Modern Statistics and Econometrics from a Computational Point of View: G63.2707 * Neil Chriss:, Adjunct Professor of Mathematics, Director of Mathematics in Finance Program and Vice President, Goldman Sachs Asset Management. Web Page: www.math.nyu.edu/faculty/~chriss * Jonathan Goodman: Professor of Mathematics, Faculty Chair, Program for Mathematics in Finance. * TA: Ju-Young Lim, Courant Institute of Mathematical Sciences. Lectures: Monday Nights 7-8:50pm, by Neil Chriss. Texts * Introduction to the Theory and Practice of Econometrics, Second Edition. Judge, Hill, Griffiths, Luthkepoh and Lee. Wiley. * A Guide to Econometrics, Fourth Edition. Peter Kennedy. MIT Press. * Selected Readings to be distributed in class. Overview This course is the result of a great deal of research about what an econometrics course directed at students with strong mathematical skills who will be working in the financial world should be. It will cover statistical and econometric techniques in finance that our research suggests will be useful in a working environment. Thus the course will be aimed at learning solid practical techniques for the construction of financial models, while at the same time understanding the theoretical underpinnings of these same techniques. The course will attempt to familiarize students with the basic ideas and issues that arise in statistical modeling, while especially emphasizing powerful computational techniques that have become available and have become practical in the past 15 to 20 years. Throughout the course, examples and exercises will focus on the manipulation of financial data. A central theme of the course is the application of econometric techniques to financial data. Requirements Although the formal requirements for this course are limited, it is recommended that the students be familiar with linear algebra, scientific computing and basic probability. It is helpful, though not necessary, to have covered basic mathematical finance such as one might find in Mathematical Finance I and II. The course will rely heavily on the student's ability to compute, that is, to use either Matlab, C or C++ to read and manipulate data files. Students unable to fulfill the computational assignments within the course will not be able to pass. If you would like to find out whether you should be taking this course, see Neil Chriss or Jonathan Goodman as soon as possible. Assignments Assignments will generally be posted on my web site along with this document, downloadable data, frequent revisions of the curriculum and other interesting tid-bits. If you are taking this course, it is advisable that you frequently check my web site for information. Course Outline Lecture 1 (9/13/99): Sampling Theory and the Properties of Estimators. This lecture will define statistical model building and distinguish parametric and non-parametric modeling. Four estimation methods will be discussed: method of moments, maximum likelihood, least squares and maximum entropy estimation. Point estimates and confidence intervals. Special Reading: Frequentist and Subjectivist Perspectives of Model Building in Economics, by Dale Poirier. Lecture 2 (9/20/99): Properties of Estimators: Bias, precision, efficiency and consistency explained. Discussion of the tradeoff between the various properties in statistical estimation. The Cramer-Rao lower bound. Discussion of Edgeworth expansions, more on the bootstrap method. Special Reading: Data and Econometrician-The Uneasy Alliance, by Zvi Griliches. Lecture 3 (9/27/99): Maximum Likelihood Estimation: In-depth discussion of calculation of standard errors. Bootstrap methods versus asymptotic methods are discussed in detail. AR(1) and GARCH models are introduced as examples of likelihood function calculations. Lecture 4(10/4/99): Hypothesis Testing in Statistics: Basic notions: null hypothesis, power of a test, types of errors, significance, test statistics. Rejection criteria using asymptotic theory of statics and via Monte Carlo. Lecture 5(10/11/99): Classical Linear Regression Model: The basic linear regression model with normal errors. Discussion of singular value decompositions and "variance inflation factors". Discussion of goodness of fit criteria and hypothesis testing. Lecture 6(10/18/99): Classical Linear Regression II: Time series modeling and vector auto-regression. Principle components. Significance testing and factor selection. Lecture 7(10/25/99): Classical Linear Regression III: The three most common data problems: heteroskedasticity, autocorrelation in residuals and multicollinearity. Lecture 8(11/1/99): Introduction to Bayesian Statistics: The role of prior beliefs in data interpretation. The notion of "Bayesian learning". Computational methods for sampling the posterior distribution including rejection and Markov chain methods (Gibbs sampler). Lecture 9(11/8/99): Introduction to Decision Theory: The notion of the risk of an estimator. The notion of dominant and admissible estimators. James-Stein rule. Lecture 10(11/15/99): Statistics in the Presence of Faulty Data: Proposed topics include E-M algorithm, methods for identification of ouliers. Robust estimators and data trimming techniques: breakdown points of estimators. Guest Lecture. Lecture 11(11/22/99): Statistical Model Selection and the Evils of Data Mining: Proposed topics include computational techniques for determining the distribution of a variable that arises as the result of a large search, induced order statistics and multiple comparison theory. Lecture 12(11/29/99): The Nature of Financial Data: Guest Lecture by Robert Ferstenberg, head of research, ITG Inc. Lecture 13(12/6/99): Statistical Estimation of Preypayment Models: Guest Lecture.