A R/S approach to Trends Breaks Detection

This note focuses on a pointwise estimation of the Hurst exponent H, and on its reliability as a method to detect breaking signals inside a given financial time–series. The idea is that, although classical H can give information about the average scaling behavior of data, its estimation over proper subsamples of the original time–series can reveal variability which is perfectly compliant with sudden changes in direction that are typical of financial markets. The behavior of the pointwise estimation of H is then analyzed on different proxies of market price levels (namely: log–returns, squared log–returns, and the absolute value of log–returns), focusing on the relationships existing with bursts in the markets and those observable in such indicators as well. In this context we find that breaks in the upward/downward tendency of financial time–series are generally anticipated by analogous movements in the estimated H values given on the squared log–returns.