Continuous-Time Random Walk with multi-step memory: an application to market dynamics★
Center for Polymer Studies and Department of Physics, Boston University,
2 Faculty of Physics, University of Warsaw, Pasteur Str. 5, 02093 Warsaw, Poland
a e-mail: firstname.lastname@example.org
Received in final form: 11 July 2017
Published online: 27 November 2017
An extended version of the Continuous-Time Random Walk (CTRW) model with memory is herein developed. This memory involves the dependence between arbitrary number of successive jumps of the process while waiting times between jumps are considered as i.i.d. random variables. This dependence was established analyzing empirical histograms for the stochastic process of a single share price on a market within the high frequency time scale. Then, it was justified theoretically by considering bid-ask bounce mechanism containing some delay characteristic for any double-auction market. Our model appeared exactly analytically solvable. Therefore, it enables a direct comparison of its predictions with their empirical counterparts, for instance, with empirical velocity autocorrelation function. Thus, the present research significantly extends capabilities of the CTRW formalism.
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