Re: Akaike Information Criterion
- From: vontressms@xxxxxx
- Date: Wed, 4 Jun 2008 12:16:43 -0700 (PDT)
On Jun 4, 10:44 am, Robert Buchanan <j.robert.bucha...@xxxxxxxxxxx>
wrote:
Hello,
I've been doing some self-study of forecasting and have a question
about calculating the AIC. I have a time series of data and wish to
determine the linear model of order p which is most appropriate for
the data. Suppose the time series is {r_t} with t=1,2,...,T. I am
fitting a linear model of the form:
r_t = x_0 + x_1 r_(t-1) + ... + x_p r_(t-p) + e_t
I have seen several different definitions of the AIC, most commonly
AIC(k) = Log(sigmahat_k^2) + 2k/T
I think my question is on calculating sigmahat_k^2. Do I have to use
least squares to estimate the parameters x_0, x_1, ..., x_p, then
calculate e_t for t=k+1, k+2, ..., T, and then find the sum of squares
of the e_t, and then divide by T-p? Or is there an easier way to do
this?
Thanks,
Bob Buchanan
Bob,
You under stand the problem correctly. Sigmahat_p^2 is the mean square
for errors: residual sum of squares divided by the number of
observations (N) minus the number of regression paramters (p+1)). It's
the average of the squared residuals, e_t, but using N-p-1 as the
divisor instead of N. Then plot AIC(p) against p. It should level off
and pick the value of p where it starts to level off. Additional
parmeters do not imporve the fit.
Mark
.
- References:
- Akaike Information Criterion
- From: Robert Buchanan
- Akaike Information Criterion
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