  We propose a new Directed Continuous-Time Random Walk (CTRW) model with
memory. As CTRW trajectory consists of spatial jumps preceded by waiting times,
in Directed CTRW, we consider the case with only positive spatial jumps.
Moreover, we consider the memory in the model as each spatial jump depends on
the previous one. Our model is motivated by the financial application of the
CTRW presented in [Phys. Rev. E 82:046119][Eur. Phys. J. B 90:50]. As CTRW can
successfully describe the short term negative autocorrelation of returns in
high-frequency financial data (caused by the bid-ask bounce phenomena), we
asked ourselves to what extent the observed long-term autocorrelation of
absolute values of returns can be explained by the same phenomena. It turned
out that the bid-ask bounce can be responsible only for the small fraction of
the memory observed in the high-frequency financial data.
