| Título: | A characterisation of, and hypothesis test for, continuous local martingales |
| Autores: |
Jones, Owen D.; Dept. of Mathematics and Statistics, University of Melbourne Rolls, David A.; Dept. of Psychological Sciences, University of Melbourne |
| Fecha: | 2011-01-01 |
| Publicador: | Electronic communications in probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
continuous martingale hypothesis; crossing-tree; realised volatility; time-change 60G44; 62G10 |
| Descripción: | 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. |
| Idioma: | No aplica |
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