Adaptive Test for Jump

TL;DR

This paper introduces an adaptive jump test for high-frequency financial data, combining multiple statistics to detect jumps effectively under various market conditions.

Contribution

It develops a novel adaptive testing procedure that integrates existing jump detection methods with the Cauchy combination rule, accommodating stochastic market factors and microstructure noise.

Findings

The test is asymptotically independent under the null and dense alternatives.

It is consistent under finite-activity jumps.

Simulation results show superior performance across different scenarios.

Abstract

We develop an adaptive jump test for discretely observed high-frequency semimartingales by combining the A"it-Sahalia--Jacod ratio statistic (A"it-Sahalia and Jacod, 2009) and the Lee--Mykland extreme-return statistic (Lee and Mykland, 2008) with the Cauchy combination rule. Allowing stochastic It^o drift, volatility, and leverage, we show asymptotic independence under the continuous-path null and dense local alternatives, yielding an analytically calibrated test with closed-form power; under finite-activity jumps, the test is consistent. We also extend the method to additive microstructure noise. Simulations show that the combined procedure performs well under both dense and sparse alternatives and is typically best overall.