# Bootstrap data in order to get an estimate of the variance

I have a return series of 60 obs. From this returns I compute a non parametric measure. What is the best way in your opinion to get a consistent estimate of the variance of this measure?

I did it in this way: I compute a number of X block bootstrap (to take into account of returns dependence) and then for each bootstrap a compute the measure than I get X measure and I compute the variance. It is correct?

## 1 Answer

It sounds like what you are describing is a form of percentile bootstrap. This is generally a good way to find the variance of a statistic, including of some complex non-parametric one. But one of the advantages of percentile bootstrap method is that you can estimate a confidence interval directly, without relying on the variance of the statistic and an assumed distribution. For example, you can take the 0.025 and 0.975 quantiles of your X measures from X bootstrap resamples, to give a 95% confidence interval.

Whether this is the best way to estimate the variance of your non-parametric measure we can't tell you without knowing more about the problem and the data. But it is likely to be a reasonably good way.

Caveat - I don't quite understand the reference in your second paragraph to returns' dependence.

• I've also read that block bootstrap is only consistent (or at least the method you appear to mention is) when you have stationary procceses (some of them don't work propperly even in WSS procceses). For some special kind of non-stationary series, however, some types of block-bootstrap appears to work well. With all of this in mind, my advice is to check what kind of model better suits your data (e.g. using a PACF). If you are sure of the stationarity of your data, I see no problem on your technique. Apr 13 '12 at 7:52
• Dear Peter, thank you so much for your reply. I could improve it using your suggestion about confidence interval. Yes, my series is stationary. Apr 13 '12 at 7:54
• Ahh, I'd missed that this was a time series. I've added the time series tag. I would have answered slightly differently knowing that, but @Nesp's comment covers off the issues well. Apr 14 '12 at 7:05