[R-SIG-Finance] Resampling Methods for Dependent Data

[Brian G. Peterson]

Wei-han Liu wrote:
> Hi:
> Yes, I know 'tsboot' package and it is designed to generate resample 
> using fixed or random block lengths. However, I am curious if it can be 
> used to bootstrap heavy-tailed data and extremes.
> Wei-han

Resampling, by definition, only works from the sample available.  If the 
sample has extremes, then the distribution generated by resampling with 
replacement will have heavy tails.  This is a natural result of the rule 
of large numbers...  With a sufficient number of samples, the tails will 
fill out with resampling.

One of the theoretical problems with small initial sample sizes is that 
the tails may not be representative in a resampling context.  If you've 
never seen large loss events, then the distribution resulting from 
resampling may not have heavy tails.  This is why other types of 
analysis are generally employed along with a simple bootstrap such as 
copula or skew-t fitting, or a Monte Carlo simulation with a fat-tailed 
assumption.

Regards,

   - Brian

> ----- Original Message ----
> From: Brian G. Peterson <brian at braverock.com>
> To: Wei-han Liu <weihanliu2002 at yahoo.com>
> Cc: r-sig-finance at stat.math.ethz.ch
> Sent: Wednesday, June 18, 2008 6:05:03 PM
> Subject: Re: [R-SIG-Finance] Resampling Methods for Dependent Data
> 
> Wei-han Liu wrote:
>  > I am reading a book by Lahiri (2003): Resampling Methods for Dependent
>  > Data.  I am trying to implement some of the techniques that book has
>  > introduced, e.g. model-based bootstrap, block bootstrap method, and
>  > bootstrapping heavy-tailed data and extremes.
>  > Could somebody share any information helpful in this regard?
> 
> There has been a ton of information posted on this list on bootstrapping
> techniques.  I suggest searching the list archive. Jrff has already
> suggested the 'tsboot' package, which has been previously discussed here
> in some depth.
> 
> When you have more specific questions, successes, or failures in your
> investigation of these techniques, please share them with the list so
> others can benefit from your experience.  Bootstrap techniques are so
> important in modern financial analytics that just about anything you
> discover (good or bad) will likely be useful to someone else on this list.
> 
> Regards,
> 
>   - Brian
> 
>