Continuous-Time Random Walk with multi-step memory: an application to market dynamics
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 establ...
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| Published in | The European physical journal. B, Condensed matter physics Vol. 90; no. 11; pp. 1 - 15 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
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01.11.2017
Springer Springer Nature B.V |
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| Abstract | 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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| AbstractList | 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. |
| ArticleNumber | 228 |
| Audience | Academic |
| Author | Gubiec, Tomasz Kutner, Ryszard |
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| CitedBy_id | crossref_primary_10_1016_j_eneco_2019_05_015 crossref_primary_10_1140_epjb_e2019_90453_y crossref_primary_10_1088_1742_5468_ab2709 crossref_primary_10_3390_e23121576 |
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| Snippet | An extended version of the Continuous-Time Random Walk (CTRW) model with memory is herein developed. This memory involves the dependence between arbitrary... |
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| SubjectTerms | Autocorrelation functions Comparative analysis Complex Systems Computer memory Condensed Matter Physics Current State and Outlook Empirical analysis Fluid- and Aerodynamics Histograms Markets Physics Physics and Astronomy Random variables Random walk Regular Article Solid State Physics Stochastic processes Topical issue: Continuous Time Random Walk Still Trendy: Fifty-year History |
| Title | Continuous-Time Random Walk with multi-step memory: an application to market dynamics |
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