Can we calculate moments (mean, var, skewness, kurtosis) of a signal in frequency domain? The computation of the mean, variance, skewness and kurtosis of a time series in the time domain is straightforward from their definition formulae. 

I need these statistic values in different frequency bands. Currently I apply different bandpass filters to the signal and repeat to compute the statistics. I'm curious if it is possible to compute them from the spectrum in the frequency domain?
If your time series $x(t)=s(t)+n(t)$ where $s(t)$ is a deterministic signal,and $n(t)$ is independent Gaussian noise,  it has a pdf of the form
$$
p(x(t))=\frac{1}{\sqrt{2 \pi} \sigma} \exp\left( -\frac{1}{2} \left(\frac{x(t) - s(t)}{\sigma}\right)^2\right)
$$
the first moment is
$$
E\left\{ x(t) \right\} = s(t) 
$$
which is NOT the DC component of the Fourier Transform of a sample. The first moment is not a constant and the time series is not WSS, and the first moment is not equal to the time average.