  We propose methods to infer jumps of a semi-martingale, which describes
long-term price dynamics based on discrete, noisy, high-frequency observations.
Different to the classical model of additive, centered market microstructure
noise, we consider one-sided microstructure noise for order prices in a limit
order book. We develop methods to estimate, locate and test for jumps using
local order statistics. We provide a local test and show that we can
consistently estimate price jumps. The main contribution is a global test for
jumps. We establish the asymptotic properties and optimality of this test. We
derive the asymptotic distribution of a maximum statistic under the null
hypothesis of no jumps based on extreme value theory. We prove consistency
under the alternative hypothesis. The rate of convergence for local
alternatives is determined and shown to be much faster than optimal rates for
the standard market microstructure noise model. This allows the identification
of smaller jumps. In the process, we establish uniform consistency for spot
volatility estimation under one-sided microstructure noise. A simulation study
sheds light on the finite-sample implementation and properties of our new
statistics and draws a comparison to a popular method for market microstructure
noise. We showcase how our new approach helps to improve jump detection in an
empirical analysis of intra-daily limit order book data.
