Reply to “Comment on ‘Tests of scaling and universality of the distributions of trade size and share volume: Evidence from three distinct markets’ ”
- 24 June 2009
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review E
- Vol. 79 (6), 068102
- https://doi.org/10.1103/physreve.79.068102
Abstract
Analyzing trade-by-trade data for three distinct markets, we showed that the cumulative distributions of trade size display power-law tails , with exponents in the “Lévy stable domain” . Moreover we reported that the exponent values are consistent for all stocks irrespective of stock-specific variables such as market capitalization, industry sector, or the specific market where the stock is traded. Our conclusions were based on using two distinct estimation methods. Rácz et al. now propose that one of the estimators we used has slow convergence for a pure power law, particularly as tail exponents approach the boundary . We examine the robustness of our results to specific estimation method by additional analysis using five distinct techniques to estimate . We find results that are fully consistent with those we had reported, providing compelling evidence that our conclusions hold regardless of estimation procedure.
Keywords
This publication has 21 references indexed in Scilit:
- Comment on “Tests of scaling and universality of the distributions of trade size and share volume: Evidence from three distinct markets”Physical Review E, 2009
- Tests of scaling and universality of the distributions of trade size and share volume: Evidence from three distinct marketsPhysical Review E, 2007
- Size matters: some stylized facts of the stock market revisitedZeitschrift für Physik B Condensed Matter, 2006
- Scaling theory of temporal correlations and size-dependent fluctuations in the traded value of stocksPhysical Review E, 2006
- On the origin of power-law fluctuations in stock pricesQuantitative Finance, 2004
- On the origin of power-law tails in price fluctuationsQuantitative Finance, 2004
- Hydraulic conductivity, velocity, and the order of the fractional dispersion derivative in a highly heterogeneous systemWater Resources Research, 2002
- Statistical properties of share volume traded in financial marketsPhysical Review E, 2000
- A simple robust estimation method for the thickness of heavy tailsJournal of Statistical Planning and Inference, 1998
- A Simple General Approach to Inference About the Tail of a DistributionThe Annals of Statistics, 1975