different moving average filters differences
Hi: All of those moving averages require future values of $X$ which in DSP terminology means that they are non causal filters and physically not realizable. Also, in general you should not have $X[n]$ on both sides of the equation because simplification is then possible and this means that it's no longer an equally weighted filter.  So, if you fix that and move the index back one so that you have $Y[n] = 1/3 *(X[n-1] + X[n-2] + X[n-3])$ then that is a causal filter that is realizable.