BITCOIN ADAPTIVE MOVING AVERAGE

What is Bitcoin Adaptive Moving Average?

An adaptive moving average changes how quickly it follows price instead of applying the same response to every candle. The aim is to move more readily when prices make clearer progress and less readily when they repeatedly reverse. It remains a summary of observed prices, with a different way of managing delay.This page contains Kaufman’s adaptive moving average, or KAMA, and the MESA adaptive average, or MAMA. They are separate calculations. Kaufman’s method compares start-to-finish progress with the sum of intervening moves. MAMA estimates changing cycle position in smoothed prices, then adjusts how much each new close contributes to its average.

Measure progress versus backtracking

Imagine walking ten steps forward and ten back: much movement, little progress. KAMA’s efficiency ratio makes that comparison. It divides the absolute change over the window by the sum of absolute candle-to-candle changes. Near 1 describes a direct path; near zero describes more backtracking.

Read KAMA with price

KAMA is a dollar price. Being above it and seeing it rise are separate facts. Maketo’s KAMA reading is Rising when the close is above the line and the line is above its value five candles earlier. The opposite pair produces Falling. A crossing alone can leave the reading Mixed.

Read MAMA with its following line

The MAMA view includes FAMA, a second average which follows it more slowly. Its directional reading compares these two lines instead of using the KAMA price-and-slope rule. The lines can cross while Bitcoin remains below an earlier high: they describe recent response rather than recovery of a particular price.

How Adaptive Moving Average is calculated

Kaufman’s efficiency ratio divides the absolute net change over 10 candles by the sum of absolute candle-to-candle changes. It interpolates between 2- and 30-period smoothing limits. MAMA uses fast and slow phase-response limits. The page is published on Kaufman adaptive average, fast 2, period 10, slow 30. A period counts candles at the interval you choose, so the same setting covers a different stretch of time on a one-hour chart than on a daily one. How smoothing and missing candles are handled.

A calculation you can follow

Consider one illustrative KAMA update after the average has started. Assume the prior adaptive average is $100,000 and the latest close is $109,000. Suppose the window ends $9,000 higher and the sum of absolute price moves is also $9,000. The efficiency ratio is 1.Default fast and slow lengths are 2 and 30. Their response factors are 2 / 3 and 2 / 31. Efficiency 1 selects the faster factor.KAMA squares that factor: (2 / 3)² = 4 / 9. It moves the old average by 4 / 9 of the $9,000 gap.The new average is $100,000 + $4,000 = $104,000. A less direct price path would select a smaller adjustment.Even at maximum efficiency, the line does not jump to the latest close. Adaptive describes a changing response, not the removal of all delay.

KAMA efficiency window

The default period is ten candle-to-candle changes, requiring eleven closes. A longer period changes the history used to judge directness. It does not change the fast and slow limits unless you alter those separately.

KAMA fast and slow lengths

The fast length must be shorter than the slow length. They become response factors before blending and squaring. A fast length of 2 therefore does not make KAMA identical to a conventional two-candle exponential average.

MAMA limits

Defaults are 0.5 for the fast limit and 0.05 for the slow limit. These are response factors, not candle counts. FAMA uses half the current response factor. Maketo displays the first MAMA and FAMA values after a 33-candle run.

Adaptation happens after prices change

A new move affects the average only after its price arrives. Sudden reversals can still leave an adaptive line behind. Smoothness describes the plotted line, not certainty about the next observation.

Starting history affects early values

Both variants repeatedly update earlier calculated values. Early readings depend on the starting convention and available history. A known data gap resets the calculation; missing prices are not silently treated as unchanged prices.

Adaptive Moving Average compared with Weighted Moving Average

A linear weighted average always applies the same age-based weights for a given period. Adaptive methods change their response according to the observed price path. Hull reduces delay by combining weighted averages, which is a different mechanism again. Open Bitcoin Weighted Moving Average.

Are KAMA and MAMA interchangeable names?

No. KAMA uses a progress-versus-backtracking ratio. MAMA uses a cycle-position calculation and a following line. Grouping them on one page keeps their related purpose together while preserving their different settings.

What happens if every price is unchanged?

Maketo uses an efficiency ratio of 1 when total movement in the window is zero. If the whole available run is constant, the average stays at that price. If only the latest window is flat after an earlier move, an older average can still differ from the close and continue approaching it.

Why does changing interval affect adaptation?

Combining short candles into a longer candle removes the path taken inside that period. This changes measured backtracking or cycle position even when the final closing price is unchanged.