pierre clauss <pierreclauss <at> yahoo.fr> writes: > > Hello everybody, > I need your help about the package SN and the skew student distribution. Il will be very grateful if I have the solution. > > I construct a stochastic model with a white noise not gaussian but following a skew student distribution. I > fit the noise on monthly data to obtain the four parameters. The question is : how to annualize the > parameters to use my model for simulate daily data for example ? > > If the volatility is estimated to 3 for example, I need to multiply this by sqrt(12) to have for the parameter > of volatility of the skew student : 3*sqrt(12)*sqrt(dt) with "dt" the time increment parameter (1/12 for > monthly data, 1/261 for daily data, and so on). Do I do the same thing (and what is the multiplicative factor > ?) for the parameters of asymmetry and the degree of freedom ? >
I'm not sure about your application, but I'll take a crack at it. It sounds like you've got a continuous-time stochastic process (you don't say explicitly). For a Brownian motion, you would just do what you suggest -- scale the variance by sqrt(dt) (I don't see exactly why daily data have dt=1/261 -- although 365*5/7 = 261, so I guess you're counting weekdays (trading days??) only). Unfortunately, it's not nearly as transparent (to me) what stochastic differential equation would lead to aggregated data that were skew-Student. The review paper on Azzalini (SN's author)'s web site ( http://azzalini.stat.unipd.it/SN/review-web.ps ) cites some papers in computational finance, which I'm guessing is your area -- your best bet is probably to go back to those papers and see if they deal with the effects of temporal aggregation. VERY crudely, you can just experiment with this yourself by simulating values from a particular skew-Student distribution, aggregating them, and then looking at the properties of the resulting distribution -- *do* the asymmetry and df change? (I bet they do -- in some sense temporal aggregation must lead to a distribution that is "more normal", larger df and smaller skew -- but reversing this could be quite ugly). good luck Ben Bolker finance ______________________________________________ [email protected] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
