Power law for the calm-time interval of price changes

Abstract

In this paper, we describe a newly discovered statistical property of time series data for daily price changes. We conducted quantitative investigation of the calm-time intervals of price changes for 800 companies listed in the Tokyo Stock Exchange, and for the Nikkei 225 index over a 27-year period from January 4, 1975 to December 28, 2001. A calm-time interval is defined as the interval between two successive price changes above a fixed threshold. We found that the calm-time interval distribution of price changes obeys a power law decay. Furthermore, we show that the power-law exponent decreases monotonically with respect to the threshold.

Conditions for the emergence of scaling in the inter-event time of uncorrelated and seasonal systems

“…Whereas the second class of behavior has been observed in the response times of Einstein's and Darwin's corrependence [16]. Finally, the third class of behavior has been observed in earthquakes and the stock exchange [9,10,11,12].…”

“…In the case of the stock exchange [10], it was shown that the scaling exponent tends to decrease as the threshold on the normalized fluctuations increases. In other words, when waiting times between large fluctuations are considered, the scaling exponent approaches α = 1 indicating possibly a different mechanism like a queue model [21] or a power-law injection, whereas when small variations are considered the exponent is close to α = 2, which could be a signature of seasonality [9] or uncorrelated probability variations.…”

Properties of low-variability periods in financial time series

“…"silent" or "calm") periods [23]. Such a behaviour has been independently verified by Kaizoji et al [24].…”

An Empirical Research of Human Behavior Dynamics in Network Course Learning

“…A lot of researchers have found that such as web browsing [1], [5], blog comments [6], market trading [7], human communication behavior [8]- [10], logistics transportation [11] and other human behavior all obey the power law relationship .Therefore, many researchers studied the method to determine whether a distribution is a power law distribution and an estimate of the power exponent.…”