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Complexity measure, kernel density estimation, bandwidth selection, and the efficient market hypothesis

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  • Matthieu Garcin

    (Research Center - Léonard de Vinci Pôle Universitaire - De Vinci Research Center)

Abstract

We are interested in the nonparametric estimation of the probability density of price returns, using the kernel approach. The output of the method heavily relies on the selection of a bandwidth parameter. Many selection methods have been proposed in the statistical literature. We put forward an alternative selection method based on a criterion coming from information theory and from the physics of complex systems: the bandwidth to be selected maximizes a new measure of complexity, with the aim of avoiding both overfitting and underfitting. We review existing methods of bandwidth selection and show that they lead to contradictory conclusions regarding the complexity of the probability distribution of price returns. This has also some striking consequences in the evaluation of the relevance of the efficient market hypothesis. We apply these methods to real financial data, focusing on the Bitcoin.

Suggested Citation

  • Matthieu Garcin, 2023. "Complexity measure, kernel density estimation, bandwidth selection, and the efficient market hypothesis," Working Papers hal-04102815, HAL.
    • Handle: RePEc:hal:wpaper:hal-04102815
    Note: View the original document on HAL open archive server: https://hal.science/hal-04102815
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    References listed on IDEAS

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    Keywords

    bandwidth selection; Bitcoin; kernel density estimation; market information; nonparametric density; Shannon entropy;
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