R help - Nov 2007 - Bootstrap Correlation Coefficient with Moving Block Bootstrap

Hello.

I have got two problems in bootstrapping from
dependent data sets.

Given two time-series x and y. Both consisting of n
observations with x consisting of dependent and y
consisting of independent observations over time. Also
assume, that the optimal block-length l is given.

To obtain my bootstrap sample, I have to draw
pairwise, but there is the problem of dependence of
the x-observations and so if I draw the third
observation of y, I cannot simply draw the third
observation of x (to retain the serial correlation
structure between x and y), because I devided x into
blocks of length l and I have to draw blocks, then I
draw from x.

1.
How can I compute a bootstrap sample of the
correlation coefficient between x and y with respect
to the dependence in time-series of x?

2.
How does it look like, if x and y both consist of
dependent observations?



I hope you can help me. I got really stuck with this
problem.

Sincerly
Klein.

It sounds like you should sample x and y together using the
block bootstrap.  If you have the usual situation, x and y in columns
and observations in rows, then sample blocks of rows.

Even though observations in y are independent, you would take
advantage of that only for bootstrapping statistics that depend only
on y.

The answer to your second question is the same as the first - sample
blocks of observations, keeping x and y together.

Tim Hesterberg					
>Hello.
>
>I have got two problems in bootstrapping from
>dependent data sets.
>
>Given two time-series x and y. Both consisting of n
>observations with x consisting of dependent and y
>consisting of independent observations over time. Also
>assume, that the optimal block-length l is given.
>
>To obtain my bootstrap sample, I have to draw
>pairwise, but there is the problem of dependence of
>the x-observations and so if I draw the third
>observation of y, I cannot simply draw the third
>observation of x (to retain the serial correlation
>structure between x and y), because I devided x into
>blocks of length l and I have to draw blocks, then I
>draw from x.
>
>1.
>How can I compute a bootstrap sample of the
>correlation coefficient between x and y with respect
>to the dependence in time-series of x?
>
>2.
>How does it look like, if x and y both consist of
>dependent observations?
>
>
>
>I hope you can help me. I got really stuck with this
>problem.
>
>Sincerly
>Klein.