From stoffer at pitt.edu  Fri Oct 21 04:16:23 2005
From: stoffer at pitt.edu (stoffer@pitt.edu)
Date: Fri, 21 Oct 2005 04:16:23 +0200 (CEST)
Subject: [Rd] Error in arima reporting (PR#8231)
Message-ID: <20051021021623.C8B23BB72@slim.kubism.ku.dk>

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

-- 


-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
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



[Rd] Error in arima reporting (PR#8231)
stoffer@pitt.edu