Choosing Kernel Density Bandwidths with a Complexity Criterion for Bitcoin Returns

Summary

This document examines nonparametric kernel estimation of the probability density of price returns. Because the estimated distribution depends strongly on the bandwidth, the authors propose selecting it by maximizing a new complexity measure drawn from information theory and the study of complex systems. The stated aim is to avoid both overfitting and underfitting.

The work reviews other bandwidth-selection approaches and reports that they can lead to conflicting assessments of how complex return distributions are. Those differences also affect judgments about the relevance of the efficient market hypothesis. The methods are applied to real financial data, with Bitcoin as the focus. The document does not specify the proposed measure’s formula, the competing selectors, sample details, or the empirical conclusions about market efficiency, so it conveys the research question and approach more clearly than the evidence or practical performance of the estimator.

Key ideas

• Kernel density estimates of returns can change substantially with the chosen bandwidth.
• The proposed bandwidth rule maximizes a complexity measure motivated by information theory and complex systems.
• The criterion is intended to limit both overfitting and underfitting.
• Different bandwidth-selection methods can imply conflicting views of return-distribution complexity.
• Those differences can affect how researchers evaluate the efficient market hypothesis.

Tags

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


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









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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.