Yes, it will have issues with long memory: the smoothed signal would accurate reproduce the peaks / valleys.
Two solutions:
- use shorter memory: rather than 1/16th, use 1/8th, or 1/4th. The data generated this way will be more volatile.
- scale up observations: rather than having data series in -5 - +5 range, scale them up by 10 (or 16, using left shifts) for example. The resulting moving average will be correspondingly scaled up.