A seismometer for Ito semimartingales

Benvenuti Francesco, Department of Mathematical Sciences, Aalborg University
Renò Roberto, ESSEC Business School

We propose a joint test to detect whether an Ito semimartingale exhibits drift and/or volatility explosions. The joint test exploits simultaneous estimation of the localized average of the increments and the localized return autocovariance to capture different explosion patterns as a function of the localizing window. Using infill asymptotics on irregularly sampled and noisy observations, we show that the test allows to pin down the location of the drift and volatility explosion rates. Simulations show the effectiveness of our methodology in small samples and allow to study the power and the size of our test. We provide an empirical application, where we detect drift and volatility explosions in high-frequency financial data contaminated by market microstructure noise. This talk is based on joint work with Roberto Renò (ESSEC Business School).

Area: CS25 - Statistical analysis of high-frequency prices (Francesco Benvenuti)

Keywords: Drift burst; Volatility burst; Semimartingale; High-frequency econometrics; Nonparametric statistics.

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