A novel approach to detect volatility clusters in financial time series

The self-similarity index has been consolidated as a widely applied measure to quantify long-memory in stock markets. In this article, though, we shall provide a novel methodology allowing the detection of clusters of volatility in series of asset returns. With this aim, the concept of a volatility series is introduced. We found that the existence of clusters of high/low volatility in the series leads to an increasing Hurst exponent of the volatility series. Some empirical applications were carried out. In fact, we artificially generated processes with clusters of volatility. The (mean) self-similarity exponents of their volatility series were compared with those from a Brownian motion and the S&P500 index. As a result, the greater the number of periods used in the calculation of the self-similarity exponent, the smoother the graph of the volatility series, and hence, the higher its exponent. Accordingly, the more likely the clusters of volatility appear. A dynamic study on the evolution of the self-similarity index of the volatility series of the S&P500 was also performed. It was observed that the greater its self-similarity exponent, the more frequent the volatility changes (which usually corresponds to falls in the index), and hence, the more likely the volatility clusters appear. (C) 2019 Elsevier B.V. All rights reserved.