Macroeconometrics: Advanced Time Series Analysis


The course is devoted to some of the Time Series Analysis methods which are used in macroeconometrics. The main topic is the study of VAR models, and in particular of non-stationary cointegrated VAR models. VAR models allow to simultaneously represent the dynamic behavior of a small number of time series. They are mainly used to compute forecasts, to evaluate the future impacts of economic shocks and to test structural hypothesis. Since many macroeconomic series are considered as non-stationary, the study of cointegrated non-stationary VAR models is then of particular interest. The course will end by a very short presentation of Dynamic Factor Models and FAVAR models.

At the end of this course, students should be able to:

  • Solve elementary exercises concerning stationary and non-stationary VAR models, cointegration and common trends, and analyze shocks propagation in these models through Choleski decomposition or using a structural approach.
  • Analyze outputs of VAR estimation on real data, in the stationary and non-stationary frameworks and in particular: chose the cointegration rank of a cointegrated non-stationary VAR as well as the correct specification for the deterministic terms, run tests on the coefficients, analyze IRFs.


  • General introduction : Time Series Analysis in Macroeconometrics
  • Stationary VAR processes:  General properties of stationary vector processes, innovations process, stationary VAR processes and invertibility, forecasting with a VAR model, Maximum Likelihood estimation of a VAR model, tests, Granger causality tests, information criteria, Impulse Response functions, structural VAR approach.
  • Non stationary VAR processes: Issues about non stationarity (spurious regressions, shocks persistency), non-stationary vector processes and cointegration, common trends and Wold representation of a non-stationary cointegrated vector process. Initial cointegration tests and Engle-Granger 2 steps estimation procedure. Error correction form of a cointegrated non stationary VAR model, Johansen ML estimation procedure and tests (cointegration rank, restrictions on parameters), Impulse Response Functions, structural approach.
  • Introduction to Factor Augmented VAR models (FAVAR): very short presentation of Dynamic Factor Models and FAVAR models, and of their use in macroeconometrics


BROCKWELL P.J. et DAVIS R.A. (1990). Time Series. Theory and Methods. Springer-Verlag.

GOURIEROUX C. et MONFORT A. (1995). Séries temporelles et modèles dynamiques, 2ème ed., Economica.

HAMILTON J.D. (1994). Time Series Analysis, Princeton Univ. Press.

JOHANSEN S. (1995). Likelihood-based inference in cointegrated Vector Auto-Regressive models, Oxford University Press.

JUSELIUS K. (2006). The cointegrated VAR model, Oxford Univ Press.

KILIAN L., LÜTKEPOHL H. (2017), Structural Vector Autoregressive Analysis, Cambridge University Press

LÜTKEPOHL H. (2005). New Introduction to Multiple Time Series Analysis, Springer Verlag.