Electronic Journal of Statistics

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

Laurent Duvernet, Christian Y. Robert, and Mathieu Rosenbaum

Full-text: Open access

Abstract

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

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

Dates
First available in Project Euclid: 19 November 2010

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1290176384

Digital Object Identifier
doi:10.1214/10-EJS585

Mathematical Reviews number (MathSciNet)
MR2738534

Zentralblatt MATH identifier
1329.62211

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

Keywords
Semi-martingales multifractal processes limit theorems hypothesis testing

Citation

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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