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Granger-causal analysis of VARMA-GARCH models

Author

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  • Tomasz Wozniak
Abstract
Recent economic developments have shown the importance of spillover and contagion effects in financial markets. Such effects are not limited to relations between the levels of financial variables but also impact on their volatility. I investigate Granger causality in conditional mean and conditional variances of time series. For this purpose a VARMA-GARCH model is used. I derive parametric restrictions for the hypothesis of noncausality in conditional variances between two groups of variables, when there are other variables in the system as well. These novel conditions are convenient for the analysis of potentially large systems of economic variables. Such systems should be considered in order to avoid the problem of omitted variable bias. Further, I propose a Bayesian Lindley-type testing procedure in order to evaluate hypotheses of noncausality. It avoids the singularity problem that may appear in the Wald test. Also, it relaxes the assumption of the existence of higher-order moments of the residuals required for the derivation of asymptotic results of the classical tests. In the empirical example, I find that the dollar-to-Euro exchange rate does not second-order cause the pound-to-Euro exchange rate, in the system of variables containing also the Swiss frank-to-Euro exchange rate, which confirms the meteor shower hypothesis of Engle, Ito & Lin (1990).

Suggested Citation

  • Tomasz Wozniak, 2012. "Granger-causal analysis of VARMA-GARCH models," Economics Working Papers ECO2012/19, European University Institute.
    • Handle: RePEc:eui:euiwps:eco2012/19
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    References listed on IDEAS

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    Blog mentions

    As found by EconAcademics.org, the blog aggregator for Economics research:
    1. Some Recent Papers on Granger Causality
      by Dave Giles in Econometrics Beat: Dave Giles' Blog on 2012-12-03 00:30:00

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    Cited by:

    1. Woźniak, Tomasz, 2015. "Testing causality between two vectors in multivariate GARCH models," International Journal of Forecasting, Elsevier, vol. 31(3), pages 876-894.
    2. Matthieu Droumaguet & Tomasz Wozniak, 2012. "Bayesian Testing of Granger Causality in Markov-Switching VARs," Economics Working Papers ECO2012/06, European University Institute.

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    More about this item

    Keywords

    Granger causality; second-order noncausality; VARMA-GARCH models; Bayesian testing;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • 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
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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