# The Arnaud Legoux Moving Average: Information Value vs. Information Confidence

In this Spotlight we’re looking at the Arnaud Legoux Moving Average (ALMA) which was developed as an alternative to conventional moving averages. Specifically, Legoux sought to create a smooth moving average without compromising responsiveness. To learn more, check out the video or continue reading below.

The ALMA indicator is a linear filter whose coefficients are determined using a Gaussian distribution. Legoux then adds an offset towards the end of the lookback period.

This is different than a Simple Moving Average (SMA) which places equal weight to all the datapoints in the lookback period. A six period SMA for example, locates the average of that period by adding the prices for each bar and dividing by 6. We may envision this as a flat distribution where each datapoint has equal weight:

When averaging over a longer period, say by applying a SMA(20), one will then see a smoother and more esthetically pleasing output. However, this will have limited information value as it is further removed, i.e. lagging, from the current price action.

## Information Value vs. Information Confidence

A Weighted Moving Average (WMA) on the other hand is more responsive to recent price changes. Successively more weight is added, attributing most weight to the latest, and least to the first datapoint in the period. This approach may be illustrated as follows:

Accordingly, the most recent datapoint is considered the most valuable (information rich) in predicting future price action. In reality however, the opposite is the case. The closer we get to the current price point, the greater the uncertainty about future movement.

Only hindsight knowledge can provide clarity on where the WMA should have plotted. For example, if we apply an WMA to the closing price for the past 6 days, our expectation for day 2 is clear because we already have the price information from day 3 and 1. If the price was \$10 on day 1 vs. \$12 on day 3, we can with confidence assume that the MA should plot around \$11 on day 2.

However, the information confidence for the last day is lower, because we do not yet have tomorrows price data (unavailable). If we go on available price data, one may cautiously assume a price range between \$9 and \$12. The WMA line for day 1 may therefore plot anywhere between \$10 and \$11,5.

## TMA vs. the ALMA Indicator

A third approach is available with the Triangular Moving Average (TMA). As the name implies, weight increments are assigned in a triangular pattern. From the first datapoint towards the mid-point, the weight increases linearly. Likewise, from the mid-point to the last datapoint, the weight decreases linearly. Therefore, the mid-point is considered more important than those at the front- and back-end. One may illustrate this approach as follows:

The Arnaud Legoux Moving Average has a similar approach to the WMA and TMA, but allows for an adjustable Gaussian distribution offset. By default, the ALMA indicator places the weight towards the end of the lookback period:

Finally, a sigma parameter will change the shape of the filter. A large sigma value applies a wide standard deviation whereas smaller values will narrow the focus.

To sum up, the ALMA indicator is a linear filter whose coefficients are determined using a Gaussian distribution. One may therefore define the tradeoff between smoothing and responsiveness as per user preference.

## Conclusion:

The WMA follows price closely, moving fast but may generate a number of “noise signals” The SMA on the other hand has a smooth output but with considerable lag. Finally, a TMA will center the weight of the available datapoints to the mid-point. The ALMA indicator applies an adjustable Gaussian offset, allowing a balance between information value and information confidence as per user preference. Finally, all of the above indicators fall within the linear filter category, including the ALMA indicator.