Power-law behaviour in time durations between extreme returns

This paper studies time durations between extreme returns with the aim of testing whether they follow power-law behaviour. Using the Hill estimator to identify extreme returns and estimate time durations, empirical evidence for intraday returns for the S&P 500, DAX and IBEX-35 stock market indexes indicates that the time durations between extreme events are well characterized by a <inline-formula id="ILM0001"><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="rquf_a_822538_ilm0001.gif"/></inline-formula>-Weibull density with power-law behaviour tails. We also characterize the conditional time duration for an autoregressive conditional duration model with a <inline-formula id="ILM0002"><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="rquf_a_822538_ilm0002.gif"/></inline-formula>-Weibull distribution.