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An improved test for continuous local martingales

Rolls, David A. and Jones, Owen D. 2015. An improved test for continuous local martingales. Communications in Statistics - Theory and Methods 44 (13) , pp. 2674-2688. 10.1080/03610926.2013.788709

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We present a new test for the “continuous martingale hypothesis”. That is, a test for the hypothesis that observed data are from a process which is a continuous local martingale. The basis of the test is an embedded random walk at first passage times, obtained from the well-known representation of a continuous local martingale as a continuous time-change of Brownian motion. With a variety of simulated diffusion processes our new test shows higher power than existing tests using either the crossing tree or the quadratic variation, including the situation where non-negligible drift is present. The power of the test in the presence of jumps is also explored with a variety of simulated jump diffusion processes. The test is also applied to two sequences of high-frequency foreign exchange trade-by-trade data. In both cases the continuous martingale hypothesis is rejected at times less than hourly and we identify significant dependence in price movements at these small scales.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Publisher: Taylor & Francis
ISSN: 0361-0926
Date of Acceptance: 15 March 2013
Last Modified: 26 Feb 2020 11:45

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