Dear Alireza,

I have a question that nobody have provided me a good response. I know that the 'best' con* images(in the case that one interested in principal in generating con* images to take forwards to
a second level analysis) will obtain by proper modeling of the non-sphericity and using maximum likelihood parameter estimates (the default in SPM5). But when I said yes to AR(1) the degree of freedom is the same when I say no to AR(1)(for one single subject).Does that mean that there is no correlation structure in error so I have to say no to AR(1)?

No. The degrees of freedom for a maximum likelihood (ML) estimate are the same as an OLS
estimate, under sphericity (i.e., the largest that they can be). This is why they are the same
when you tell SPM that the data are spherical, by omitting AR(1).

You are absolutely right that the optimal estimator for second-level analyses are the ML
estimates and these will always have the same d.f. as the OLS estimates under i.i.d assumptions.
In previous versions of SPM we used OLS estimates and used the serial correlations to adjust
the d.f. (as in a Greenhouse-Geiser correction). This post-hoc adjustment to the d.f. is
unnecessary when you use the serial correlations to get ML estimates.

I hope this helps - Karl