Wilder’s Smoothing AKA Smoothed Moving Average is to duke it out in the ‘Technical Indicator – Fight for Supremacy‘ so here is some info about how it is calculated along with an Excel Spreadsheet for your interest:
Wilder’s Smoothing (WS-MA) was developed buy J. Welles Wilder, Jr. and first presented in his landmark book New Concepts in Technical Trading Systems (June 1978). He used it as a component in several of his other indicators including the RSI which is one of the most popular technical indicators of all time.
Despite being very different in how they are calculated, Wilder’s Smoothing and the EMA are actually the same indicator. To reveal the equivalent EMA simply multiply the period by two and subtract one, test it for yourself; a 50 period WS-MA is equivalent to a 99 period EMA. You can also reveal the EMA smoothing period from any two data sets using the following formula:
N = (2-( (MA-MA[1]) / (Close-MA[1]) ) ) / ( (MA-MA[1]) / (Close-MA[1]) )
Below you can see how the weighting is applied to a 50 period WS-MA, EMA and SMA:
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How To Calculate Wilder’s Smoothing:
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It starts as a Simple Moving Average (SMA):
WSMA1 = Simple MA = SUM(CLOSE, N)/N
After that it is calculated according to the following formula:
WSMA(i) = (SUM1-WSMA1+CLOSE(i))/N
Where:
WSMA1 = Wilder’s Smoothing for the first period.
WSMA(i) = Wilder’s Smoothing of the current period (except for the first one).
CLOSE(i) = The current closing price.
N = The smoothing period.
Here is an example of a 3 period Wilder’s Smoothing AKA Smoothed Moving Average:
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Wilder’s Smoothing Excel File
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I have put together an Excel Spreadsheet containing Wilder’s Smoothing and made it available for FREE download. It contains a ‘basic’ version displaying the example above and a ‘fancy’ one that will automatically adjust to the length you specify. Find it at the following link near the bottom of the page under Downloads – Technical Indicators: Wilder’s Smoothing (WS-MA).
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Smoothed Moving Average and a Simple Moving Average
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Test Results
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We tested Wilder’s Smoothing through 300 years of data across 16 global markets to reveal if it is an effective trading tool – see the results.
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