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Testing for Causation Using Infinite Order Vector Autoregressive Processes


  • Lütkepohl, Helmut


Tests for Granger-causality have been performed in numerous empirical studies. These tests are usually based on finite order vector autoregressive (VAR) processes, and the assumption is made that the model fitted to the available data corresponds to the true data generating mechanism. In the present study, the more general assumption is made that a finite order VAR model is fitted to a potentially infinite order process. The order is assumed to increase with the sample size. Asymptotic properties of tests for Granger-causality as well as other types of causality concepts are derived. Some limited small sample results are obtained using simulation methods.

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  • Lütkepohl, Helmut & POSKITT, D.S., 1996. "Testing for Causation Using Infinite Order Vector Autoregressive Processes," Econometric Theory, Cambridge University Press, vol. 12(01), pages 61-87, March.
  • Handle: RePEc:cup:etheor:v:12:y:1996:i:01:p:61-87_00

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    References listed on IDEAS

    1. Hardle, Wolfgang & Linton, Oliver, 1986. "Applied nonparametric methods," Handbook of Econometrics,in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 38, pages 2295-2339 Elsevier.
    2. Mikosch, T., 1991. "Functional limit theorems for random quadratic forms," Stochastic Processes and their Applications, Elsevier, vol. 37(1), pages 81-98, February.
    3. Andrews, Donald W K, 1991. "Asymptotic Normality of Series Estimators for Nonparametric and Semiparametric Regression Models," Econometrica, Econometric Society, vol. 59(2), pages 307-345, March.
    4. Phillips, Peter C. B., 1977. "An approximation to the finite sample distribution of Zellner's seemingly unrelated regression estimator," Journal of Econometrics, Elsevier, vol. 6(2), pages 147-164, September.
    5. Linton, Oliver, 1993. "Adaptive Estimation in ARCH Models," Econometric Theory, Cambridge University Press, vol. 9(04), pages 539-569, August.
    6. Newey, Whitney K, 1990. "Semiparametric Efficiency Bounds," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 5(2), pages 99-135, April-Jun.
    7. Phillips, Peter C B, 1977. "A General Theorem in the Theory of Asymptotic Expansions as Approximations to the Finite Sample Distributions of Econometric Estimators," Econometrica, Econometric Society, vol. 45(6), pages 1517-1534, September.
    8. repec:cup:etheor:v:9:y:1993:i:4:p:539-69 is not listed on IDEAS
    9. Newey, Whitney K., 1988. "Adaptive estimation of regression models via moment restrictions," Journal of Econometrics, Elsevier, vol. 38(3), pages 301-339, July.
    10. Chesher, Andrew & Spady, Richard, 1991. "Asymptotic Expansions of the Information Matrix Test Statistic," Econometrica, Econometric Society, vol. 59(3), pages 787-815, May.
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