# FE641 Multivariate Statistics and Advanced Time Series in Finance

Course Catalog Description

# 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.

Campus Fall Spring Summer
On Campus
Web Campus

Instructors

Professor Email Office

# 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

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

Course Resources

# Textbook

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

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

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

Materials:
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

HW 40%

Midterm 20%

Final Exam 40%

Lecture Outline

Week 1 Review of Statistical concepts. Estimators, Confidence intervals, Testing, Two way tables, Regression, ANOVA, logistic regression Lecture notes
Week 2 Principal Component Analysis, Independent Component Analysis, Scree plot, Returns and from PCA Ch. 9 in  and notes
Week 3 Factor models for asset returns. BARRA type models. Application to portfolio optimization. Ch. 15 in , Ch. 6 in
Week 4 Discriminant Analysis and Mixture models. Introduction to classification. Regime switching and Hidden Markov Chains. Lecture notes
Week 5 Lasso Regression and related sparse regression techniques. Applications to finance. Copula methods and applications to risk management. Lecture notes and Ch. 19 in 
Week 6 Bayesian Statistics Methods. Hierarchical Bayes. Conjugate prior/posterior techniques. Sequential Bayes. Applications to estimating parameters for financial models. Ch. 8 in  and Ch. 12 in  lecture notes
Week 7 Midterm Examination
Week 8 Review of Univariate Time series ARIMA and ARCH type models. Notes and Ch. 1 in 
Week 9 Time series with an external component. ARIMAX models. Granger Causality. Ch. 2 in  and notes
Week 10 Long Memory time series models. Hurst parameter estimation, R/S analysis. ARFIMA/FARIMA, FIGARCH models. Ch. 8 in 
Week 11 Vector autoregressive and moving average VAR, VARMA models Ch. 3 in , Ch. 11 in 
Week 12 Unit root non-stationarity, Co-integration. Co-integrated VAR and VARMA. Error corrected models. Ch. 5 in  and Ch. 12 in 
Week 13 Multivariate volatility models. Multivariate GARCH. Cholesky decomposition and volatility modeling. Ch. 7 in 
Week 14 Multivariate volatility (cont.). Go-GARCH, Dynamic orthogonal components, principal volatility components Ch. 13 in