Mathematics in Finance MS Program Courant Institute, New York University MODERN STATISTICAL INFERENCE AND ECONOMETRICS

Fall 2003 David J. Hait

E-Mail: [email protected]

Textbooks Required: ECONOMETRIC ANALYSIS by Greene (Fifth Edition) Recommended: ESTIMATION AND INFERENCE IN ECONOMETRICS by Davidson and MacKinnon Course Outline (subject to modification!!) Week

Topic

1

ESTIMATION AND INFERENCE: Summary statistics; measures of location and dispersion; skewness and kurtosis; introduction to maximum likelihood estimation; point and interval estimation; hypothesis testing; consistency, efficiency; and unbiasedness (Greene Appendix B,C,D, 17).

2

LINEAR REGRESSION MODELS I: Assumptions of the model, OLS regression; analysis of variance; finite-sample results; simple hypothesis tests; data problems; large-sample properties of estimators; instrumental variables (Greene 2, 3, 4, 5)

3

LINEAR REGRESSION MODELS II: Complex hypothesis tests; restricted least squares; dummy variables; model stability; non-nested models (Greene 6,7,8).

4

NON-LINEAR REGRESSION: Eliminating non-linearity; estimation via least-squares minimization (Greene 9, D&M 2, 3)

5, 6

LINEAR REGRESSION MODELS III: Non-spherical disturbances; generalized least squares; heteroskedasticity; serial correlation; systems of regression equations (Greene 10, 11.1-11.6, 12, 14.1-14.2)

7, 8

TIME SERIES MODELS: Introduction to time-series models; spectral analysis and identification; estimation of ARMA models; autocorrelated residuals in least-squares regression; nonstationarity, unit roots and cointegration (Greene 20)

9

MAXIMUM LIKELIHOOD ESTIMATION: The three classical tests; MLE and nonlinear regression models, GARCH modeling (Greene 17, 11.8)

1

10

FACTOR ANALYSIS: Principal components and MLE factor analysis methods (instructor’s notes)

11

PANEL DATA MODELS: Fixed effects and random effects models (Greene 13)

12, 13, 14

TBD