Path: utzoo!utgpu!jarvis.csri.toronto.edu!mailrus!ncar!umigw!mariano
From: mariano@umigw.MIAMI.EDU (Arthur Mariano)
Newsgroups: comp.dsp
Subject: Re: Just one more AR/MA/ARMA/Marple-type question
Keywords: AR MA ARMA Sir Lawrence Marple confusion p ip N << >>
Message-ID: <1420@umigw.MIAMI.EDU>
Date: 6 Jan 90 05:07:20 GMT
References: <1819@mrsvr.UUCP>
Lines: 23

In article <1819@mrsvr.UUCP>, kohli@gemed (Jim Kohli) writes:
...
> When I learned about autocorrelations, the autocorrelation
> vector was either considered to be the same dimension as the
> dataset (i.e., p=N), or it was padded with zeroes (p>N).

Dear Jim, This wrong. Real data is noisy. Thus, your estimated
correlations do not equal the true correlations. A good correlation estimate
uses the same data in the numerator as the denominator, viz.
C(k)=sum x(s)*x(s+k)/(sum sqrt(x(s)*x(s+k))), where x is the detrended
(very important) data, k is the lag, * is multiplication and the sum is
over all possible s. A rule of thumb is never calculate your correlation
function for lags greater than 1/4 the data length. The rationale behind
this is that for large lags, very few (relative to zero and small lags)
data points go into the products needed for C(k), e.g. for lags equal to
N-1, only one product can be calculated. Thus large lags have high
estimation error that will corrupt fits to or transforms of your
ESTIMATED correlation function. So keep p small to get best results.
Cheers, Arthur
-- 
Arthur Mariano                     Inet: mariano@umigw.miami.edu [128.116.10.1]
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