Testing for Jumps in a Discretely Observed Process

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...

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Bibliographic Details
Published in:The Annals of statistics 2009-02, Vol.37 (1), p.184-222
Main Authors: Aït-Sahalia, Yacine, Jacod, Jean
Format: Article
Language:English
Subjects:
60H10
60J60
62F12
62M05
Coefficients
Consistent estimators
discrete sampling
Estimates
Estimators
Exact sciences and technology
General topics
high-frequency
Integers
Jumps
Markov processes
Mathematics
Monte Carlo simulation
Null hypothesis
Poisson distribution
Probability and statistics
Probability theory and stochastic processes
Sciences and techniques of general use
Statistical discrepancies
Statistical theories
Statistical variance
Statistics
Stochastic models
Stochastic processes
Studies
test
Time series
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Description
Summary: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 Itô 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.
ISSN:0090-5364
2168-8966
DOI:10.1214/07-AOS568