# [R-SIG-Finance] Multivariate random number generation for skewed distribution of asset class returns

Eric Berger er|cjberger @end|ng |rom gm@||@com
Tue Jan 14 16:55:47 CET 2020

```Ilya suggests to "take chunks of time instead of one observation". In the
academic literature this method is referred to as the "block bootstrap".
See, for example, "Bootstraps for Time Series" by Peter Buhlmann, which
discusses model-based bootstraps, sieve bootstraps and block bootstraps.
You might also Google these terms to look for other sources of information.

HTH,
Eric

On Tue, Jan 14, 2020 at 5:12 PM Ilya Kipnis <ilya.kipnis using gmail.com> wrote:

> This is a question I was actually asked by the head of AI/ML for a fairly
> large company and I'll give the same answer here:
>
> Perform the bootstrapping of your choice. That is, take the empirical
> returns, and just sample from them. If you want to preserve
> autocorrelations, take chunks of time instead of one observation. If you
> want to add some random noise, feel free to create some noise distributions
> as well.
>
> Hope this helps.
>
> On Tue, Jan 14, 2020 at 9:32 AM shawn tan via R-SIG-Finance <
> r-sig-finance using r-project.org> wrote:
>
> > Hi R-SIG-Finance mailing list,
> > I have a query about performing a Monte Carlo random number generation
> for
> > asset class returns which accounts for the distribution of the asset
> class
> > (mean, variance, skewness and possibly kurtosis) while also taking into
> > consideration the correlation/covariance matrix of the asset classes.
> > I came across the R package, mvtnorm, which is able to take the asset
> > classes' means, covariance matrix for a normal distribution, through the
> > function rmvnorm(n, mean = muvec, sigma = covmat), where n is number of
> > trials, mean is the mean vector and sigma is the covariance matrix.
> > However, this package does not allow for a skewed distribution or excess
> > kurtosis. Historical data for my asset class returns show both positive
> and
> > negative skewness. Additionally, the Johnson distribution function in R
> > package, SuppDists, does not seem to account for covariances as inputs.
> > Hence, is there an R package/function that allows me to perform the
> random
> > number generation for multivariate returns, which accounts for mean,
> > variance, correlation, skewness and even kurtosis as inputs under the
> Monte
> > Carlo simulation?
> > Thank you
> > Best regards,
> > Sjedi
> >         [[alternative HTML version deleted]]
> >
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