Calculating a moving average

Summarizing a list of numbers into one representative number can be done by calculating the average. The equation for the arithmetic mean is to add up all the values and divide by the number of values. However, if the values being summed over are extremely large, the total sum may overflow.

In Haskell, the range for Int is at least from -2^29 to 2^29-1. Implementations are allowed to have an Int type with a larger range. If we try to naively average the numbers 2^29-2 and 2^29-3 by first calculating their sum, the sum may overflow, producing an incorrect calculation for the average.

A moving average (or running average) tries to escape this drawback. We will use an exponential smoothing strategy, which means numbers that were seen previously contribute exponentially less to the value of the running mean. An exponential moving average reacts faster to recent data. It can be used in situations for detecting price oscillations or spiking a neuron in a neural network...