In this test, emphasis is placed in the comparison of two measures of variance: the Bipower Variation which is robust to jump contribution and the Realized Variance which includes the contribution of jumps to the total variance. And based on a high frequency data set of exchange rates, a statistically significant test of the difference between these two measures of variance provides evidence on the presence of jumps. ...
e the joint asymptotic distribution of BVt and RVt as M Where And using It can be seen that there is no coincidence of the fact that asymptotically similar to a situation encountered in Hausman’s test in 1978. Asymptotically, RVt is the most efficient estimate of the integrated variance and under the no jumps assumption, BVt is less efficient estimator, therefore the difference of RVt – BVt is independent of RVt on the volatility path following of the Hausman (1978) test. According on Huang and Tauchen (2005), the power of each absolute return should be less than 2 to be robust to jumps for the statistics. With the results from Barndorff-Nielsen and Shephard (2006), Andersen, Bollerslev and Diebold in 2004 used time series to test for daily jumps: Where on the assumption of no jumps: Another test for daily jumps is: The results of research conducted by Andersen, Bollerslev, Diebold and Labys (2001, 2003) and Barndorff-Nielsen and Shephard (2004a) show that the sample performance is improved by basing the test on the logarithm of the variation measures. Therefore the test is: And the maximum adjustment: The logarithmic adjustment to is: And the maximum adjustment is: The OP-versions of these tests are equivalent to the ratio jump of Barndorff-Nielsen and Shephard’s results in 2006. A simple t-test on the Relative Jump measure is: Where the classical estimate of the variance of the mean Another form is: Where : a HAC estimator of the variance of the mean. A bootstrap version is: Where : a bootstrap estimate of the variance of the mean. The Relative Jump can get a bootstrap confidence interval (tlow, tup) for the t test. b) Empirical results: The Monte Carlo findings developed z-tests for performing the jumps in a fairly realistic scenario and analyzed on daily
Literature review 1. BNS 2004 – 2006 a) Theoretical background In order not to require a fully observed state variable as is realized in Ait-Sahalia's approach in 2001, evidence is provided by Barndorff-Nielsen and Shephard (2004a, 2006) of the presence of jumps in higher frequency financial time series…
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62 pages (15500 words)Dissertation
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