               Handout: lec5,   Data set used:   m-bnd.txt
Week 6: Structural Specification of VARMA Models
               Handout: lec6 ,   Data set used: flourc.txt

Week 7: Structural Specification of VARMA Models (continued)
              Handout: lec7
Week 8: Empirical structural specification & Seasonal models: R-Program--Kronid
               Handout: lec7app, lec8, data set:   hous.dat
Week 9: State-space models and the Kalman filter
               Handout:  lec9, data set:
Week 10: Multivariate volatility models
               Handout: lec10,   data set:  m-gmspln5002.txt

Homework assignment
HW1:  due on April 7 (before class). Dataset: data-1.txt
HW2 : due on April 14 (before class). Data set used: de-inv.txt
HW3 : due on April 28. Data sets: w-Aaa.txt, w-Baa.txt
HW4 : due on May 20. Data sets:
s1.txt, s2.txt

Solutions to HW Assignments:
HW1 and computer output.

Additional R scripts:
(1) Compute and plot cross-correlation matrices: ccm.R
(2) Estimation of transfer function models (one input & one output series): tfm.R

(3) Compute the multivariate Ljung-Box statistics: mq.R
(4) Identify the order of a VAR process: VARorder.R
(5) Estimate a VAR model: VAR.R
(6) Compute the forecasts of a VAR model: VARpred.R
(7) Compute the impulse response function of VAR models: VARirf.R
(8) Co-intrgration test: coint.R

In class exam: midterm & solutions

Final Project:  Due on Week 10 (Friday 5:00 pm)
(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.

SCA and R are used for most analyses. S-plus is also used for
Kalman filter and multivariate volatility modeling. Other packages
can also be used.  We shall give some demonstrations in class.
Students may use other packages that are not discussed in class.

Old in-class exam: exam07 & exam07opt.txt & Solution

*** Additional data sets used and handout at Tsing-Hua ***
Lecture: lec0.pdf
(a) Unemployment rates of Illinois, Michigan and Ohio: m-3state-un.txt
(b) West Germany data set: investiment, income and consumption: de-inv.txt
(c) Monthly returns of Deciles 1 and 9 portfolios of the U.S. market: m-dec19.txt
(d) Taiwan quarterly exports and imports: twn-expimp.txt
(e) Taiwan unemployment rates: twn-table25.txt