  One of the open questions of modern cosmology is the nature and properties of
the Dark Matter halo and its substructures. In this work we study the
gravitational effect of dark matter substructures on pulsar timing
observations. Since millisecond pulsars are stable and accurate emitters, they
have been proposed as plausible astrophysical tools to probe the gravitational
effects of dark matter structures. We study this effect on pulsar timing
through Shapiro time delay (or Integrated Sachs-Wolfe (ISW) effect) and Doppler
effects statistically, showing that the latter dominates the signal. For this
task, we relate the power spectrum of pulsar frequency change to the matter
power spectrum on small scales, which we compute using the stable clustering
hypothesis. We compare this power spectrum with the reach of current and future
observations of pulsar timing designed for gravitational wave (GW) detection.
Our results show that while current observations are unable to detect these
signals, the sensitivity of the upcoming Square Kilometer Array (SKA) is only a
factor of few weaker than our optimistic predictions.
