Testing for jumps in the stochastic volatility models

This paper proposes the Lagrange multiplier (LM) test, or the score test, for jumps in the stochastic volatility (SV) model in the cases where the innovation term follows the normal and Student t-distributions. The tested null hypothesis is that the jump density has zero variance, which is expressed by Dirac’s delta function. It is shown that the unknown jump probability, which is an unidentified parameter under the null hypothesis, is cancelled out in the LM test statistic, and hence this test is free from the estimation problem of unidentified parameters, which is known as the Davies problem [R.B. Davies, Hypothesis testing when a nuisance parameter is present only under the alternative, Biometrika 64 (1977) 247–254]. Monte Carlo experiments show that the null distribution of the LM test statistic can be approximated by the normal distribution with sufficient accuracy.