Weired Actual Autocorrelations when Estimating an Ar(1)

[colonia_space]

Hi everyone,
i am total beginner in eviews, currently doing an intership where i have to analyse some time series. so it might happen that i am going to raise the one or another question in future.
My current problem is:
I have a time series of foreign trade volumes from 1991 to 2011 which of course has an strong upward trend. unit root tests say me that this series has an unit root i.e. is not stationary (has an stochastic trend). Makes it any sense to estimate the series with an ar(1) model with deterministic trend like
yt= y0+a0*t+a1*yt-1?
And is it the correct specification of this model in eviews simply
y c t ar(1) ?? (Does c account for the intercept (starting value?) and t here is simply a count variable. does it capture the linear trend, when i enter it like this?)
Although Eviews compute this equation without errors and the fitting seems to be good, when i look in view->arma structure->correlogram i see that the "actual" values of the autocorrelation were very different from the real autocorrelation of the series, which i get when i look at them in the series window. In the equation window ACF gets negative at lag 15 and generally decays much faster than in the series window, where i guess the right values were displayed. When i simply compute the eqation y ar(1) without intercept and deterministic trend, the AR modell is not stationary (which seems reasonable to me, because the ar part now has to model the upward trend in the data), but the ACF in the equation windows now is exactly the same than in the series windows...What's the thing with this?
Furthermore the Q Statistics show that there are high serial correlation of the error terms so the model is obsolete, but nevertheless i want to understand the problem with the ACF in the equation windows and what it has to do with the deterministic trend.

Greetings Andreas