Bootstrapped skewness adjusted t-statistic

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Christian 2015-5-14

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评论： Nicolás Waissbluth 2015-11-2

Hi there, I have been doing everything in my power but I just can't figure it out. Here is the problem.

I have about 700 numbers (long-term buy-and-hold abnormal returns) and I want to do a t-test on them. As my data is highly positively skewed, I have to use a technique called bootstrapped skewness adjusted t-statistic. At least that's what they do in all the papers, so I need to do that as well.

I randomly select 350 of the 700 values. That I do 1000 times. So I have 1,000 bootstrapped resamples with size 350. On those resampled I conduct a (skewness adjusted) t-test. It could be a normal t-test, that's not important here. Next, I have to use my newly obtained 1,000 t-statistics to find the critical values for the 1% significance level. That is quickly done by using the quantile function. So, I just took my newly obtained distribution of t-values and checked which value the highest 1% starts at. That value I compare with the t-stat of the original, empirical data. If it exceeds it, my data is significantly different from zero. (this is basically a one-sided test. I did a two sided test, but that is not important for the moment)

Here's what I can't wrap my head around. I draw from the data that I want to test. Let's just assume that all 700 values are a lot higher than zero, so the 350 values I pick are also all > 0. Now I run t-tests on my 1000 bootstrapped resamples. The 1000 t-stats will all be really high. But now, so will the critical t-values! The t-value of the real data might not exceed the high critical values, because they were bootstrapped from the real, really significant data. IMHO, that makes no sense at all.

I know this is a very specific Statistics issue, but maybe there is someone out there who can help. Pls save me, I am exhausted! :-)

Best, Christian

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Answer 1

Star Strider 2015-5-14

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I don’t understand what you’re applying the bootstrap to, but see if the bootci function will do what you want. There are also several bootstrapping functions in the Financial Toolbox (that I don’t have and so have no experience with).

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Christian 2015-5-14

It is outside my expertise too, but that's about to change hopefully ;-) Figured this one out by the way! Really complicated process that yields a t-statistic that's hardly different from the regular one.. Two days of life gone ;-)

Thanks again for your help Star Stride, much appreciated!

Star Strider 2015-5-15

My pleasure!

Sorry I couldn’t actually contribute something.

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Answer 2

Nicolás Waissbluth 2015-10-24

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If you look closely at "Improved Methods for Tests of Long-Run Abnormal Stock Returns" by Lyon et al (1999), you'll see that the statistic calculated in the bootstrapping is not the same as the one calculated with all the data, but rather a shifted version to ensure it has zero mean (i.e. the distribution under the null hypothesis). Therefore, the 1000 t statistics you calculate to get an empirical distribution will have zero mean, even if your data is significantly different from zero.

I wrote an R implementation of this test. You might want to take a look and translate it to MATLAB.

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Star Strider 2015-10-24

I know nothing about R, and I don’t have access to the paper (which is just as well, since I’m not an economist). Which of those files are the actual code and which are the documentation?

What should someone who wants to code that in MATLAB be looking for?

Nicolás Waissbluth 2015-11-2