Self-modulation processes and resulting generic 1/f fluctuations

Misako Takayasu and Hideki Takayasu

Physica A: Statistical Mechanics and its Applications, 2003, vol. 324, issue 1, 101-107

Abstract: We analyze high precision data of transaction intervals in a foreign exchange market, and show that it is nicely approximated by a non-stationary Poisson process whose expectation value is given by a moving average of its own trace. Generalizing this result we introduce novel stochastic processes called the self-modulation processes. By the self-modulation effect, clustering occurs automatically resulting in fat-tailed interval distributions including the Zipf's law in an extreme case. We prove rigorously that the corresponding power spectrum follows the 1/f spectrum.

Date: 2003
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:324:y:2003:i:1:p:101-107

DOI: 10.1016/S0378-4371(03)00003-7

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