FRAMA: an average that adapts using fractal dimension

What it measures

FRAMA measures the fractal dimension of recent price — a number between one and two describing how rough the path is — and uses it to set its smoothing.

A dimension near one means the path is close to a straight line, and the average speeds up. Near two means it is space-filling chop, and the average slows almost to a stop.

It is the most mathematically grounded of the adaptive averages, and in practice it behaves similarly to KAMA while reacting to a different property of the data.

How it is calculated

These are the steps Basis performs, verified against the published definition.

1. 1

   Split the lookback window in half and measure the price range of each half and of the whole.

2. 2

   Compare the sum of the two half-ranges against the full range; a path that doubles back covers more ground than its net range.

3. 3

   Convert that ratio into a fractal dimension using logarithms.

4. 4

   Map the dimension onto a smoothing constant and apply it to the previous value and the current price.

Settings

A period of sixteen or higher, and even, is the usual requirement. Below that the dimension estimate is unstable enough that the adaptation becomes random rather than responsive.

How to read it

• Read it as a trend line whose responsiveness you do not have to manage. Flat means rough, sloping means smooth.
• The transition from flat to sloping is often earlier than a fixed average would show, because roughness falls before displacement becomes obvious.
• It is a good candidate for the baseline of a system precisely because it does not need re-tuning between regimes.
• The dimension itself is worth watching alongside the average, where an implementation exposes it. A market whose dimension falls steadily is one getting more orderly, and that transition tends to precede the part of a trend that is obvious on price.

Where it misleads

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