Electronic Journal of Statistics

Testing the type of a semi-martingale: Itō against multifractal

Laurent Duvernet, Christian Y. Robert, and Mathieu Rosenbaum

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We consider high frequency observations of a semi-martingale. From these data, we build simple test statistics allowing to distinguish between the two following situations: i) the data generating process is an Itō semi-martingale; ii) the data generating process is a Multifractal Random Walk. We also investigate the finite sample behavior of the test statistics on some simulated data.

Article information

Electron. J. Statist., Volume 4 (2010), 1300-1323.

First available in Project Euclid: 19 November 2010

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Zentralblatt MATH identifier

Primary: 60F05: Central limit and other weak theorems 60G44: Martingales with continuous parameter 62G10: Hypothesis testing

Semi-martingales multifractal processes limit theorems hypothesis testing


Duvernet, Laurent; Robert, Christian Y.; Rosenbaum, Mathieu. Testing the type of a semi-martingale: Itō against multifractal. Electron. J. Statist. 4 (2010), 1300--1323. doi:10.1214/10-EJS585. https://projecteuclid.org/euclid.ejs/1290176384

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