OPEN-SOURCE SCRIPT
Atualizado 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
■ 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.
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)
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.
Notas de Lançamento
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.
Script de código aberto
Em verdadeiro espírito do TradingView, o criador deste script o tornou de código aberto, para que os traders possam revisar e verificar sua funcionalidade. Parabéns ao autor! Embora você possa usá-lo gratuitamente, lembre-se de que a republicação do código está sujeita às nossas Regras da Casa.
Aviso legal
As informações e publicações não se destinam a ser, e não constituem, conselhos ou recomendações financeiras, de investimento, comerciais ou de outro tipo fornecidos ou endossados pela TradingView. Leia mais nos Termos de Uso.
Script de código aberto
Em verdadeiro espírito do TradingView, o criador deste script o tornou de código aberto, para que os traders possam revisar e verificar sua funcionalidade. Parabéns ao autor! Embora você possa usá-lo gratuitamente, lembre-se de que a republicação do código está sujeita às nossas Regras da Casa.
Aviso legal
As informações e publicações não se destinam a ser, e não constituem, conselhos ou recomendações financeiras, de investimento, comerciais ou de outro tipo fornecidos ou endossados pela TradingView. Leia mais nos Termos de Uso.