Decimator effect on wide sense stationary input
The decimator by integer $M$ can be shown to be the following block: 

$$ x[n] \longrightarrow \boxed{ \downarrow M } \longrightarrow y[n] = x[Mn] $$

Assuming that the input $x[n]$ is WSS it has the ACS as 
$$ r_x[k] = E\{ x[n] x^*[n+k] \} $$

Then the output autocorrelation can be defined as: 
$$ r_y[n,n+k] = E\{ y[n] y^*[n+k] \} = E\{ x[Mn] x^*[Mn+Mk] \} = r_x[Mk]$$

as can be seen, the output auto-correlation $r_y[n,n+k] = r_y[k] = r_x[Mk]$ also depends on the lag $k$ and therefore we can conclude that $y[n]$ is also WSS. 

(of course the mean of $y[n]$ is also independent of time $n$.)