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A characterisation of, and hypothesis test for, continuous local martingales

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	A characterisation of, and hypothesis test for, continuous local martingales
2.	Creator	Author's name, affiliation, country	Owen D. Jones; Dept. of Mathematics and Statistics, University of Melbourne
2.	Creator	Author's name, affiliation, country	David A. Rolls; Dept. of Psychological Sciences, University of Melbourne
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	continuous martingale hypothesis; crossing-tree; realised volatility; time-change
3.	Subject	Subject classification	60G44; 62G10
4.	Description	Abstract	We give characterisations for Brownian motion and continuous local martingales, using the crossing tree, which is a sample-path decomposition based on first-passages at nested scales. These results are based on ideas used in the construction of Brownian motion on the Sierpinski gasket (Barlow and Perkins 1988). Using our characterisation we propose a test for the continuous martingale hypothesis, that is, that a given process is a continuous local martingale. The crossing tree gives a natural break-down of a sample path at different spatial scales, which we use to investigate the scale at which a process looks like a continuous local martingale. Simulation experiments indicate that our test is more powerful than an alternative approach which uses the sample quadratic variation.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	Australian Research Council
7.	Date	(YYYY-MM-DD)	2011-10-21
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ecp.ejpecp.org/article/view/1673
10.	Identifier	Digital Object Identifier	10.1214/ECP.v16-1673
11.	Source	Journal/conference title; vol., no. (year)	Electronic Communications in Probability; Vol 16
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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