Testing for jumps in a discretely observed process

2009/01/16 by Yacine Aït-Sahalia, Yacine Aı̈t-Sahalia, Jean Jacod · 12 citations
Economics, Econometrics and Finance · #Complex Systems and Time Series Analysis #Financial Risk and Volatility Modeling #Stochastic processes and financial applications

paper · pdf · doi:10.1214/07-aos568

openalex publication_date 2009/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose a new test to determine whether jumps are present in asset returns or other discretely sampled processes. As the sampling interval tends to 0, our test statistic converges to 1 if there are jumps, and to another deterministic and known value (such as 2) if there are no jumps. The test is valid for all It semimartingales, depends neither on the law of the process nor on the coefficients of the equation which it solves, does not require a preliminary estimation of these coefficients, and when there are jumps the test is applicable whether jumps have finite or infinite-activity and for an arbitrary Blumenthal-Getoor index. We finally implement the test on simulations and asset returns data.

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• Multi-asset Generalised Variance Swaps in Barndorff-Nielsen and Shephard model
• Asymptotics of the Empirical Cross-over Function
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• Predicting intraday jumps in stock prices using liquidity measures and technical indicators
• Modelling systemic price cojumps with Hawkes factor models
• Large deviations of the Threshold estimator of integrated (co-)volatility vector in the presence of jumps
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