Regularity in Stock Market Indices within Turbulence Periods: The Sample Entropy Approach

Abstract

The aim of this study is to assess and compare changes in regularity in the 36 European and the U.S. stock market indices within major turbulence periods. Two periods are investigated: the Global Financial Crisis in 2007–2009 and the COVID-19 pandemic outbreak in 2020–2021. The proposed research hypothesis states that entropy of an equity market index decreases during turbulence periods, which implies that regularity and predictability of a stock market index returns increase in such cases. To capture sequential regularity in daily time series of stock market indices, the Sample Entropy algorithm (SampEn) is used. Changes in the SampEn values before and during the particular turbulence period are estimated. The empirical findings are unambiguous and confirm no reason to reject the research hypothesis. Moreover, additional formal statistical analyses indicate that the SampEn results are similar both for developed and emerging European economies. Furthermore, the rolling-window procedure is utilized to assess the evolution of SampEn over time.

Symbolic Encoding Methods with Entropy-Based Applications to Financial Time Series Analyses

“…The results support the evidence that stock market efficiency measured by entropy decreases during extreme events as the sequential regularity in time series increases in such cases. This conclusion is important for academics and practitioners and it is consistent with the existing literature which documents that turbulent periods are usually found to reduce the entropy of financial markets (e.g., [18,[20][21][22][23]).…”

“…The down arrows show an entropy decrease, while the up arrows illustrate an entropy increase. As one can observe, the results are rather mixed and heterogenous, and they are not in line with expectations, since the literature documents that the market informational efficiency measured by entropy of index returns usually decreases during extreme event periods [18,[20][21][22][23]. Therefore, there is no reason to recommend the use of encoding methods with one threshold for financial time series analyses within extreme event periods.…”

“…Ortiz-Cruz et al [20] indicated (based on the multi-scale Approximate Entropy procedure) that returns from crude oil markets were less uncertain during economic downturns. Olbrys and Majewska [18] utilized a different approach, i.e., the Sample Entropy algorithm, to estimate the sequential regularity and entropy of the daily time series of 36 stock market indices within two extreme event periods: (1) the Global Financial Crisis in 2007-2009 and (2) the COVID-19 pandemic outbreak in 2020-2021. In general, the empirical results support the hypothesis that the regularity in financial time series usually increases, while the entropy and informational efficiency of stock markets usually decrease during various turbulence periods due to the existence of patterns in returns.…”

“…In general, the chances for price prediction rise within a crisis and economic downturns. To sum up, various methods based on entropy enable investors to evaluate the aforementioned problems (see, e.g., [18] and the references therein).…”

Entropy-Based Applications in Economics, Finance, and Management

“…Finally, in the last paper of this Special Issue [ 13 ], the authors assess and compare changes in regularity in the 36 European and the United States stock market indices within major turbulence periods. Two periods are investigated: the Global Financial Crisis in 2007–2009 and the COVID-19 pandemic outbreak in 2020–2021.…”