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Exponential moving average is a running average of a set of observations, where the weight of each observation is inversely exponentially weighted as a function of how old it is. It is a relatively simple thing to do.

Given a set of observations O1, O2, O3, ... ON the running exponential moving average A1, A2, A3, ... AN can be calculated in real time, at each time N, with the expression ...

AN = AN-1 (1 - X) + ON X

... where X is a weighting factor that determines that amount of smoothing. For instance, if X were zero, then the smoothing is infinite, and O does not contribute at all to A, and if X were one, then smoothing is zero, and A follows O with no smoothing at all. In a more useful example, if X were 0.2, then the smoothing would be five, and A would follow O with a time constant of five iterations, i.e. after five iterations we would be at about 63% of one step change and after 25 iterations we would be at about 95% of one step change.

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