What Is the Transfer Function of a Moving Average (FIR Filter)?
The frequency response of the moving average is called the asinc or psinc, the aliased sinc or periodic sinc (sinc for cardinal sine), or the Dirichlet function. 

Since the sum of the moving average filter coefficients is equal to one, it preserves constant signal, hence is somewhat lowpass. When the length $N=2$, the shape in the frequency domain is shaped like a cosine, hence decreasing. 

Otherwise, it ripplles in the frequency domain. When the length is even, the amplification at Nyquist is $0$, when odd, of $1/N$, as shown below:



So it's globally lowpass, not the best, but one of the fastest to compute, allowing fast recursive computations.