ENSAE Paris - École d'ingénieurs pour l'économie, la data science, la finance et l'actuariat

Time Series 3A-CI/MS


ZAKOÏAN Jean-Michel

Department: Finance


This time series course aims to recall the various methods introduced in previous courses that explicitly relate to the processing and modeling of time series. It covers the basics seen in the linear time series course of the second year of ENSAE. The lecture is complemented by tutorial sessions.
At the end of this course, students should be able to:

  •     Decompose a series in the presence of a trend/cycle/seasonnality.
  •     Estimate and analyze ARMA models,  estimate and analyze error-correction models.


  1. Basic concepts (operators, ergodicity and stationarity, mean,  autocovariance function, sample estimators)
  2.  Autoregressive, moving average and ARMA processes (theory and properties)
  3. Model building (ACF, PACF, residuals analysis)
  4.  Forecasting with ARMA models
  5.  Unit root and ARIMA models (unit root tests, modelling)
  6. Seasonal time series


Hamilton (1994), Time Series Analysis, Princeton University Press.
Gouri eroux and Monfort (1995), Séries temporelles et modéles dynamiques, Economica
Tsay, Analysis of Financial Time Series, John Wiley & Sons, Inc Slides, notes, codes