  In this paper, the higher order dynamics of individual illiquid stocks are
investigated. We show that considering the classical powers correlation could
lead to a spurious assessment of the volatility persistency or long memory
volatility effects, if the zero returns probability is non-constant over time.
In other words, the classical tools are not able to distinguish between
long-run volatility effects, such as IGARCH, and the case where the zero
returns are not evenly distributed over time. As a consequence, tools that are
robust to changes in the degree of illiquidity are proposed. Since a
time-varying zero returns probability could potentially be accompanied by a
non-constant unconditional variance, we then develop powers correlations that
are also robust in such a case. In addition, note that the tools proposed in
the paper offer a rigorous analysis of the short-run volatility effects, while
the use of the classical power correlations lead to doubtful conclusions. The
Monte Carlo experiments, and the study of the absolute value correlation of
some stocks taken from the Chilean financial market, suggest that the
volatility effects are only short-run in many cases.
