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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. 
  • 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.