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Temporal aggregation and causality in multiple time series models

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  • Breitung, Jörg
  • Swanson, Norman Rasmus

Abstract

In this paper we characterize what has sometimes been referred to in the literature as instantaneous causality, by examining the consequences of temporal aggregation in (possibly) Granger causal systems of variables. Our approach is to compare the concept of contemporaneous correlation due to Swanson and Granger (1997) with that of Granger causality. Using asymptotic theory based on large aggregation intervals we derive conditions for a correspondence between both concepts. These results allow us to differentiate between spurious contemporaneous correlation arising because of aggregation, and true Granger causality. Monte Carlo experiments indicate that the asymptotic results provide a reliable guidance for finite samples and finite aggregation intervals.

Suggested Citation

  • Breitung, Jörg & Swanson, Norman Rasmus, 1998. "Temporal aggregation and causality in multiple time series models," SFB 373 Discussion Papers 1998,27, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    • Handle: RePEc:zbw:sfb373:199827
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    References listed on IDEAS

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    1. Pierce, David A. & Haugh, Larry D., 1977. "Causality in temporal systems : Characterization and a survey," Journal of Econometrics, Elsevier, vol. 5(3), pages 265-293, May.
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    5. Granger, C. W. J., 1980. "Testing for causality : A personal viewpoint," Journal of Economic Dynamics and Control, Elsevier, vol. 2(1), pages 329-352, May.
    6. Granger, C W J, 1969. "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods," Econometrica, Econometric Society, vol. 37(3), pages 424-438, July.
    7. Lutkepohl, Helmut & Burda, Maike M., 1997. "Modified Wald tests under nonregular conditions," Journal of Econometrics, Elsevier, vol. 78(2), pages 315-332, June.
    8. Zellner, Arnold & Montmarquette, Claude, 1971. "A Study of Some Aspects of Temporal Aggregation Problems in Econometric Analyses," The Review of Economics and Statistics, MIT Press, vol. 53(4), pages 335-342, November.
    9. Larry D. Haugh & David A. Pierce, 1977. "Causality in temporal systems: characterizations and a survey," Special Studies Papers 87, Board of Governors of the Federal Reserve System (U.S.).
    10. Granger, C. W. J., 1988. "Some recent development in a concept of causality," Journal of Econometrics, Elsevier, vol. 39(1-2), pages 199-211.
    11. Brewer, K. R. W., 1973. "Some consequences of temporal aggregation and systematic sampling for ARMA and ARMAX models," Journal of Econometrics, Elsevier, vol. 1(2), pages 133-154, June.
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    1. Breitung, Jörg, 1998. "Neuere Entwicklungen auf dem Gebiet ökonometrischer Strukturmodelle: Strukturelle Vektorautoregressionen," SFB 373 Discussion Papers 1998,80, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.

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    More about this item

    Keywords

    Granger causality; instantaneous causality; contemporaneous correlation; temporal aggregation; stock and ow variables;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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