By using regular time-steps we define discrete-time random walks and flights on subordinate (directed) Continuous-Time Hierarchical (or Weierstrass-Mandelbrot) Walks and Flights, respectively. The obtained results can be considered as a kind of warning that indicates some persistent, non-linear, long-term autocorrelations (artifacts) accompanying the recording of empirical high-frequency financial (and probably other types of) time-series by regular time-steps, indeed.

PACS numbers: 05.45.Tp, 02.50.--r, 05.40.--a