https://doi.org/10.1140/epjb/e2015-60687-x
Regular Article
Self-similarity and non-Markovian behavior in traded stock volumes
1
Departement of Mathematics, East Carolina
University, Greenville,
NC
27858,
USA
2
Departement of Physics, East Carolina University,
Greenville, NC
27858,
USA
3
M. Smoluchowski Institute of Physics, Jagiellonian
University, ul. Łojasiewicza
11, 30-348
Kraków,
Poland
a
e-mail: bierm@ecu.edu
Received:
23
August
2015
Received in final form:
13
September
2015
Published online:
18
November
2015
The volume traded daily for 17 stocks is followed over a period of about half a century. We look at the volume of stocks traded in a certain time interval (day, week, month) and analyze how long that traded volume keeps monotonically increasing or decreasing. On all three times scales we find that the sequence of traded volumes behaves neither like a sequence of independent and identically distributed variables, nor like a Markov sequence. A compressed exponential survival function with the same parameters at all timescales is firmly established. A day with an increase (decrease) of traded volume is most likely followed by a day with a decrease (increase) of traded volume. We show how the apparent self-similarity results because the small day-to-day anticorrelation carries over when larger time intervals are considered. The observed small anticorrelation can be explained as a consequence of market forces and trader reactions.
Key words: Statistical and Nonlinear Physics
© The Author(s) 2015. This article is published with open access at Springerlink.com
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