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Bootstrap-Assisted Tests for Skewness, Kurtosis, and Normality Under Unknown Dependence

Author

Listed:
  • Charisios Grivas

    (Aalborg University)

  • Zacharias Psradakis

    (Birkbeck Business School)

  • Marian Vavra

    (National Bank of Slovakia)

Abstract

This paper considers tests for skewness, kurtosis and normality of the one-dimensional marginal distribution of a stationary fractional process, which may exhibit short memory, antipersistence or long memory. The autoregressive-sieve bootstrap is used to obtain Pvalues and critical values for tests based on studentized empirical coefficients of skewness and kurtosis. These studentized coefficients are constructed using variance estimators obtained by the same bootstrap procedure. Notably, such tests, as well as variants based on non-studentized statistics, can be implemented in a straightforward manner without requiring knowledge or estimation of the memory parameter of the process. Monte Carlo simulations show that the bootstrap-assisted tests perform well for sample sizes that are typical in applied settings. The methodology is further illustrated through an application to realized measures of stock-return volatility.

Suggested Citation

  • Charisios Grivas & Zacharias Psradakis & Marian Vavra, 2026. "Bootstrap-Assisted Tests for Skewness, Kurtosis, and Normality Under Unknown Dependence," Working and Discussion Papers WP 10/2026, Research Department, National Bank of Slovakia.
    • Handle: RePEc:svk:wpaper:1146
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    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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