An improved test for continuous local martingales

Rolls, David A. and Jones, Owen D. ORCID: https://orcid.org/0000-0002-7300-5510 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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Abstract

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:	02 Nov 2022 10:16
URI:	https://orca.cardiff.ac.uk/id/eprint/98059

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