What's the Laplace transfer function of a moving average?
$$\frac{y_k}{x_k}=\frac{1+z^{-1}+z^{-2}+z^{-3}+...+z^{-N+1}}{N}$$

can be re-written as

$$\frac{y_k}{x_k}=\frac{1}{N}\frac{1-z^{-N}}{1-z^{-1}}$$

That should be straightforward to model in the s-domain by replacing z by $$e^{sT}$$

i.e.
$$H(s)=\frac{1}{N}\frac{1-e^{-sTN}}{1-e^{-sT}}$$
$$$$

This is a SINC function in the frequency domain whose magnitude versus frequency is of the form:
$$\dfrac{sin(\pi fN)}{Nsin(\pi f)}$$


(source)