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Robust causality test of infinite variance processes

Author

Listed:
  • Akashi, Fumiya
  • Taniguchi, Masanobu
  • Monti, Anna Clara

Abstract

This paper develops a robust causality test for time series with infinite variance innovation processes. First, we introduce a measure of dependence for vector nonparametric linear processes, and derive the asymptotic distribution of the test statistic by Taniguchi et al. (1996) in the infinite variance case. Second, we construct a weighted version of the generalized empirical likelihood (GEL) test statistic, called the self-weighted GEL statistic in the time domain. The limiting distribution of the self-weighted GEL test statistic is shown to be the usual chi-squared one regardless of whether the model has finite variance or not. Some simulation experiments illustrate satisfactory finite sample performances of the proposed test.

Suggested Citation

  • Akashi, Fumiya & Taniguchi, Masanobu & Monti, Anna Clara, 2020. "Robust causality test of infinite variance processes," Journal of Econometrics, Elsevier, vol. 216(1), pages 235-245.
    • Handle: RePEc:eee:econom:v:216:y:2020:i:1:p:235-245
    DOI: 10.1016/j.jeconom.2020.01.016
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    References listed on IDEAS

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    1. Francesco Bravo, 2009. "Blockwise generalized empirical likelihood inference for non-linear dynamic moment conditions models," Econometrics Journal, Royal Economic Society, vol. 12(2), pages 208-231, July.
    2. Smith, Richard J, 1997. "Alternative Semi-parametric Likelihood Approaches to Generalised Method of Moments Estimation," Economic Journal, Royal Economic Society, vol. 107(441), pages 503-519, March.
    3. Yuichi Kitamura & Michael Stutzer, 1997. "An Information-Theoretic Alternative to Generalized Method of Moments Estimation," Econometrica, Econometric Society, vol. 65(4), pages 861-874, July.
    4. Parente, Paulo M.D.C. & Smith, Richard J., 2011. "Gel Methods For Nonsmooth Moment Indicators," Econometric Theory, Cambridge University Press, vol. 27(1), pages 74-113, February.
    5. Benoit Mandelbrot, 1963. "New Methods in Statistical Economics," Journal of Political Economy, University of Chicago Press, vol. 71, pages 421-421.
    6. Shiqing Ling, 2005. "Self‐weighted least absolute deviation estimation for infinite variance autoregressive models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(3), pages 381-393, June.
    7. Fumiya Akashi, 2017. "Self-weighted generalized empirical likelihood methods for hypothesis testing in infinite variance ARMA models," Statistical Inference for Stochastic Processes, Springer, vol. 20(3), pages 291-313, October.
    8. Davis, Richard & Resnick, Sidney, 1985. "More limit theory for the sample correlation function of moving averages," Stochastic Processes and their Applications, Elsevier, vol. 20(2), pages 257-279, September.
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    More about this item

    Keywords

    Granger causality; Nonparametric hypothesis testing; Generalized empirical likelihood; Self-weighting;
    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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