Constructing an adaptive moving average with an efficiency ratio and filter

What the line is built to do

The adaptive moving average is built to update slowly while price drifts sideways and to update quickly when price accelerates, reverses, or leaves a range. Construction starts from two n-period inputs and ends in a first-signal-only entry rule that holds until the opposite signal.

Editorial framing: TradersWeek reads this archive workflow as three layers. First, score how cleanly price traveled. Second, turn that score into a squared speed that almost freezes in chop. Third, wrap the line in a self-scaling band so the buy and sell rules can be audited as one procedure. That three-layer reading is editorial and is not attributed to the archive.

Score how cleanly price traveled

Construction starts from two n-period inputs. Price direction is the signed net change between the current observation and the observation n periods earlier. Volatility is the sum of absolute one-period price changes over the same n-period window, treated as a positive noise total. The worked window is 10 periods.

The efficiency ratio is direction divided by volatility. It equals 1 when every bar in the window travels the same way. It approaches 0 when net change is near zero relative to the path. In that sense the ratio is a cleanliness score: a one-way window sits at the top of the scale, and a back-and-forth window sits near the bottom.

Turn that score into a squared speed

Exponential speeds are converted with the mapping 2 divided by n plus 1. The example uses a 2-period fast constant of 0.6667 and a 30-period slow constant of 0.0645.

A scaled smoothing constant interpolates between those two speeds with the efficiency ratio, then is squared so the adaptive weight nearly stalls when the window is mostly noise. A high efficiency ratio therefore leans toward the fast constant. A low efficiency ratio leans toward the slow constant, and squaring pulls that already small weight still closer to a stall.

Each new adaptive moving average value equals the prior value plus the squared constant times the gap between current price and that prior value. The first 10 observations must be seeded with raw prices before the recursion is defined.

Wrap the line in a self-scaling band

The trend filter is a chosen percentage of the n-period standard deviation of successive adaptive-average changes. The worked percentage is 0.15. Small reversals that stay inside that band are ignored.

Rule-based entry uses only the first buy when the adaptive average exceeds its recent low by more than the filter, and only the first sell when the recent high exceeds the adaptive average by more than the filter. The position is held until the opposite signal. Later crossings in the same direction are not new entries.

Editorial note: because the band is a percentage of the variability of successive adaptive-average changes, it scales with the line itself. Combined with first-signal-only entry, the long and short rules become one procedure that can be audited from the same inputs. That audit reading is editorial and is not attributed to the archive.