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Testing for jumps in the EGARCH process

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  • Shi, Xiuhong
  • Kobayashi, Masahito

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.

Suggested Citation

  • Shi, Xiuhong & Kobayashi, Masahito, 2009. "Testing for jumps in the EGARCH process," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(9), pages 2797-2808.
    • Handle: RePEc:eee:matcom:v:79:y:2009:i:9:p:2797-2808
    DOI: 10.1016/j.matcom.2008.05.003
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    References listed on IDEAS

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    More about this item

    Keywords

    Davies problem; Dirac's delta function; Exponential GARCH; Jump process; Lagrange multiplier test;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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