Testing for jumps in the EGARCH process

Xiuhong Shi and Masahito Kobayashi

Mathematics and Computers in Simulation (MATCOM), 2009, vol. 79, issue 9, 2797-2808

Abstract: This paper considers testing for jumps in the exponential GARCH (EGARCH) models with Gaussian and Student-t innovations. The Wald and log likelihood ratio tests contain a nuisance parameter unidentified under the null hypothesis of no jumps, and hence are unavailable for this problem, because jump probability and variance of jumps in the test statistic cannot be estimated under the null hypothesis of no jumps. It is shown that the nuisance parameter is cancelled out in the Lagrange multiplier (LM) test statistic, and hence that the test is nuisance parameter-free. The one-sided test is also proposed using the nonnegative constraint on jump variance. The actual size and power of the tests are examined in a Monte Carlo experiment. The test is applied to daily returns of S&P 500 as an illustrative example.

Keywords: Davies problem; Dirac's delta function; Exponential GARCH; Jump process; Lagrange multiplier test (search for similar items in EconPapers)
JEL-codes: C12 C22 (search for similar items in EconPapers)
Date: 2009
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:79:y:2009:i:9:p:2797-2808

DOI: 10.1016/j.matcom.2008.05.003

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