General Autocorrelation Function.
An example of a class of statistics of the form (8.1) where
and are all zero are ACF estimates

(8.7) 
Suppose we are interested only in a selected set
of ACF samples at delays
.
The problem is to obtain the joint PDF of
the feature vector
denoted by
The elements of can be written as quadratic forms
where
and so forth. The pattern is such that is nonzero
only on the super and subdiagonals spaced away from the
main diagonal.
If the sample mean is subtracted from prior
to calculation of the ACF estimates, the quadratic
forms (8.1) still hold, but the
elements of
are changed. For example,
the th element of
is now
instead of
, where
is the Kronecker delta; the remaining matrices
are more complicated, but each element in the matrices
can be evaluated by means of a single sum.
Baggenstoss
20170519