Return volatility duration analysis of NYMEX energy futures and spot

Return volatility plays a key role in quantifying risk, optimizing the portfolio and pricing modelling of financial market. The study focusing on the return volatility of energy market can help greatly understand the energy fluctuating behaviors. In this paper, we introduce a concept of volatility duration into the analysis of the New York Mercantile Exchange (NYMEX) energy market, where the daily closing prices of the futures and spot for the crude oil, natural gas, heating oil and propane are adopted. The volatility duration is defined as the shortest passage time that the future's volatility intensity takes to go beyond or below the current volatility intensity which is time-varying and considered as the basic intensity reference. Then, two main aspects of the statistical properties analysis for the energy volatility duration time series are focused on: one is about the empirical probability distributions and their scaling behaviors are observed; another is about the complexity properties of the energy volatility durations, which are discussed by the entropy measures of the composite multiscale entropy (CMSE) and the composite multiscale cross-sample entropy (CMSCE) approaches.