By means of a novel version of the Continuous-Time Random Walk (CTRW) model with memory , we describe, for instance, the stochastic process of a single share price on a double-auction market within the high frequency time scale. The memory present in the model is understood as dependence between successive share price jumps , while waiting times between price changes are considered as i.i.d. random variables. The range of this memory is defined herein by dependence between three successive jumps of the process. This dependence is motivated both empirically, by analysis of empirical two-point histograms , and theoretically, by analysis of the bid-ask bounce mechanism containing some delay  . Our model turns out to be  analytically solvable, which enables a direct comparison of its predictions with  empirical counterparts, for instance, with so significant and commonly used quantity as a velocity autocorrelation function. This work strongly extends the capabilities of the CTRW formalism.
A novel version of the Continuous-Time Random Walk (CTRW) model with memory is developed. This memory means the dependence between arbitrary number of successive jumps of the process , while waiting times between jumps are considered as i.i.d. random variables. The dependence was found by analysis of empirical histograms for the stochastic process of a single share price on a market within the high frequency time scale, and justified theoretically by considering bid-ask bounce mechanism containing some delay characteristic for any double-auction market . Our model turns out to be exactly analytically solvable, which enables a direct comparison of its predictions with their empirical counterparts, for instance, with empirical velocity autocorrelation function. Thus this paper significantly extends the capabilities of the CTRW formalism.
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