$y_{MA}$ = $ε_t$ + $ε_{t-1}$ <- stationary
$y_{AR}$ = $ε_t$ + $y_{AR_{t-1}}$
$y_{AR_{t-1}}$ = $ε_t$ + $ε_{t-1}$ + $y_{AR_{t-2}}$
$y_{AR_{t-2}}$ = $ε_t$ + $ε_{t-1}$ + $ε_{t-2}$ + $y_{AR_{t-3}}$ <- non-stationary?
etc.
The MA time series is stationary. This makes sense to me because you're summing up normally distributed mean 0 random variables, but then, an AR process, if the $y_{AR_{t-i}}$ terms are all also sums of normally distributed mean 0 random variables, why is it non-stationary? Again here, you're summing normally distributed mean 0 random variables. I'm obviously not understanding something here, where is the flaw in my logic?