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

Introduction to time series econometrics


ZAKOÏAN Jean-Michel

Département : Finance


The objective of this course is to present the fundamental concepts of time series analysis. 

Completion of this course will enable you to move on to more advanced courses on time series modeling.

At the end of the course, the student should be able to

  • Compute and interpret a correlogram, discuss the concepts of stationarity and white noise.  
  • Derive the probabilistic and statistical properties of linear time series models.
  • Choose an appropriate ARIMA model for a given set of data and use it for forecasting. 
  • Handle multivariate time series and dicuss the notions of cointegration and causality.


  1. Generalities on univariate second-order stationary processes - Autocovariances, partial autocorrelations - Innovations - Wold theorem - Asymptotic properties of empirical moments.
  2. AR, MA, ARMA, SARIMA processes - Canonical representation - Identification, estimation, tests and forecasting - Model building - Nonstationary models, Unit root tests.
  3. Stationary vector processes - Multivariate AR models - Statistical Inference - Causality tests, impulse-response analysis.
  4. Non-stationary vector processes and definition of cointegration - Cointegrated VAR models and error-correction models (ECM) - Estimation of cointegrated VAR - Testing for Cointegration.


  • Brockwell, P.J. and R.A. Davis (1991) Time Series: Theory and Methods. 2nd Edition, Sringer.
  • Brockwell, P.J. and R.A. Davis (2002) Introduction to Time Series and Forecasting. Sringer.
  • Gouriéroux, C.  and A. Monfort (1997) Time Series and Dynamic Models,  Cambridge University Press, Cambridge.
  • Hamilton, J. D. (1994)  Time Series Analysis. Princeton University Press.