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A Bootstrap Causality Test for Covariance Stationary Processes

  • Javier Hidalgo
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    This paper examines a nonparametric test for Granger-causality for a vector covariance stationary linear process under, possibly, the presence of long-range dependence. We show that the test converges to a non-distribution free multivariate Gaussian process, say vec (B(µ)) indexed by µ ? [0,1]. Because, contrary to the scalar situation, it is not possible, except in very specific cases, to find a time transformation g(µ) such that vec (B(g(µ))) is a vector with independent Brownian motion components, it implies that inferences based on vec (B(µ)) will be difficult to implement. To circumvent this problem, we propose bootstrapping the test by two alternative, although similar, algorithms showing their validity and consistency.

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    File URL: http://sticerd.lse.ac.uk/dps/em/em462.pdf
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    Paper provided by Suntory and Toyota International Centres for Economics and Related Disciplines, LSE in its series STICERD - Econometrics Paper Series with number /2003/462.

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    Date of creation: Nov 2003
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    Handle: RePEc:cep:stiecm:/2003/462
    Contact details of provider: Web page: http://sticerd.lse.ac.uk/_new/publications/default.asp

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    1. Sims, Christopher A & Stock, James H & Watson, Mark W, 1990. "Inference in Linear Time Series Models with Some Unit Roots," Econometrica, Econometric Society, vol. 58(1), pages 113-44, January.
    2. An, Hong-Zhi & Chen, Zhao-Guo & Hannan, E. J., 1983. "The maximum of the periodogram," Journal of Multivariate Analysis, Elsevier, vol. 13(3), pages 383-400, September.
    3. Hannan, E J & Terrell, R D, 1973. "Multiple Equation Systems with Stationary Errors," Econometrica, Econometric Society, vol. 41(2), pages 299-320, March.
    4. 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.
    5. Granger, C W J, 1969. "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods," Econometrica, Econometric Society, vol. 37(3), pages 424-38, July.
    6. Hosoya, Yuzo, 1977. "On the Granger Condition for Non-Causality," Econometrica, Econometric Society, vol. 45(7), pages 1735-36, October.
    7. Robinson, P M, 1991. "Automatic Frequency Domain Inference on Semiparametric and Nonparametric Models," Econometrica, Econometric Society, vol. 59(5), pages 1329-63, September.
    8. L Giraitis & J Hidalgo & Peter M. Robinson, 2001. "Gaussian estimation of parametric spectral density with unknown pole," LSE Research Online Documents on Economics 297, London School of Economics and Political Science, LSE Library.
    9. repec:cup:etheor:v:12:y:1996:i:1:p:61-87 is not listed on IDEAS
    10. Liudas Giraitis & Javier Hidalgo & Peter M Robinson, 2001. "Gaussian Estimation of Parametric Spectral Density with Unknown Pole," STICERD - Econometrics Paper Series /2001/424, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    11. Javier Hidalgo, 2000. "Nonparametric Test for Causality with Long-Range Dependence," Econometrica, Econometric Society, vol. 68(6), pages 1465-1490, November.
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