Journal article

An Improved Test for Continuous Local Martingales

David A Rolls, Owen D Jones

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS | TAYLOR & FRANCIS INC | Published : 2015

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 diff..

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University of Melbourne Researchers