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## Program

### Updated A.Y. 2019-2020

Prerequisites

Linear algebra (operations with matrices and vectors, trace of a matrix, properties of symmetric matrices, quadratic forms, eigenvectors, eigenvalues, diagonalization).

Calculus.

Syllabus

The following syllabus is to be considered temporary and may change in the future.

Econometrics

Simple linear regression model:

• OLS estimators: derivation through first order conditions.
• Definition and interpretation of the coefficient of determination.
• Unbiasedness of OLS estiamtors: theory and practice (with Matlab).
• Conditional variance of OLS estiamtors: theory and practice (with Matlab).
• Unbiased estimator of error variance.
• Statistical inference: hypothesis testing and t-statistic.
• Statistical inference: the Capital Asset Pricing Model and the beta of a stock.

Multiple linear regression model:

• Recap of matrix algebra and gradient of a function.
• OLS estimators: derivation through first order conditions.
• Unbiasedness of OLS estiamtors.
• Conditional variance-covariance matrix of OLS estiamtors.
• Unbiased estimator of error variance.
• Multicollinearity.
• Blueness of the OLS estimator: the Gauss-Markov theorem.
• Multiple hypothesis testing.
• Maximum Likelihood Estimator.
• Model comparison.
• OLS asymptotics.
• OLS diagnostics.

Bibliography

Wooldridge J. M.  (2016). Introductory Econometrics: A Modern Approach.

Brooks C. (2014). Introductory Econometrics for Finance.

Time Series

• Introductory concepts: trends, seasonality and returns.
• Strongly stationarity: definition and main properties.
• IID noise.
• Weekly stationarity: definition and main properties.
• Ergodicity
• AR, MA and ARMA processes.
• Vector Auto-Regressive processes: estimation and identification.
• Cointegration.

Bibliography

Wei (2006). Time Series Analysis: Univariate and Multivariate Methods. Addison-Wesley.

Brockwell P.J. and Davis R.A. (2002). Introduction to Time Series and Forecasting, Springer.

Brockwell P.J. and Davis R.A. (1991). Time Series: Theory and Methods. Springer.