Introduction

The main objective is to equip students with advanced statistical analytical techniques to have better success in the financial engineering domain. This course is preparing the students to use tools whenever statistical analysis of data is involved and to provide students with a solid foundation of statistical problem solving empirical methods with the ability to summarize, and calibrate observed multivariate data.

Course Description

The course is an advanced statistics course designed to incorporate the newest areas of statistics research and applications in the Stevens Institute curriculum. Topics include multivariate statistics methods such as principal components, independent components, factor analysis, discriminant analysis, mixture models, and lasso regression. Advanced topics in time series such as Granger causality, vector auto regressive models, co-integration, and error corrected models, VARMA models and multivariate volatility models will be presented.

Course Outcomes

A student graduating this course:

1. Will understand and summarize complex data sets through graphs and numerical measures
2. Will know how good estimators are by providing confidence intervals or approximate confidence intervals
3. Will know how to estimate and calibrate parameters of mathematical models using real data
4. Assess relationships between multiple random variables and stochastic processes
5. Use the techniques learned to study multivariate data from most domains
6. Will gain experience in analyzing multivariate time series data
7. Will gain knowledge of multivariate time series models, including vector AR and ARMA models with exogenous variables
8. Will have a good understanding of co-integration and error-correction models
9. Will have a good understanding of factor models and their applications
10. Will have a good understanding of structural specification of a linear vector process
11. Will be able to model multivariate volatility

Textbook

[1] Multivariate Time Series Analysis with R and Financial Applications by Ruey S. Tsay (2014), Wiley: ISBN: 978-1118617908.

[2] Modeling financial time series with S-Plus®, by E. Zivot, and Wang, J. (2007), Springer Science & Business Media.

[3] Analysis of Financial Time Series, 3rd Ed., Tsay (2010), Wiley.

Additional References

1. Time Series Analysis: Forecasting and Control, 4th ed., by Box, Jenkins and Reinsel (2008), Wiley. Chapters 10 and 11.
2. A Course in Time Series Analysis by Pena, Tiao and Tsay (2001), John-Wiley. Chapters 14 and 15.
3. Time Series Analysis by J. Hamilton (1994), Princeton University Press. Chapters 10, 11, 13, 18, 19 & 20.
4. Time Series Analysis by State Space Models by Durbin and Koopman (2001), Oxford University Press.
5. Elements of Multivariate Time Series Analysis by G. C. Reinsel (1993), SpringerVerlag.
6. Introductory Statistics with R, by Peter Daalgard, Springer; (2004). Corr. 3d printing edition January 9.
7. Probability and Stochastic Processes, by Ionut Florescu, (2014) Wiley, ISBN: 978-0-470-62455-5
8. An Introduction to Statistical Learning with Applications in R by G. James, D. Witteb, T. Hastie, R. Tibshirani, (2013), Springer, ISBN: 1-4614-7137-0
9. New Introduction to Multiple Time Series Analysis by H. Lutkepohl, SpringerVerlag, (2005). ISBN: 3-540-26239-3.
10. Applied Multivariate Statistical Analysis by R.A. Johnson and D.W. Wichern, 6th ed., (2007) Prentice Hall. ISBN 0-13-187715-1
11. Nonlinear Time Series: Nonparametric and Parametric Methods, J Fan and Q. Yao. New York: Springer-Verlag, 2003. ISBN 0-387-95170-9. 

Grading Policies

HW 40%

Midterm 20%

Final Exam 40%