Choosing and Tuning the EMA Smoothing Factor

Summary

The document explains that an exponential moving average’s smoothing factor controls how quickly past observations lose influence. One proposed calibration method starts by choosing how much weight a particular lag should retain, then selects the factor so that the lagged observation has that weight after normalization. This frames the factor as a memory choice rather than a universal constant.

It also notes that a model of price dynamics can guide the choice by allowing the researcher to study the estimator’s variance. A separate response mentions a smoothing value used in a branded risk-management implementation and points to research on alternative values. The discussion does not derive a complete EMA formula or establish one best setting; the suggested weight depends on normalization and the chosen horizon, while model-based tuning depends on the assumptions about price behavior.

Key ideas

• The smoothing factor determines how quickly an exponential moving average forgets older observations.
• Choose a factor by specifying the desired normalized weight of an observation at a selected lag.
• A model of price dynamics can help tune the factor by analyzing estimator variance.
• The document offers no universal setting and gives only a brief reference to a risk-management convention.

Tags

# Smoothing factor of Exponential Moving Average


# Smoothing factor of Exponential Moving Average












I'm trying to implement an Exponential Moving Average indicator, but I'm sort of stuck on the smoothing factor. What I've come up with:

$$\frac{1}{N}\sum\limits_{k=0}^N \alpha^{k} P_k$$ Where N is the window of days in consideration, k loops through the days, $ \alpha $ is a smoothing factor and P is the price.

What should I use for a smoothing factor? Is there any general guidelines? And am I even near the final product?

## Answer by lehalle (score 1)

https://quant.stackexchange.com/a/21690

The smoothing factor is a way to specify the memory of your estimator. This view provides a simple and natural way to tune $a$. Say you want the $k$th term in the past to weight for 1% in your estimation. It gives you $$\frac{\alpha^k}{ A} = \frac{1}{100},$$ with $A$ your normalizing factor (see @Gordon's remark).

Of course you can do better than that. For instance if you assume a model on $P(t)$ dynamics, plug it into the moving average and try to control the variance of the sliding estimator.

## Answer by AfterWorkGuinness (score 0)

https://quant.stackexchange.com/a/21681

In the proprietary/branded Risk Metrics implementation of EWMA, I believe a smoothing factor of .97 is used. Here is a paper that discusses different smoothing factors for EWMA

http://www.tandfonline.com/doi/abs/10.1080/00036846.2014.982853?journalCode=raec20

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.