  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.
