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
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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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