Theory

Moving averages are used as a basis for many technical indicators. A moving average is a sort of local average around a given point. In signal processing terms the moving average acts as a lowpass filter, removing high frequency "noise" from the signal.

Implementation

The signal parameter is a one dimensional array. It makes sense to use the typical price as this input.

import numpy as np

def simple_moving_average(signal, points):
    """
    Calculate the N-point simple moving average of a signal


    Inputs:
        signal: numpy array -   A sequence of price points in time
        points: int         -   The size of the moving average

    Outputs:
        moving_average:     numpy array -   The moving average at each point in the signal
    """
    moving_average = np.zeros(len(signal))

    for i in range(points):
        moving_average[i] = np.sum(signal[0:i + 1])/(i+1)

    for i in range(points, len(signal)):
        moving_average[i] = np.sum(signal[i + 1 - points:i + 1])/(points)

    return moving_average

Results

Comparing the simple moving average to the typical price reveals the behaviour of the SMA: it is smoother than the typical price signal and it lags behind the typical price signal.

It is also worth comparing moving averages of different periods:

Note that the 20 point moving average is smoother than the 10 point moving average and lags even further behind the typical price.