generate AR(1) data

[Heber Farnsworth]

This is probably a simple question but I'm stumped and if someone knows 
the answer off the top of their head it would greatly speed up my code.

I need to generate a large number of random (Gaussian) vectors that 
have an AR(1) correlation structure.  Obviously I could do this in a 
loop but this is slow.  I would rather rotate a vector of IID normal 
draws so that the result will have the right covariance matrix.  So 
what I need is the matrix square root of a symmetric toeplitz matrix

1   .5  .25  .125 ...
.5   1  .5    .25 ...
.25 .5  1   .5 ...

etc (here the correlation is .5).  It seems inefficient to try to 
compute this square root numerically.  Isn't it known in closed form?

Heber Farnsworth



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