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observer84
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Posts: 195
Joined: December 29th, 2010, 7:51 am

independence test for jump diffusion

March 13th, 2012, 8:26 am

Hi all,I couldnt find anything related to the topic. I have fitted a jump diffusion model to time series data by a bayesian estimation scheme and also obtained latent state variables, such as jump times and sizes. Jumps are heavily clustered in my state variables estimates.So, visually you can clearly see that the independence assumption of the jump component is violated. Are there any tests to test for the independence of the jump times? I was thinking about fitting an AR(1) model to the jump times and checking whether the lagged coefficient is statistically significant or something like that.Best regards,obs
 
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Edgey
Posts: 219
Joined: March 23rd, 2005, 11:01 am

independence test for jump diffusion

March 14th, 2012, 12:52 pm

If the jumps are independent then they should arrive according to an exponential function. Fit the parameter, and invert the function and you have a uniform 0,1 distribution. Plot your arrival times onto that U(0,1) distribution and they should be equally distributed.
 
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croot
Posts: 104
Joined: July 23rd, 2006, 8:30 pm

independence test for jump diffusion

March 14th, 2012, 1:04 pm

@obs by "jump diffusion model" do you mean Merton ? If something else, what estimators did you use?
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