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# STEVENS FA 641 - Syllabus

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FA641 Multivariate Statistics and Advanced Time Series in FinanceIntroductionCourse DescriptionCourse OutcomesTextbookAdditional ReferencesGrading PoliciesFA641 Multivariate Statistics and Advanced TimeSeries in FinanceCourse Catalog DescriptionIntroductionThe 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 SummerOn Campus XWeb Campus XInstructorsProfessor Email OfficeMore InformationCourse DescriptionThe course is an advanced statistics course designed to incorporate the newest areas of statistics research andapplications in the Stevens Institute curriculum. Topics include multivariate statistics methods such as principalcomponents, 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 OutcomesA student graduating this course:1. Will understand and summarize complex data sets through graphs and numerical measures2. Will know how good estimators are by providing confidence intervals or approximate confidence intervals3. Will know how to estimate and calibrate parameters of mathematical models using real data4. Assess relationships between multiple random variables and stochastic processes5. Use the techniques learned to study multivariate data from most domains6. Will gain experience in analyzing multivariate time series data7. Will gain knowledge of multivariate time series models, including vector AR and ARMA models with exogenous variables8. Will have a good understanding of co-integration and error-correction models9. Will have a good understanding of factor models and their applications10. Will have a good understanding of structural specification of a linear vector process11. Will be able to model multivariate volatilityCourse ResourcesTextbook[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 ReferencesMaterials: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: 978-0-470-62455-58. An Introduction to Statistical Learning with Applications in R by G. James, D. Witteb, T. Hastie, R. Tibshirani, (2013), Springer, ISBN: 1-4614-7137-09. 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 0-13-187715-111. Nonlinear Time Series: Nonparametric and Parametric Methods, J Fan and Q. Yao. New York: Springer-Verlag, 2003. ISBN 0-387-95170-9. GradingGrading PoliciesHW 40%Midterm 20%Final Exam 40%Lecture OutlineTopic ReadingWeek1Review of Statistical concepts. Estimators, Confidence intervals, Testing, Two way tables,Regression, ANOVA, logistic regressionLecture notesWeek2Principal Component Analysis, Independent Component Analysis, Scree plot, Returns and fromPCACh. 9 in [3] and notesWeek3Factor models for asset returns. BARRA type models. Application to portfolio optimization. Ch. 15 in [2], Ch. 6 in[1]Week4Discriminant Analysis and Mixture models. Introduction to classification. Regime switching andHidden Markov Chains.Lecture notesWeek5Lasso Regression and related sparse regression techniques. Applications to finance. Copulamethods and applications to risk management.Lecture notes and Ch. 19in [2]Week6Bayesian Statistics Methods. Hierarchical Bayes. Conjugate prior/posterior techniques.Sequential Bayes. Applications to estimating parameters for financial models.Ch. 8 in [7] and Ch. 12 in[3] lecture notesWeek7Midterm ExaminationWeek8Review of Univariate Time series ARIMA and ARCH type models. Notes and Ch. 1 in [1]Week9Time series with an external component. ARIMAX models. Granger Causality. Ch. 2 in [1] and notesWeek10Long Memory time series models. Hurst parameter estimation, R/S analysis. ARFIMA/FARIMA,FIGARCH models.Ch. 8 in [2]Week11Vector autoregressive and moving average VAR, VARMA models Ch. 3 in [1], Ch. 11 in [2]Week12Unit root non-stationarity, Co-integration. Co-integrated VAR and VARMA. Error correctedmodels.Ch. 5 in [1] and Ch. 12 in[2]Week13Multivariate volatility models. Multivariate GARCH. Cholesky decomposition and volatilitymodeling.Ch. 7 in [1]Week14Multivariate volatility (cont.). Go-GARCH, Dynamic orthogonal components, principal volatilitycomponentsCh. 13 in

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