Abstract
ABSTRACT In this paper we design a test to detect the arrivals of jumps in asset prices contaminated by market microstructure noise. This test is defined by means of the truncated two-scales realised volatility estimator, recently introduced in Brownlees, Nualart, and Sun [2019, ‘On the Estimation of Integrated Volatility in the Presence of Jumps and Microstructure Noise’, https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2791342.], which is a robust estimator of the realised volatility in the presence of price jumps and market microstructure noise. We derive the asymptotic value of the power of the test given the significance level, and provide conditions for the test to be consistent. Simulations show that the test performs satisfactorily when the sampling frequency is high. In particular, we show that the test performs better than some prevalent jump tests. We also provide a real data example to illustrate the proposed method.
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