## IE 522 - Statistical Methods in Finance

### Semesters Offered

TitleRubricSectionCRNTypeHoursTimesDaysLocationInstructor
Statistical Methods in FinanceIE522A55481LCD1400 - 1520 T R  101 Transportation Building Liming Feng

### Official Description

Methods of statistical modeling of signals and systems with an emphasis on finance applications. Review of linear algebra, probability theory, and spectral analysis; Linear Time Invariant (LTI) and ARX models; least-squares, maximum-likelihood, non-parametric, and frequency-domain methods; convergence, consistency and identifiability of linear models; asymptotic distribution of parameter estimates; techniques of model validation; Principle Component Analysis (PCA) for dimension reduction; ARCH and GARCH processes and their related models; implementation, application, and case-studies of recursive identification; Monte Carlo simulation. Course Information: Credit is not given for both IE 522 and GE 524. Prerequisite: MATH 415.

### Course Description

Statistics is the most important tool for analyzing financial data. IE 522 covers basic probability theory and statistical methods that are fundamental for financial modeling and analysis of financial data. This course is restricted to the Master of Science in Financial Engineering students. The materials that are covered include: probability basics (probability space, probability measure, conditional probability, random variable, probability distribution, expectation, commonly used distributions, characteristic function, multivariate distribution, conditional expectation); statistical inference (descriptive statistics, R, point estimation, Monte Carlo simulation, confidence interval, hypothesis testing, maximum likelihood estimation, likelihood ratio test, resampling, normal mixture); time series models (stationarity, autocorrelation, moving averaging process, autoregressive process, ARIMA models, parameter estimation, forecasting, ARCH and GARCH models); and linear regression (simple linear regression, ordinary least squares estimation, analysis of variance, goodness of fit, multiple linear regression, statistical inference, regression diagnostics). Credit is not given for both IE 522 and GE 524. Prerequisite: MATH 415.

8/23/2016