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Backward jump continuoustime random walk: An application to market trading 
Tomasz Gubiec , Ryszard Kutner 
Uniwersytet Warszawski, Wydział Fizyki, ul. Pasteura 5, Warszawa 02093, Poland 
Abstract 
The backward jump modification of the continuoustime random walk model or the version of the model driven by the negative feedback was herein derived for spatiotemporal continuum in the context of a share price evolution on a stock exchange. In the frame of the model, we described stochastic evolution of a typical share price on a stock exchange with a moderate liquidity within a highfrequency time scale. The model was validated by satisfactory agreement of the theoretical velocity autocorrelation function with its empirical counterpart obtained for the continuous quotation. This agreement is mainly a result of a sharp backward correlation found and considered in this article. This correlation is a reminiscence of such a bidask bounce phenomenon where backward price jump has the same or almost the same length as preceding jump. We suggested that this correlation dominated the dynamics of the stock market with moderate liquidity. Although assumptions of the model were inspired by the market highfrequency empirical data, its potential applications extend beyond the financial market, for instance, to the field covered by the Le ChatelierBraun principle of contrariness. PHYSICAL REVIEW E 82, 046119 (2010͒). 
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Presentation: Article at Econophysics group of Ryszard Kutner, by Ryszard Kutner Submitted: 20150813 16:56 Revised: 20150813 17:04 