Entropy of Volatility Changes: Novel Method for Assessment of Regularity in Volatility Time Series

The goal of this research is to introduce and thoroughly investigate a new methodology for the assessment of sequential regularity in volatility time series. Three volatility estimators based on daily range data are analyzed: (1) the Parkinson estimator, (2) the Garman-Klass estimator, and (3) the Rogers-Satchell estimator. To measure the level of complexity of time series, the modified Shannon entropy based on symbol-sequence histograms is utilized. Discretization of the time series of volatility changes into a sequence of symbols is performed using a novel encoding procedure with two thresholds. Five main stock market indexes are analyzed. The whole sample covers the period from January 2017 to December 2023 (seven years). To check the robustness of our empirical findings, two sub-samples of equal length are investigated: (1) the pre-COVID-19 period from January 2017 to February 2020 and (2) the COVID-19 pandemic period from March 2020 to April 2023. An additional formal statistical analysis of the symbol-sequence histograms is conducted. The empirical results for all volatility estimators and stock market indexes are homogeneous and confirm that the level of regularity (in terms of sequential patterns) in the time series of daily volatility changes is high, independently of the choice of sample period. These results are important for academics and practitioners since the existence of regularity in the time series of volatility changes implies the possibility of volatility prediction.