Exponential Moving Average Filters

Exponential moving average filters (EMA) are another common type of filter used to filter price data for stocks, bonds and other assets. EMAs are infinite impulse response filters where the current filtered output is dependent upon all of the previous price values. With the EMA filter the impact of earlier data on the current filtered value falls off at an exponential rate. The exponential decay of the impact of earlier data may be fast or slow and is characterized by the smoothing factor, alpha.

PEMA(n) = alphaP(n) + (1-alpha)PEMA(n-1) where alpha is the smoothing factor and 0 < alpha < 1

The Price filtering action, or frequency response, of the exponential moving average filter with alpha of 0.125, 0.25 and 0.5 is shown in the figure below. The sample frequency is once per month (fs=1/month). The 3dB corner frequency for alpha = 0.125fs is 0.0215fs or 46.5 months. The 3dB corner frequency for alpha = 0.25fs is 0.047fs or 21.3 months. The 3dB corner frequency for alpha = 0.5fs is 0.115fs or 46.5 months.

 

Disclosure:

The information presented here is the opinion of the author and may quickly become outdated and is subject to change without notice. All material presented in this article are compiled from sources believed to be reliable, however accuracy cannot be guaranteed. No person should make an investment decision in reliance on the information presented here.

The information presented here is distributed for education purposes only and is not an offer to buy or sell or a solicitation of an offer to buy or sell any security or participate in any particular trading strategy.

Performance data showing past performance results is no guarantee of future returns.

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