School Seminars and Colloquia

Looking for continuous local martingales

Statistics Seminar

by Dr Owen Jones


Institution: Department of Mathematics and Statistics, The University of Melbourne
Date: Thu 3rd May 2007
Time: 12:00 PM
Location: Room 213 Richard Berry Building

Abstract: Continuous local martingales, or equivalently time-changed Brownian
motion, are a popular class of models in finance. We present a set
of statistical tests for whether or not an observed process is a
continuous time-changed Brownian motion, based on the concept of the
crossing tree.


We apply our methodology to five currency exchange rates --- AUD-USD,
JPY-USD, EUR-USD, GBP-USD and EUR-GBP --- and show that in each case,
when viewed at a moderately large time scale (that is the time between
observations is of the order 2 to 5 hours), the log-transformed series
is consistent with a continuous local martingale model.

For More Information: Dr Owen Jones: odj@mailhost.ms.unimelb.edu.au