The Average Age Of Averages by Giorgos Siligardos
A Visual Approach
Have you ever considered why you use 2/(n+1) as a smoothing
parameter when using exponential moving averages? Here
you will find a simple explanation.
When you’re using an n-period exponential moving
average, do you ever think about why it has a smoothing
parameter of 2/(n + 1)? And even if you did, there is a
chance you may not understand why this formula exists
and how it is derived. Let me explain in simple and visual
terms the underlying reasoning behind the use of 2/(n + 1) as
a smoothing parameter.
While exponential smoothing was originated by Charles
Holt in 1957 and Robert Goodell Brown in 1959, the first who
used exponential smoothing to track stock prices was most
likely P.N. Haurlan, a rocket scientist from the Jet Propulsion
Laboratory of NASA in the early 1960s. Haurlan published
his work on the subject in his 1968 booklet Measuring Trend
Values (see “Suggested reading”).
The first connection between the simple moving average
(SMA) and the exponential moving average (EMA) along
with the 2/(n + 1) conversion formula was presented in
Brown’s 1963 book, Smoothing, Forecasting And Prediction
of Discrete Time Series. Later, the conversion formula became
broadly adapted by technical analysts after the publication of Jack Hutson’s 1984 article “Filter Price Data:
Moving Averages Vs. Exponential Moving
Averages” in Technical Analysis of Stocks &
Commodities (see “Suggested reading”).
The connection between SMA and EMA
in Brown’s book originates from the idea of
equating the average age of price data for the
two smoothing methods.