Akaike Information Criterion

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

.

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