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Nonlinear causality tests and multivariate conditional heteroskedasticity: a simulation study

  • Efthymios G. Pavlidis EMAIL logo , Ivan Paya and David A. Peel
Published/Copyright: February 20, 2013
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Studies in Nonlinear Dynamics and Econometrics
From the journal Studies in Nonlinear Dynamics and Econometrics Volume 17 Issue 3

Abstract

This paper assesses the performance of linear and nonlinear causality tests in the presence of multivariate conditional heteroskedasticity, exogenous volatility regressors, and additive volatility outliers. Monte Carlo simulations show that tests based on the least squares covariance matrix estimator can frequently lead to finding spurious Granger causality. The degree of oversizing tends to increase with the sample size and is substantially larger for the nonlinear test. On the other hand, heteroskedasticity-robust tests which are based on the fixed design wild bootstrap perform adequately in terms of size and power. Consequently, reliable causality in mean tests can be conducted without the need to specify a conditional variance function. As an empirical application, we re-examine the return-volume relationship.

Keywords: causality; multivariate ARCH; exogenous volatility regressors; additive volatility outliers; robust inference; Monte Carlo simulations
Corresponding author: Efthymios G. Pavlidis, Lancaster University Management School, Lancaster LA1 4YX, UK
  1. 1

    It also holds that the performance of tests for causality in variance depends crucially on the conditional mean equation (see, e.g., Pantelidis and Pittis 2004).

  2. 2

    It is assumed that the function under consideration has convergent Taylor expansions at any point in the sample space for every parameter vector in the parameter space (see assumption A4 in Péguin-Feissolle, Strikholm, and Teräsvirta etal. 2012, p. 4).

  3. 3

    Péguin-Feissolle, Strikholm, and Terésvirta (2012) employ a Lagrange multiplier test rather than a Wald test. As proven by Engle (1984), Wald, Lagrange multiplier and likelihood ratio tests are asymptotically equivalent. We employ the Wald test to simplify the exposition when robustifying for heteroskedasticity.

  4. 4

    Chesher and Jewitt (1987) show that as the maximum htt approaches unity HC1 becomes extremely biased. HC2, HC3 and HC4 circumvent this problem by attaching less weight to influential observations.

  5. 5

    It is also worth noting that because the effect of outliers is amplified by including high powers of y and x in the test Equation (2), nonlinear tests based on HC1 are expected to perform worse than their linear counterparts. We show that this is indeed the case in Section 3.1.

  6. 6

    The results are available from the authors upon request.

  7. 7

    All experiments are conducted on the High End Computing Cluster of Lancaster University in R 2.11.1. We are grateful to the administrator, Mike Pacey, for his valuable assistance.

  8. 8

    Some of the contemporaneous results should be interpreted with caution due to the overlap in trading. More specifically, there is a 2.5 h overlap between London and New York. As Lee and Rui (2002) argue, this overlap may create problems when examining contemporaneous (but not dynamic) relations.

  9. 9

    The results reported in Table 3 are similar but not identical to those of Lee and Rui (2002). The small differences can be attributed to data revisions. From February 20th, 2003 the history of the Datastream S&P500 indices was recalculated back to the base date of 2nd January 1973 using the current constituents.

  10. 10

    On the contrary, the LS method indicates bidirectional causality. Nonlinear LS causality tests, in particular, reject the null at the 1% significance level in all cases but one.

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Published Online: 2013-02-20
Published in Print: 2013-05-01

©2013 by Walter de Gruyter Berlin Boston

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https://doi.org/10.1515/snde-2012-0067
Keywords for this article
causality; multivariate ARCH; exogenous volatility regressors; additive volatility outliers; robust inference; Monte Carlo simulations

Articles in the same Issue

  1. Masthead
  2. Masthead
  4. The Danish krone-euro exchange rate and Danmark Nationalbank intervention operations
  5. Common large innovations across nonlinear time series
  6. The forward rate premium puzzle: a case of misspecification?1)
  7. A smooth transition long-memory model
  8. Nonlinear causality tests and multivariate conditional heteroskedasticity: a simulation study
  9. Threshold linkages between volatility and trading volume: evidence from developed and emerging markets
  10. Inventory investment and the business cycle: the usual suspect
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