[R-SIG-Finance] help (regarding block bootstrap)

[Matthieu Stigler]

Brian G. Peterson a écrit :
> Yana Roth wrote:
>> Hello,
>> I am trying to do block reasampling to rearrange my data and not 
>> succeed to do random permutation and assugnement.
>> I would like to divide original time series to subsamples and then to 
>> rearange this subsamples randomly.
>>  
>> Function tsboot works only if I need to check statistic, I am 
>> interested in just rearranging the data while keeping its structure.
>>  
>> The problem is defined as follows.
>> 1. I define llentgh of block , b.
>> 2.Divide an original time series by b and receive k=n/b subsamles.
>> 3. I need to generate random vector of integers from 1 to k
>> 4 Let Z*(j) be for j=1....k be the j th row of a matrix with num of 
>> rows equal to number of blocks and number of columns equal to number 
>> of simulations.
>> 5. Assigne to each Z*(j) the blocks according to generated random 
>> vector(each column of matrix is a different order of permutations)
> For future reference, please provide reproducible code as per the 
> posting guidelines.  It makes it easier for others to help you.  Also, 
> please use a desciptive subject, as we all get a quite a lot of mail.
>
> Your procedure appears incorrect.
> Your steps 3-5 look like a homework assignment, so I'm going to ignore 
> those and focus on the block bootstrap, which has some applicability 
> to other members of this list in financial time series analysis.
>


Thanks Brian for these examples!

Actually even if it is homework I would be really interested in the 
answer ;-) this is a question I always wanted to find out, maybe is it 
the right time to ask? I looked in source code of tsboot() but got lost

Does anyone has an idea about how to generate block resampling with 
function sample()? And with overlapping and non-overlapping blocks? That 
is, (example just taken from Maddala and Li 1998, bootstraping 
cointegrating relationships in journal of econometrics 80,2 also in 
their book unit roots, coint and struc change page 328) you pick blocks:

if series is {3, 6, 7, 2, 1, 5}
-non-overlapping:  {(3,6,7), (2,1,5)}
-overlapping:  {(3,6,7), (6,7,2), (7,2, l), (2, 1,5)}

and then sample those blocks with replacement. I don't have a clear idea 
about how do to that on R... Thanks!
 
a<-1:100
boot1<-sample(a, replace=TRUE) #length 1

> I suspect that you simply misunderstood the "statistic" parameter of 
> tsboot().  I expect that you do indeed intend to use the bootstrapped 
> data to calculate one or more statstics, this is what the statistic 
> parameter is for.
>
> Block bootstrapping works by randomly sampling blocks of length l from 
> your original series.  The tsboot function also applies one or more 
> statistics to the bootstrapped data, and uses the multiple samples to 
> calculate the bias and standard error for those statistics, providing 
> you with a sensitivity analysis for those statistics on your data.
>
> Using the data series "acme" included with R, you would do something 
> like:
>
> library(boot)
> library(PerformanceAnalytics)
> data(acme)
>
> #calculate the sensitivity of standard deviation on the data:
> tsboot(tseries=acme[,2],statistic=sd,R=1000,l=12,sim="fixed",endcorr=FALSE,n.sim=1000) 
>
> # use blocks of length 12 (one year) to # create 1000 bootstrapped 
> time series
> # each of length 1000 observations
>
> #Returns:
> #Bootstrap Statistics :
> #      original       bias    std. error
> #t1* 0.05362889 0.0001614213 0.001925484
>
> # calculate sensitivity of VaR:
> tsboot(tseries=acme[,2],statistic=VaR.CornishFisher,R=1000,sim="fixed",l=12,endcorr=FALSE,n.sim=1000) 
>
>
> #Returns:
> #Bootstrap Statistics :
> #    original      bias    std. error
> #t1* 0.227064 0.009412978 0.007284343
>
> Normally, this is what you want.  The random bootstrapped series 
> itself is not useful to you, except to calculate a statistic or 
> statistics of interest, and understand their sensitivity.  If you want 
> the bootstrapped series returned, you can modify the code of the 
> tsboot function to do what you want. 
> If you want to apply your steps 3-5 to the bootstrapped data, see the 
> documentation of tsboot() for an example of defining a function to use 
> as the statistic parameter.
>
> Regards,
>
>  - Brian