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Обновлено Fractional-Diff Momentum Oscillator
Fractional-Diff Momentum Oscillator
What it does
The Fractional-Diff Momentum Oscillator is a momentum line, scaled in standard-deviation (σ) units around a zero balance, built on the fractional differencing of price — the smallest amount of differencing that makes price statistically stationary while still keeping its memory.
Why this is different (and original)
Almost every momentum oscillator works on returns — that is, price differenced once (integer order d = 1). Returns are stationary, but differencing once erases the series' memory, throwing away the slow, persistent structure that carries trend information. Raw price (order d = 0) keeps all the memory but is non-stationary and unusable by most statistical tools.
Fractional differencing uses a non-integer order (typically 0.3–0.6) that sits between the two: it removes just enough drift to reach stationarity while retaining long memory. The result is a momentum series that is both well-behaved and information-rich. This transform is standard in quantitative research but rare on retail charts, where oscillators almost universally difference once and discard the signal. That is what makes this original: it is a momentum oscillator built on a memory-preserving transform rather than plain returns.
How it works
The fixed-width fractional-difference weights are generated recursively — w(0) = 1, w(k) = −w(k−1)·(d − k + 1)/k — and truncated once they fall below a tolerance, giving a finite window. Those weights are convolved with log-price to produce the fractionally-differenced series. That series is then z-scored over the normalization window and lightly smoothed into the σ oscillator you see, centred on zero.
How to use it
Zero is the balance line. Above zero = net up-momentum; below = net down-momentum.
Dashed σ bands mark stretched momentum; dotted bands mark extremes prone to exhaustion (red on top, green on the bottom in the standard reading).
Zero-crosses (triangles) are momentum-flip events.
Divergences (circles) warn when price makes a new extreme that momentum does not confirm.
Read the EDGE row. The dashboard runs a live forward-return harness: for every momentum flip it checks whether a favourable move (≥ k×ATR within the horizon) actually occurred, and compares that Hit % against the unconditional Base %. EDGE = Hit − Base is the honest measure of whether the signal adds information on your instrument and timeframe. If EDGE is near zero, the signal is not helping there — and the tool says so.
Settings guide
01 · Data & Differencing — source, log-price toggle, differencing order d, weight tolerance, max window, and a universal price source for the harness.
02 · Normalization — z-score window and output smoothing.
03 · Calibration — horizon, favourable-move threshold (×ATR), base-rate window.
04 · Bands — momentum and extreme σ bands; divergence pivot.
05 · Display & Theme — visual style (gradient area + glow / histogram / line), regime tint, dashboard, colors.
Non-repaint
The weights are fixed and the convolution reads only closed bars — no recalculation of past values, no future leak.
Concept credit
Fixed-width window fractional differentiation — Marcos López de Prado, Advances in Financial Machine Learning (2018).
Fractional integration in time series — Hosking (1981); Granger & Joyeux (1980).
Disclaimer
For research and education only. Not financial advice, not a recommendation, and not a guarantee of future results. All statistics shown are in-sample, close-to-close, and exclude costs — a study aid, not a backtest. Do your own research and manage your own risk.
What it does
The Fractional-Diff Momentum Oscillator is a momentum line, scaled in standard-deviation (σ) units around a zero balance, built on the fractional differencing of price — the smallest amount of differencing that makes price statistically stationary while still keeping its memory.
Why this is different (and original)
Almost every momentum oscillator works on returns — that is, price differenced once (integer order d = 1). Returns are stationary, but differencing once erases the series' memory, throwing away the slow, persistent structure that carries trend information. Raw price (order d = 0) keeps all the memory but is non-stationary and unusable by most statistical tools.
Fractional differencing uses a non-integer order (typically 0.3–0.6) that sits between the two: it removes just enough drift to reach stationarity while retaining long memory. The result is a momentum series that is both well-behaved and information-rich. This transform is standard in quantitative research but rare on retail charts, where oscillators almost universally difference once and discard the signal. That is what makes this original: it is a momentum oscillator built on a memory-preserving transform rather than plain returns.
How it works
The fixed-width fractional-difference weights are generated recursively — w(0) = 1, w(k) = −w(k−1)·(d − k + 1)/k — and truncated once they fall below a tolerance, giving a finite window. Those weights are convolved with log-price to produce the fractionally-differenced series. That series is then z-scored over the normalization window and lightly smoothed into the σ oscillator you see, centred on zero.
How to use it
Zero is the balance line. Above zero = net up-momentum; below = net down-momentum.
Dashed σ bands mark stretched momentum; dotted bands mark extremes prone to exhaustion (red on top, green on the bottom in the standard reading).
Zero-crosses (triangles) are momentum-flip events.
Divergences (circles) warn when price makes a new extreme that momentum does not confirm.
Read the EDGE row. The dashboard runs a live forward-return harness: for every momentum flip it checks whether a favourable move (≥ k×ATR within the horizon) actually occurred, and compares that Hit % against the unconditional Base %. EDGE = Hit − Base is the honest measure of whether the signal adds information on your instrument and timeframe. If EDGE is near zero, the signal is not helping there — and the tool says so.
Settings guide
01 · Data & Differencing — source, log-price toggle, differencing order d, weight tolerance, max window, and a universal price source for the harness.
02 · Normalization — z-score window and output smoothing.
03 · Calibration — horizon, favourable-move threshold (×ATR), base-rate window.
04 · Bands — momentum and extreme σ bands; divergence pivot.
05 · Display & Theme — visual style (gradient area + glow / histogram / line), regime tint, dashboard, colors.
Non-repaint
The weights are fixed and the convolution reads only closed bars — no recalculation of past values, no future leak.
Concept credit
Fixed-width window fractional differentiation — Marcos López de Prado, Advances in Financial Machine Learning (2018).
Fractional integration in time series — Hosking (1981); Granger & Joyeux (1980).
Disclaimer
For research and education only. Not financial advice, not a recommendation, and not a guarantee of future results. All statistics shown are in-sample, close-to-close, and exclude costs — a study aid, not a backtest. Do your own research and manage your own risk.
Информация о релизе
Fractional-Diff Momentum Oscillator (short name: FracDiff Momentum)New in this update — a stationarity check. Fractional differencing only works if the chosen differencing order actually makes the series stationary while keeping memory. The dashboard now reports a stationarity proxy (the lag-1 autocorrelation of the differenced series) with a clear ✓ / ✕ verdict, so you can tune the differencing order until the transform is valid on your instrument rather than guessing.
New dashboard rows: Stationary (acf1), Edge floor.
New exports: EXP_Osc, EXP_dEff, EXP_ACF1, EXP_Stationary, EXP_Edge, EXP_EdgeLB, EXP_RunsZ.
Honest note: the check is a fast proxy, not a full statistical stationarity test — it tells you whether the differencing did its job, which is the practical question. The transform is not an edge; the harness measures whether its turns pay.
Информация о релизе
v2.0 — Auto min-d via a live ADF test, ADF/KPSS stationarity panel, honest out-of-sample harness, and on-price signalsAUTO minimum-d differencing: instead of a fixed order, the tool now searches for the SMALLEST d whose fractionally-differenced series passes an Augmented Dickey-Fuller stationarity test — López de Prado's FFD objective (minimum differencing → maximum memory kept). A live controller nudges d toward the stationarity boundary and rebuilds the fixed-width weights when it changes; a memory-margin setting stops it over-differencing. "Fixed" mode preserves the classic behaviour.
On-panel ADF + KPSS readout: two complementary unit-root tests replace the old lag-1 autocorrelation proxy — ADF (null = unit root; stationary when the t-stat is below its critical value) and KPSS (null = stationary; stationary when below its critical value), each shown with its threshold and a ✓/✕. The ADF t-stat is computed exactly (validated to match statsmodels).
HARNESS+ calibration: the Hit/Base/EDGE record is honest three new ways — a uniqueness-weighted EFFECTIVE sample size (overlapping forward windows aren't independent), a multiple-testing DEFLATED significance bar, and an IN-SAMPLE / OUT-OF-SAMPLE split. The new "EDGE (OOS)" row is the one to trust. Runs-test retained.
On-price signals: the momentum zero-cross turns now also plot on the price chart as tiny directional triangles — green up (below bar) on a bullish flip, red down (above bar) on a bearish flip — in addition to the in-pane markers.
Bug fix: the stationarity autocorrelation was being computed inside a conditional (a stateful ta.* call behind a ternary), which can silently skip bars — it's now hoisted to top level.
New dashboard rows (ADF, KPSS, EDGE OOS, Eff-N) and exports (EXP_ADF, EXP_KPSS, EXP_EdgeOOS, EXP_EffN); EXP_dEff now reports the live effective order. The FFD engine, oscillator, divergences, bands, theme and non-repaint behaviour are unchanged.
Descriptive momentum transform; stationarity and forward statistics are in-sample/on-symbol, not investment advice.
Информация о релизе
v2.1 — Three optional accuracy upgrades over v2.0: a robust MAD z-score, a lag-minimal smoother, and an opt-in 3-window extreme consensus. The fixed-width fractional differencing, the auto min-d ADF controller, the ADF / KPSS stationarity readout and the full HARNESS+ track-record (effective N, deflated significance, in-sample / out-of-sample split, runs-test) are unchanged — set Z-score mode = "Classic (mean/stdev)" and Output smoother = "EMA" for the original v2.0 read.1. Robust MAD z-score (default on). The fractionally-differenced series can be standardized with a median/MAD z (median absolute deviation ×1.4826) instead of mean/stdev, so a single fat-tailed bar no longer stretches the whole σ scale and the band readings stay comparable across regimes. Selectable via "Z-score mode".
2. UltimateSmoother (default on). When output smoothing is on (smoothing > 1), it can use Ehlers' lag-minimal UltimateSmoother instead of an EMA, so the σ-oscillator turns with less delay. Selectable via "Output smoother".
3. 3-window extreme consensus (opt-in, default off). The z can be taken as the MEDIAN of the z at half, one and double the normalization window — extreme only when short, medium and long windows agree. "Extreme normalization" = "Single window" (the default) reproduces v2.0.
What is unchanged. The recursive fixed-width fractional-difference weights, the FFD convolution on log-price, the live ADF auto-d controller, the on-panel ADF + KPSS stationarity tests, the confirmed-pivot divergence, the zero-cross momentum signals, and the entire HARNESS+ calibration (uniqueness-weighted effective N, Bonferroni-deflated significance bar, in-sample/out-of-sample split, runs-test) are byte-for-byte v2.0. Every export (EXP_Osc, EXP_dEff, EXP_ACF1, EXP_ADF, EXP_KPSS, EXP_Stationary, EXP_Edge, EXP_EdgeOOS, EXP_EdgeLB, EXP_EffN, EXP_RunsZ) is retained. The new layers only re-standardize and re-smooth an existing series.
Fractional differencing is a transform, not an edge — whether the turns pay is exactly what the harness measures, in-sample, close-to-close, without costs. Non-repaint: weights are fixed; the convolution uses only closed bars; the calibration resolves on confirmed bars. Concept credits unchanged (López de Prado FFD / min-d; Hosking; Granger & Joyeux; Dickey-Fuller; KPSS; Newey-West), plus the median/MAD robust z-score and Ehlers UltimateSmoother for the new layers.
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Информация и публикации не предназначены для предоставления и не являются финансовыми, инвестиционными, торговыми или другими видами советов или рекомендаций, предоставленных или одобренных TradingView. Подробнее читайте в Условиях использования.
Скрипт с открытым кодом
В истинном духе TradingView, создатель этого скрипта сделал его открытым исходным кодом, чтобы трейдеры могли проверить и убедиться в его функциональности. Браво автору! Вы можете использовать его бесплатно, но помните, что перепубликация кода подчиняется нашим Правилам поведения.
Отказ от ответственности
Информация и публикации не предназначены для предоставления и не являются финансовыми, инвестиционными, торговыми или другими видами советов или рекомендаций, предоставленных или одобренных TradingView. Подробнее читайте в Условиях использования.