The Key Role of Inter-Event Times in Volatility Clustering

Over 50 years ago, two physicists Montroll and Weiss in the physical context of dispersive transport and diffusion introduced stochastic process, named Continuous-Time Random Walk (CTRW). The trajectory of such a process is created by elementary events ‘spatial’ jumps preceded by waiting time. Since introduction, CTRW found innumerable application in different fields including high-frequency finance, where jumps are considered as price increments and waiting times represent inter-trade times. In this manuscript we show that dependencies between inter-trade times are the key element to explain long-term memory in financial time-series, even when taking into account intraday seasonality (so-called "lunch effect”). We introduce the new CTRW model with long-term memory in waiting times, able to successfully describe power-law decaying time autocorrelation of the absolute values of price changes. We test our model on the empirical data from Polish stock market.