TrainingsMasterEconomicsCoursesTime series

Master EconomicsUE Time series


This course develops the basic theoretical tools for the analysis and estimation of univariate time series models. In particular, it discusses the concepts of stationarity and non-tationarity, unit-root tests, and exposes the techniques for estimating, forecasting and testing ARMA models using practical examples. Finally, it presents some non-linear models for conditional mean and variance.

Course outline :

• Brief Review of Statistics and Probability Concepts (pre-requisites)

• Stochastic processes and stationarity

• Classical stationary processes : AR, MA, ARMA

• Estimations techniques for the classical processes

• Forecasting methods for ARMA(p,q) processes

• White noise tests and stability tests

• Optimal choice of orders and Adequacy of parameters

• Univariate Non-Stationary processes and cointegration

• Modelling Nonlinearity of the conditional expectation

• Volatility modelling for univariate processes

Professional skills

  • To master the concepts specific to time series : stationarity and non-stationarity, unit roots, cointegration, auto-regressive processes and moving-average processes.
  • Identification, estimation, validation and forecasting of SARIMA models
  • Estimation and forecasting the volatility of the univariate financial data

Languages used

Main languages used by this course:

  • Français
  • Anglais


  • Bourbonnais, R., Terraza M., Analyse des séries temporelles, Dunod, 2016.
  • Brockwell, P., Davis, R., Time Series : Theory and Methods, Springer Verlag, 1991.
  • Hamilton, J., Time Series Analysis, Princeton University Press, 1994.

Fundamental prerequisites

  • Foundations of Statistics and Probablility
  • Introduction to econometrics

Recommended prerequisites

Econometrics I : linear model.

Structure and organisation

  • Lectures : 24 hours
  • Each session is accompanied by numerical and empirical examples or home works

Volume of teachings

  • Lectures: 24 hours