Approximate entropy and sample entropy algorithms in financial time series analyses

Abstract

The goal of this comparative research is to assess regularity/irregularity in time series of stock market indices, in the context of their predictability, within the two-year pre-pandemic (2018-2019) and COVID-19 pandemic (2020-2021) periods. The approximate entropy (ApEn) and sample entropy (SampEn) statistics are used to measure and compare regularity in time series. 50 selected stock exchange indices from the continent-based regions are investigated. Changes in index regularity within two analyzed periods are quantified. The empirical results indicate that entropy of almost all equity market indices visibly decreased during the pandemic period. It means that the regularity of these indices increased, which made them more predictable and less random. Moreover, the more generalized findings are in accordance with the literature and confirm that SampEn results are more consistent and homogenous compared to the ApEn results, which mainly arises from the ApEn bias. Therefore, we can advocate the use of the SampEn algorithm rather than the ApEn for financial time series analyses.