EMA (Fractional Length EMA) [A II]

EMA (Fractional Length EMA)

Description
This is a standard Exponential Moving Average (EMA) with artificial length constraints removed. It preserves the classic EMA formula while allowing decimal and sub-1 length values. The goal is to provide a mathematically complete EMA implementation rather than a restricted preset.

Basic Formula (Pine)

Pine Script®

Key Features

Decimal Lengths
Length accepts real numbers instead of integers. Provide finer control over weighting and transition between speeds— unlocks non-integer Fibonacci, golden ratio, or custom tuning.
Sub-1 Lengths (N < 1)
Allows smoothing factors greater than 1, which changes the filter’s response characteristics while remaining mathematically valid. When N < 1, the smoothing coefficient exceeds 1 and the recursive term becomes negative-weighted. In practice, the EMA overshoots the current price, then corrects in the opposite direction on the next bar, creating zig-zag oscillations around price. This enables:
　　■Strong responsiveness to change
　　■Impulse sensitivity
　　■Use within multi-pole or stacked filter designs
　　■Combination with slower averages for spread or difference constructions

　　■ Caveats
　　Sub-1 values do not behave like traditional smoothing EMAs.
　　Overshoot and higher reactivity are expected outcomes of the formula.

Practical use example
I use an EMA with n = 0.6 for responsiveness and then smooth it with a DEMA(12). The short length captures impulses quickly Whilst the higher length DEMA filters out noise whilst maintaining reactivity. This resembles a hybrid between an oscillator and a moving average, ideal for spotting momentum changes without being overwhelmed by noise.

🇯🇵 日本語概要（Japanese Summary）
本スクリプトは、EMA（指数移動平均）を数理仕様に忠実に実装した拡張版です。特徴として、期間パラメータに1未満を含む小数値を指定可能です。これにより、従来の整数期間では不可能だった極めて細かい重み付けの調整や、高速な応答特性のシミュレーションを実現します。計算式は標準的なEMAと同一であり、パラメータの制約のみを排除しています。

中文概要（Chinese Summary）
本指標為標準 EMA 的擴充實作，核心公式保持不變，但開放了小數與小於 1 的週期設定。透過取消整數限制，提供更微細的權重微調空間。小於 1 的週期在數學上依舊有效，可呈現不同的濾波動態。本工具旨在回歸 EMA 數理定義的完整靈活性，而非創造新指標。

Disclaimer:
This script is a research tool for market structure analysis and educational purposes only. It does not constitute financial advice. Trading involves risk.

릴리즈 노트

1. Updated a typo in the EMA function.
2. Under development: This indicator is planned to from the basis of a fractional length "noisy" carrier signal that is then fed through a Kalman filter.

Fractional length EMA with length at 0.1. A band forms around price showing the raw volatility or carrier signal of price.

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