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Testing for vector autoregressive dynamics under heteroskedasticity

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  • Hafner, Christian M.
  • Herwartz, Helmut

Abstract

In this paper we introduce a bootstrap procedure to test parameter restrictions in vector autoregressive models which is robust in cases of conditionally heteroskedastic error terms. The adopted wild bootstrap method does not require any parametric specification of the volatility process and takes contemporaneous error correlation implicitly into account. Via a Monte Carlo investigation empirical size and power properties of the new method are illustrated. We compare the bootstrap approach with standard procedures either ignoring heteroskedasticity or adopting a spirit of the White correction. In terms of empirical size the proposed method clearly outperforms competing approaches without paying any price in terms of size adjusted power. We apply the alternative tests to investigate the potential of causal relationships linking daily prices of natural gas and crude oil. Unlike standard inference ignoring time varying error variances, heteroskedasticity consistent test procedures do not deliver any evidence in favor of short run causality between the two series.

Suggested Citation

  • Hafner, Christian M. & Herwartz, Helmut, 2002. "Testing for vector autoregressive dynamics under heteroskedasticity," SFB 373 Discussion Papers 2003,4, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    • Handle: RePEc:zbw:sfb373:20034
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    1. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(1), pages 122-150, February.
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    Cited by:

    1. Christian Hafner & Helmut Herwartz, 2008. "Analytical quasi maximum likelihood inference in multivariate volatility models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 67(2), pages 219-239, March.
    2. Christian M. Hafner & Helmut Herwartz, 2009. "Testing for linear vector autoregressive dynamics under multivariate generalized autoregressive heteroskedasticity," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 63(3), pages 294-323, August.

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    More about this item

    Keywords

    heteroskedasticity; bootstrap; vector autoregression; hypothesis testing; causality; energy markets;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • 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

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