question about scaling for garchSim in R

[Frank Hansen]

Hi Rmetrics core team,

If I run the default garchFit() to estimate garch(1,1) on dem2gbp (the default data) and then run garchSim() to simulate the dem2gbp data I seem to get very different standard deviations between the original dem2gbp data and the simulated data output from garchSim()

I'm probably doing something dumb, but I've read the docs and the draft of the paper in J. Stat. Software by W\"urtz, Chalabi and Luksan, but I can't figure out how to use the extended output from garchSim() to generate simulated time series with the same characteristics of the data used in garchFit.

Below is my output.

THanks

Frank Hansen

> gf.df <- garchFit()

> gf.df
Title:
 GARCH Modelling 

Call:
 garchFit() 

Mean and Variance Equation:
 data ~ garch(1, 1)
 [data = dem2gbp]

Conditional Distribution:
 norm 

Coefficient(s):
        mu       omega      alpha1       beta1  
-0.0061903   0.0107614   0.1531341   0.8059737  

Std. Errors:
 based on Hessian 

Error Analysis:
        Estimate  Std. Error  t value Pr(>|t|)    
mu     -0.006190    0.008462   -0.732 0.464447    
omega   0.010761    0.002838    3.793 0.000149 ***
alpha1  0.153134    0.026422    5.796  6.8e-09 ***
beta1   0.805974    0.033381   24.144  < 2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Log Likelihood:
 -1106.608    normalized:  -0.5605916 

Description:
 Thu Aug 19 11:42:48 2010 by user:  

> gs.ex.df <- garchSim( garchSpec(gf.df),n=1974, extended=TRUE)
> head(gs.ex.df)
GMT
                   garch       sigma         eps
2005-03-24  0.0021844729 0.002570202  0.84992253
2005-03-25  0.0031580105 0.002600374  1.21444479
2005-03-26  0.0006590028 0.002721554  0.24214205
2005-03-27 -0.0024301833 0.002639870 -0.92056921
2005-03-28  0.0046903885 0.002676885  1.75218180
2005-03-29  0.0001290736 0.002988736  0.04318667
> sd(dem2gbp)
  DEM2GBP 
0.4702445 
> sd( gs.ex.df)
       garch        sigma          eps 
0.0031823660 0.0004845456 1.0008265912