# Re: [R] Bootstrap Correlation Coefficient with Moving Block Bootstrap

From: Tim Hesterberg <timh_at_insightful.com>
Date: Thu, 06 Dec 2007 09:08:20 -0800

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.

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