Statistics & Operations Research (STAT-UB)

This course examines modern statistical methods as a basis for decision making in the face of uncertainty. Topics include probability theory, discrete and continuous distributions, hypothesis testing, estimation, and statistical quality control. With the aid of computers, these statistical methods are used to analyze data.

Presents an introduction to statistical models and their application to decision making. Topics include the simple linear regression model, inference in regression analysis, sensitivity analysis, and multiple regression analysis.

Presents a mathematical background for the stochastic processes that are widely employed as modeling tools in finance. The emphasis is on an intuitive approach and examples rather than on proofs and mathematical rigor. Topics include random walks, martingales, Markov chains, Poisson process and other continuous time Markov chains, Brownian motion, geometric Brownian motion, and other diffusion processes. The relevance of the considered processes to financial modeling is stressed throughout. In particular, applications to pricing of derivative securities and to modeling of the term structure of interest rates are discussed.

Covers the basic concepts of probability. Topics include the axiomatic definition of probability; combinatorial theorems; conditional probability and independent events; random variables and probability distributions; expectation of functions of random variables; special discrete and continuous distributions, including the chi-square, t, F, and bivariate normal distributions; law of large numbers; central limit theorem; and moment generating functions. The theory of statistical estimation is introduced with a discussion on maximum likelihood estimation.

Consists of two distinct components: statistical inference and regression analysis. Statistical inference topics include the principles of statistical estimation and inference, Neyman Pearson Lemma, testing of means, variances, tests of independence, and nonparametric methods. Regression analysis discusses the general linear regression model, least squares estimation, departures from standard assumptions, autocorrelation, multicollinearity, analysis of residuals, choice of variables, and nonlinear models.

This is a data-driven, applied statistics course focusing on the analysis of data using regression models. It emphasizes applications to the analysis of business and other data and makes extensive use of computer statistical packages. Topics include simple and multiple linear regression, residual analysis and other regression diagnostics, multicollinearity and model selection, autoregression, heteroscedasticity, regression models using categorical predictors, and logistic regression. All topics are illustrated on real data sets obtained from financial markets, market research studies, and other scientific inquiries.

A model-based approach to forecasting time series data, with emphasis on model building, foundations, and applications. Students will use the methodology of the course to analyze data sets of their choice in two projects. Weekly homework assignments on data analysis and theory. Topics of the course include the following: Autocorrelation vs. trend; Mean Squared Error for measuring forecast performance; Conditional distribution of future given present and past; Mean reversion (stationarity) and differencing; ARIMA models, their properties, and the corresponding forecasts; Box-Jenkins approach to statistical modeling: estimation, identification, diagnostic checking; Model Selection using informaiton criteria; Exponential Smoothing; Linear vs. Nonlinear models; Chaos; Best possible forecast vs. best linear forecast; ARCH/GARCH models for forecasting volatility; Fractional ARIMA and long-memory models; Seasonal ARIMA models; Unit root tests and cointegration.

This is an introductory course in stochastic processes. Presents classes of stochastic processes, which are widely used as modeling tools in many fields of application, including finance, economics, accounting, and actuarial science. Covers basic theory of discrete and continuous time Markov chains, Brownian motion and its generalization, and martingales. Also discusses statistical aspects of these processes. In the final part of the course, introduces the idea of stochastic integration and develops the rules of stochastic calculus. If time permits, also considers some stochastic differential equations.

Discusses the mathematical and technical aspects of investments. Topics include measurement of interest and discount rates, accumulated value and present value, annuities, sinking funds, amortization of debt, and determination of yield rates on securities. Applications include bond evaluation, mortgages, capital budgeting, and depreciation methods.

Independent study provides an opportunity for a select group of upperclassmen each year to work one-on-one with a faculty member on a topic selected by the student and approved by the supervising faculty member. Each student is expected to spend as much time on the independent study as would be spent on a regular course, and the topic selected may not replicate an existing course. An information sheet with important guidelines about Independent Study is available at stern.nyu.edu/portal-partners/current-students/undergraduate/resources-policies/forms.

This course examines modern statistical methods as a basis for decision making in the face of uncertainty. Topics include probability theory, discrete and continuous distributions, hypothesis testing, estimation, and statistical quality control. With the aid of computers, these statistical methods are used to analyze data. Also presented are an introduction to statistical models and their application to decision making. Topics include the simple linear regression model, inference in regression analysis, sensitivity analysis, and multiple regression analysis.

This course examines modern statistical methods as a basis for decision making in the face of uncertainty. Topics include probability theory, discrete and continuous distributions, hypothesis testing, estimation, and statistical quality control. With the aid of computers, these statistical methods are used to analyze data.

Presents an introduction to statistical models and their application to decision making. Topics include the simple linear regression model, inference in regression analysis, sensitivity analysis, and multiple regression analysis.