  In this paper, we provide non-parametric statistical tools to test
stationarity of microstructure noise in general hidden Ito semimartingales, and
discuss how to measure liquidity risk using high frequency financial data. In
particular, we investigate the impact of non-stationary microstructure noise on
some volatility estimators, and design three complementary tests by exploiting
edge effects, information aggregation of local estimates and high-frequency
asymptotic approximation. The asymptotic distributions of these tests are
available under both stationary and non-stationary assumptions, thereby enable
us to conservatively control type-I errors and meanwhile ensure the proposed
tests enjoy the asymptotically optimal statistical power. Besides it also
enables us to empirically measure aggregate liquidity risks by these test
statistics. As byproducts, functional dependence and endogenous microstructure
noise are briefly discussed. Simulation with a realistic configuration
corroborates our theoretical results, and our empirical study indicates the
prevalence of non-stationary microstructure noise in New York Stock Exchange.
