# Re: [R] GLS models - bootstrapping

From: Christian Kamenik <christian.kamenik_at_giub.unibe.ch>
Date: Wed 21 Feb 2007 - 11:16:32 GMT

Dear Lillian,

I tried to estimate parameters for time series regression using time series bootstrapping as described on page 434 in Davison & Hinkley (1997) - bootstrap methods and their application. This approach is based on an AR process (ARIMA model) with a regression term (compare also with page 414 in Venable & Ripley (2002) - modern applied statistics with S) I rewrote the code for R (this comes without any warranty):

fit <- function( data )
{ X <- cbind(rep(1,100),data\$activ)

para <- list( X=X,data=data)
assign("para",para)
d <- arima(x=para\$data\$temp,order=c(1,0,0),xreg=para\$X)    res <- d\$residuals
res <- res[!is.na(res)]
list(paras=c(d\$model\$ar,d\$reg.coef,sqrt(d\$sigma2)),

res=res-mean(res),fit=X %*% d\$reg.coef) }
beaver.args <- fit( beaver )
white.noise <- function( n.sim, ts) sample(ts,size=n.sim,replace=T) beaver.gen <- function( ts, n.sim, ran.args ) { tsb <- ran.args\$res

fit <- ran.args\$fit
coeff <- ran.args\$paras
ts\$temp <- fit + coeff[4]*arima.sim( model=list(ar=coeff[1]),

```                             n=n.sim,rand.gen=white.noise,ts=tsb )
```
ts }
new.beaver <- beaver.gen( beaver, 100, beaver.args )

beaver.fun <- function(ts) fit(ts)\$paras beaver.boot <- tsboot( beaver, beaver.fun, R=99,sim="model",

```                n.sim=100,ran.gen=beaver.gen,ran.args=beaver.args)
```
names(beaver.boot)
beaver.boot\$t0
beaver.boot\$t[1:10,]

Maybe there is a more elegant way for doing this. Anyway, boot.ci should give you confidence intervals.

Let me know how you are doing.

Best, Christian

> From: Lillian Sandeman <l.sandeman>
> Date: Mon, 2 Oct 2006 13:59:09 +0100 (BST)
>
> Hello,
>
> I am have fitted GLS models to time series data. Now I wish to bootstrap
> this data to produce confidence intervals for the model.
>
> However, because this is time series data, normal bootstrapping is not
> applicable. Secondly, 'tsboot' appears to only be useful for ar models -
> and does not seem to be applicable to GLS models.
>
> I have written code in R to randomly sample blocks of the data (as in
> Davison & Hinkley's book - bootstrap methods and their application) and
> use this resampling to re-run the model, but this does not seem to be the
> correct approach since Confidence Intervals produced do not show the
> underlying pattern (cycles) in the data [even when block length is
> increased, it only picks up a little of this variation].
>
> Any help as to how to proceed with this would be greatly appreciated, as I
> cannot find anything applicable on the R pages. Alternatively, if there
> is another method to proceed with this (other than bootstrapping), I would
> also be happy to try it.
>
> Thankyou,
>
> Lillian.

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