Nonparametric Tests for Analyzing the Fine Structure of Price Fluctuations

We consider a semimartingale model where (the logarithm of) an asset price is modeled as the sum of a Levy process and a general Brownian semimartingale. Using a nonparametric threshold estimator for the continuous component of the quadratic variation (integrated variance), we design a test for the presence of a continuous component in the price process and a test for establishing whether the jump component has finite or infinite variation based on observations on a discrete time grid. Using simulations of stochastic models commonly used in finance, we confirm the performance of our tests and compare them with analogous tests constructed using multipower variation estimators of integrated variance. Finally, we apply our tests to investigate the fine structure of the DM/USD exchange rate process and of SPX futures prices. In both cases, our tests reveal the presence of a non-zero Brownian component, combined with a finite variation jump component.

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