g13abf
g13abf
© Numerical Algorithms Group, 2002.
Purpose
G13ABF Univariate time series, sample autocorrelation function
Synopsis
[xm,xv,r,stat,ifail] = g13abf(x,nk<,ifail>)
Description
The data consist of n observations x , for i=1,2,...,n from a
i
time series.
The quantities calculated are
(a) The sample mean
n
--
> x
-- i
_ i=1
x= ------
n
(b) The sample variance (for n>=2)
n
-- _ 2
> (x -x)
-- i
2 i=1
s = -----------
(n-1)
(c) The sample autocorrelation coefficients of lags k=1,2,...,K,
where K is a user-specified maximum lag, and K<n, n>1.
The coefficient of lag k is defined as
n-k
-- _ _
> (x -x)(x -x)
-- i i+k
i=1
r = ------------------
k n
-- _ 2
> (x -x)
-- i
i=1
(d) A test statistic defined as
K
-- 2
STAT=n > r ,
-- k
k=1
which can be used to test the hypothesis that the true
autocorrelation function is identically zero.
If n is large and K is much smaller than n, STAT has a
2
(chi) distribution under the hypothesis of a zero
K
autocorrelation function. Values of STAT in the upper tail
of the distribution provide evidence against the
hypothesis.
Parameters
g13abf
Required Input Arguments:
x (:) real
nk integer
Optional Input Arguments: <Default>
ifail integer -1
Output Arguments:
xm real
xv real
r (nk) real
stat real
ifail integer