Nonparametric tests for pathwise properties of semimartingales
AbstractWe propose two nonparametric tests for investigating the pathwise properties of a signal modeled as the sum of a L\'evy process and a Brownian semimartingale. Using a nonparametric threshold estimator for the continuous component of the quadratic variation, we design a test for the presence of a continuous martingale component in the process and a test for establishing whether the jumps have finite or infinite variation, based on observations on a discrete time grid. We evaluate the performance of our tests using simulations of various stochastic models and use the tests to investigate the fine structure of the DM/USD exchange rate fluctuations and SPX futures prices. In both cases, our tests reveal the presence of a non-zero Brownian component and a finite variation jump component.
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Bibliographic InfoPaper provided by Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa in its series Working Papers - Mathematical Economics with number 2010-02.
Length: 22 pages
Date of creation: Jan 2010
Date of revision:
Threshold estimator; central limit theorem; test for finite variation jumps; test for Brownian component.;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-05-22 (All new papers)
- NEP-ECM-2010-05-22 (Econometrics)
- NEP-ETS-2010-05-22 (Econometric Time Series)
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