Open Access
2010 Testing the type of a semi-martingale: Itō against multifractal
Laurent Duvernet, Christian Y. Robert, Mathieu Rosenbaum
Electron. J. Statist. 4: 1300-1323 (2010). DOI: 10.1214/10-EJS585


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.


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Laurent Duvernet. Christian Y. Robert. Mathieu Rosenbaum. "Testing the type of a semi-martingale: Itō against multifractal." Electron. J. Statist. 4 1300 - 1323, 2010.


Published: 2010
First available in Project Euclid: 19 November 2010

zbMATH: 1329.62211
MathSciNet: MR2738534
Digital Object Identifier: 10.1214/10-EJS585

Primary: 60F05 , 60G44 , 62G10

Keywords: Hypothesis testing , limit theorems , Multifractal processes , semi-martingales

Rights: Copyright © 2010 The Institute of Mathematical Statistics and the Bernoulli Society

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