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## Syllabus

### 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.
• Omitted and irrelevant variables.
• Measurement errorrs.
• OLS asymptotics.

Bibliography

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

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

Time Series

• Introduction to time series (trends, seasonality, co-integration), log-returns.
• Convergence to equilibrium of an AR(1) process.
• Strongly stationary processes: definition and properties.
• White noise.
• Covariance-stationarity: definition and main properties.
• Random walk.
• Gaussian processes.
• Non-stationary processes and  order of integration. Consequences of non-stationarity on regression models.
• Mean-ergodic and variance-ergodic processes. Sufficient conditions for ergodicity. Ergodicity of gaussian processes.
• Memory of a process and the test for the autocorrelation coefficient.
• Lag operator. Polynomials of the lag operator.
• ARMA, AR and MA processes: definition. Invertibility and causality: definition.
• Mean, variance, co-variance and stability condition for AR(1)-processes.
• Causality and explosiveness of AR(1)-processes.
• Stability region for AR(2) processes. Variance, Co-variance, autocorrelation and partial autocorrelation of AR(p) processes.
• Selection of the autoregressive order: ACF vs PACF.
• Moving Average Processes: stationarity, invertibility, ACF and PACF.
• Moving Average vs. Autoregressive.
• Invertibility and Causality of AMRA(p,q).
• ARIMA models
• The Box-Jenkins procedure.
• Vector Auto-Regressive Models: structural, reduced-form and companion representation.
• Stationarity conditions of VAR models.
• Triangularisation and identification of structural VAR.
• Wold Theorem and the Impulse response function.
• Co-integration: definition and examples. Vector Error Correction Models: estimation and interpretation.

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.