Stocks & Commodities V. 31:3 (22-26): The Average Age Of Averages by Giorgos Siligardos

Stocks & Commodities V. 31:3 (22-26): The Average Age Of Averages by Giorgos Siligardos
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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.

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