When arima is used to fit a time series, the output gives an
estimate of the mean of the series, but calls it the intercept.
For example, if x(t) = a + b x(t-1) + w(t) is a stationary AR(1)
and w(t) is white noise, then mu = a + b mu, or a = mu (1-b),
where mu = E(x(t)). Unless b=0, the mean mu and the intercept a
are not the same. Here's a quick R example:
> x = arima.sim(list(order=c(1,0,0), ar=.9), n=100) + 10
> arima(x, order = c(1, 0, 0))
Coefficients:
ar1 intercept
0.8704 9.8067
s.e. 0.0496 0.6729
So x is an AR(1) with mean 10. The "intercept" estimate
in this example should be 9.8067*(1-.8704). Either change the
output to read "mean" instead of "intercept", or report the
intercept instead of the mean.
Thanks-
David
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David S. Stoffer
Department of Statistics
University of Pittsburgh
Pittsburgh, PA 15260
phone: [412] 624-8496
fax: [412] 648-8814
email: stoffer at pitt.edu
web: http://www.stat.pitt.edu/stoffer
voice: hey dave
