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QUERY: Estimating autocorrelation time

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Mon, 15 Feb 1999 16:40:07 +0000

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 Greetings. Standard time series texts like Box, Jenkins, and Reinsel (1994, p. 30) and Priestley (1981, p. 319) remind us that if z.t is a stationary process with mean mu.z, covariances gamma.k = C( z.t, z.{t+k} ), variance sigma.z^2 = gamma.0, autocorrelations rho.k = gamma.k / gamma.0 and z.bar = ( 1 / n ) * sum( z.t, t = 1 ... n ), then the variance of z.bar is given by                             [ n-1 ]                          2 [ ----- ]                   sigma.z [ \ k ]      V( z.bar ) = -------- [ 1 + 2 ) ( 1 - -- ) rho ] ,                      n [ / n k ]                             [ ----- ]                             [ k = 1 ] and a large-sample approximation to this is given by                                        2                                 sigma.z                    V( z.bar ) = -------- tau ,                                    n where                                   infinity                                    -----                                     \                      tau = 1 + 2 ) rho                                     / k                                    -----                                     k = 1 is called the *autocorrelation time* for the series. I am looking for pointers into the literature on how best to estimate tau (e.g., simply putting in the usual estimate of rho.k for all k from 1 to K for large K does not work very well because beyond a certain point you are just adding in noise, so some kind of thresholding appears to be a good idea, but with a cut-off at | rho.k | <= C for what value of C?). If anyone can suggest good papers or books that cover this topic, please send advice directly to [log in to unmask] and I will post a summary of the replies. Many thanks and best wishes, David Draper ============================================================================ Dr. David Draper Statistics Group web http://www.bath.ac.uk/~masdd Department of email [log in to unmask]   Mathematical Sciences voice UK (01225) 826 222, nonUK +44 1225 826 222 University of Bath fax UK (01225) 826 492, nonUK +44 1225 826 492 Claverton Down Bath BA2 7AY England   ============================================================================ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

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