Short and Long Run Causality Measures: Theory and Inference Articles uri icon



publication date

  • January 2010

start page

  • 42

end page

  • 58


  • 1


  • 154

International Standard Serial Number (ISSN)

  • 0304-4076

Electronic International Standard Serial Number (EISSN)

  • 1872-6895


  • The concept of causality introduced by Wiener [Wiener, N., 1956. The theory of prediction, In: E.F. Beckenback, ed., The Theory of Prediction, McGraw-Hill, New York (Chapter 8)] and Granger [Granger, C.
    W.J., 1969. Investigating causal relations by econometric models and
    cross-spectral methods, Econometrica 37, 424&-459] is defined in terms of
    predictability one period ahead. This concept can be generalized by
    considering causality at any given horizon h
    as well as tests for the corresponding non-causality [Dufour, J.-M.,
    Renault, E., 1998. Short-run and long-run causality in time series:
    Theory. Econometrica 66, 1099&-1125; Dufour, J.-M., Pelletier, D.,
    Renault, É., 2006. Short run and long run causality in time series:
    Inference, Journal of Econometrics 132 (2), 337&-362]. Instead of tests
    for non-causality at a given horizon, we study the problem of measuring
    causality between two vector processes. Existing causality measures have
    been defined only for the horizon 1, and they fail to capture indirect
    causality. We propose generalizations to any horizon h
    of the measures introduced by Geweke [Geweke, J., 1982. Measurement of
    linear dependence and feedback between multiple time series. Journal of
    the American Statistical Association 77, 304&-313]. Nonparametric and
    parametric measures of unidirectional causality and instantaneous
    effects are considered. On noting that the causality measures typically
    involve complex functions of model parameters in VAR and VARMA models,
    we propose a simple simulation-based method to evaluate these measures
    for any VARMA model. We also describe asymptotically valid nonparametric
    confidence intervals, based on a bootstrap technique. Finally, the
    proposed measures are applied to study causality relations at different
    horizons between macroeconomic, monetary and financial variables in
    the US.