The correlation between different quantities, observed in high-frequency financial data, is a commonly used measure of the dependence between them. In some cases, the results obtained by correlation analysis may be misleading, for instance, uncorrelated quantities are not always independent. In our work we give an important example of such a case. This example is significant in the description of the stochastic evolution of a typical share price on a stock exchange within a high-frequency time scale.

The above given example can be approximated by a simple formula, which included in the Continuous-Time Random Walk (CTRW) model with memory makes this model exactly solvable. Our version of the CTRW model is an extension of that presented on the previous FENS 5 conference [1] and published soon after [2]. This version of the CTRW contains memory over two steps in contrast to the one-step memory presented before. Such an extension improves, for instance, agreement of the theoretical velocity autocorrelation function with its empirical counterpart obtained for the continuous quotation or tick-by-tick financial data.

[1] http://science24.com/paper/23311

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