Fractional Differencing for Technical Analysis: Reducing Noise in MACD, ATR, and RSI Signals

TL;DR 

This analysis explores whether fractional differencing can make common trading indicators more predictive.

👉 The purpose is not to prove or disprove the usefulness of MACD, RSI, ROC, Bollinger Bands, or Z-Score, but to test whether these signals can be made more predictive by make it less noisy and easier for models to use.

Key Takeaways

The findings suggest that most common indicators built on raw prices were not truly predictive — in fact, many of them actively reduced model predictive capacity given the configuration used in the test. After applying fractional differencing, however, these same indicators became far less noisy and, in many cases, genuinely predictive. On average, the predictive capacity was improved by 60–80%, showing that fractional differencing fundamentally reshapes how useful these signals are.

From Harmful to Helpful

Some features didn’t just improve; they flipped from being detrimental to predictive. Standout cases included:

• Z-Score in Coffee, Corn, Cocoa, and UK Sugar
• Bollinger Band Lower in Palladium and Copper

By Asset Class

• Strongest improvements: Commodities (Corn, Cotton, Cocoa, Palladium) and FX majors (USD/JPY, DXY, USD/SEK) — clear evidence that fractional differencing stabilizes their signals.
• Equities (US500) also showed reliable, consistent gains across multiple indicators.
• Mixed signals: Energy markets (Oil, Natural Gas), where indicators like RSI and ROC sometimes weakened — likely because fractional differencing smoothed out genuine volatility bursts.
• Weaker effects: Currencies like EUR/GBP, where long-term cycles appear to carry useful predictive information that fractional differencing filtered out.

By Indicator

• MACD (trend) and ROC (momentum): Showed the largest average gains, confirming their predictive value emerges once price memory is reduced.
• RSI (overbought/oversold): Became much cleaner in equities and currencies, though less effective in energy.
• Z-Score and Bollinger Bands: Delivered the biggest transformations — in several assets flipping from misleading to predictive.

Horizon Effect

Improvements were stronger at longer horizons (480 vs 96 15-minute bars), reinforcing that fractional differencing is particularly valuable when filtering out short-term noise and focusing on medium-term predictive structure.

Fractional Differencing Impact at a Glance

Biggest Winners (Clear Improvements):

• 🟢 Commodities: Corn, Cotton, Cocoa, Palladium
• 🟢 Currencies: USD/JPY, DXY, USD/SEK
• 🟢 Indices: US500 (S&P 500)

Turned from Harmful → Helpful:

• 🔄 Z-Score: Coffee, Corn, Cocoa, UK Sugar
• 🔄 Bollinger Band Lower: Palladium, Copper

Mixed or Weaker Results:

• ⚪ Energy: Oil (Crude, Brent) and Natural Gas — sometimes oversmoothed
• ⚪ EUR/GBP: Some indicators weakened (long cycles may still matter)

Indicators with the Biggest Gains:

• 📈 MACD (trend) and ROC (momentum) → most consistent improvements
• ⚖️ RSI → much less noisy in most assets, weaker in energy
• 📊 Z-Score & Bollinger Bands → often flipped from misleading to predictive

Overall Lesson:

👉 Fractional differencing reduced noise and improved predictive power across most markets and indicators — especially at longer horizons (480 vs 96).

What is Fractional Differencing?

Financial prices are non-stationary — their average and variance change over time. Models struggle with this because the data doesn’t stay “stable.”

• Regular differencing (d = 1) solves this by taking the change between two prices:

Here, only the changes are kept.

• But this wipes out too much.
• Fractional differencing (0 < d < 1) uses a weighted combination of past values, keeping part of the memory while stabilizing the series.

👉 A good analogy is removing static from a radio: the music (signal) is still there, but the noise is reduced.

For a deep dive into how this works, see my article:

Fractional Differencing in Time Series

Why Technical Indicators?

Technical indicators are tools that transform raw price data into signals that are easier to interpret.

• MACD highlights trends.
• RSI points out when markets may be overbought or oversold.
• ROC measures the speed of price changes (momentum).
• Bollinger Bands track volatility and price ranges.
• Z-Score shows how far prices are from their typical average.

The challenge is that these indicators are usually calculated on raw prices, which are unstable and constantly shifting. This instability can make the indicators noisy and less reliable than they appear.

By applying fractional differencing before computing these indicators, we can check whether the resulting signals are cleaner, more stable, and more useful for analysis or prediction.

Setup

Here’s how the experiment was set up:

• Data: 15-minute price bars for commodities, currencies, and indices, covering 2024 coming from Capital.com.

Transform: Each instrument was fractionally differenced with its own d value (between 0.1 and 0.4, see d Values Used section below).

ndicators: MACD, RSI, ROC, Bollinger Bands, and Z-Score, computed on both the original and the fractionally differenced series, with these exact settings:

• MACD (line only, no signal): fast EMA 8, slow EMA 21 → MACD = EMA(8) − EMA(21)
• RSI: 9-period RSI using simple rolling means for gains/losses
• ROC: 6-period Rate of Change → (price − price.shift(6)) / price.shift(6)
• Bollinger Bands: 30-period SMA with ±2.5 standard deviations (upper & lower bands)
• Z-Score: 30-period rolling standardization → (price − mean₃₀) / std₃₀

Target: Trend Scanning labels, created using a lookback of 96 bars (≈1 day) and 480 bars (≈5 days). For the original series, the labels were based on the original price. For the fractionally differenced series, the labels were based on the fractionally differenced price. For more information on how this is calculated, check the Trend Scanning section of this article.

Model: Bagged decision trees.

Cross-Validation: TimeSeriesSplit was used — unlike random shuffling, this splits the data into sequential training and testing windows. That way, the model is always tested on data that comes after the training set, just like in real trading.

Metric: Mean Decrease Accuracy (MDA). This works by scrambling (permuting) the values of one feature (say, MACD) and checking how much model accuracy drops.

• If accuracy falls a lot → that feature had strong predictive power.
• If accuracy barely changes → that feature wasn’t very useful (or was too noisy).

👉 In simple terms, MDA tells us how much predictive power each indicator has in the model.

• If scrambling an indicator makes the model much worse, it means the model was relying on it heavily.
• If scrambling it doesn’t change much, that indicator had little or no predictive value.

d Values Used

Each instrument was assigned a d value based on prior stationarity analysis.You can read more about how these values were chosen here: From Commodities to Currencies: Making Price Data Stationary with Fractional Differencing

Price: Raw vs. Fractionally Differenced

Legend:

✅ Improvement  |  ⚠️ Weak  |  🔁 Mixed  |  🌟 Flip 

The analysis demonstrates that applying fractional differencing delivers a clear and consistent improvement in predictive stability. For most instruments, the reduction in “damage” — measured by mean decrease accuracy (MDA) — falls within the 60–80% range. This is notable because indicators based on raw prices were often negative contributors (with negative MDA values, meaning they actively reduced model accuracy). After fractional differencing, these indicators became far less destructive, and some cases even makes the indictor predictive.

Key Highlights

• Strongest improvements: Palladium, Corn, US Cotton, and the US500 index — with gains often exceeding 70%. These markets benefited as fractional differencing stabilized cyclical patterns (commodities) and dampened noise spikes (indices).
• Modest effects: Natural Gas and EUR/GBP showed smaller improvements (e.g., only ~6% for Natural Gas at the 480-bar horizon). In such cases, the underlying series may already exhibit more stationary dynamics, leaving less room for improvement.
• Biggest turnaround: US Cocoa at the 480-bar horizon flipped from negative to positive MDA. While raw-price indicators reduced predictive accuracy, the fractionally differenced version provided useful information — evidence that fractional differencing can unlock hidden predictive structure obscured by noise.

👉 In summary, the findings indicate that fractional differencing not only reduces noise but also has the potential to transform unhelpful technical indicators into predictive signals.

MACD: Trend Detection with Fractional Differencing

Legend:

✅ Improvement  |  ⚠️ Weak  |  🔁 Mixed  |  🌟 Flip 

The analysis shows that fractional differencing provides a major boost to MACD in most markets, cutting down noise and improving predictive stability.

Key Highlights

• Big winners: GBP/JPY, USD/JPY, Coffee Arabica, and Copper improved by 60–78%. Here, fractional differencing helps MACD lock onto cleaner up-and-down swings instead of being distracted by background “drift” in prices.
• Solid improvements: DXY, US500, Cocoa, and Cotton gained 40–65%. These markets often have steady but choppy movements, and fractional differencing seems to strip out some of that chop, letting MACD show clearer signals.
• Mixed or weak gains: Gold, EUR/USD, Natural Gas, and Platinum saw only 0–20% improvements. That’s likely because these markets already behave in a way where MACD works decently, so there wasn’t much extra noise to remove.
• Notable negatives: Oil Crude (-56% at 96 lookback) and Silver (-10% at 96) actually got worse. In these cases, fractional differencing may have “over-smoothed” the data, washing away the kind of wild but useful swings that MACD needs to catch.

👉 Overall: Most instruments improved — often by a lot. Fractional differencing seems to act like a “smart filter”: it takes away the messy background movement but leaves enough structure for MACD to pick out meaningful trends.

RSI: Overbought and Oversold Signals on Fractionally Differenced Data

Legend:

✅ Improvement  |  ⚠️ Weak  |  🔁 Mixed  |  🌟 Flip 

The results indicate that fractional differencing substantially improves RSI stability in most markets, making overbought/oversold signals less noisy and more predictive.

Key Highlights

• Biggest gains: US500, DXY, Coffee Arabica, Palladium, and Cocoa improved by 75–94%. These markets tend to trend cleanly once noise is stripped away, so RSI does a much better job of spotting when prices are running too hot or too cold.
• Solid improvements: Copper, GBP/JPY, Silver, USD/JPY, and USD/CHF gained 50–70%. These are markets that can swing around a lot, and fractional differencing helps smooth out the whiplash so RSI isn’t constantly faking traders out.
• Moderate cases: EUR/USD, GBP/USD, and Platinum saw 15–45% gains. They already move in steadier patterns, so there just wasn’t as much “mess” for fractional differencing to clean up.
• Notable negatives: Natural Gas, Oil Brent, and Oil Crude actually got weaker in spots. These markets live on big, sharp moves, and by filtering too much, fractional differencing may have dulled RSI’s ability to catch those bursts.

👉 Overall: RSI based on fractionally differenced data is simply more reliable — especially for stocks, currencies, and commodities that like to trend. In really wild markets, though, a little bit of noise might actually be part of the signal, which is why RSI sometimes loses its edge there.

ROC: Momentum Strength Improved by Fractional Differencing

Legend:

✅ Improvement  |  ⚠️ Weak  |  🔁 Mixed  |  🌟 Flip 

The analysis shows that fractional differencing had a strong positive effect on ROC (Rate of Change), which measures momentum speed. By filtering out long-memory noise, fractional differencing turns raw momentum signals into more stable and predictive indicators.

Key Highlights

• Biggest winners: Corn, US500, Cocoa, Copper, and USD/JPY improved by 70–85%. These markets often build momentum gradually, so once the background noise is cleared out, ROC does a much better job of catching those runs.
• Solid gains: DXY, Gold, USDCAD, Silver, and USD/CHF rose 50–70%. Here, fractional differencing seems to cut down on the random wiggles, letting real price pushes stand out.
• Moderate cases: EUR/USD, GBP/USD, GBP/JPY, and Platinum saw 30–55% gains. The effect is still helpful, but these markets already had steadier trends, so the payoff wasn’t as dramatic.
• Notable negatives: Oil Crude totally collapsed (-493% at 96, -393% at 480). This looks like ROC got over-smoothed and lost the ability to catch the wild jumps that actually matter in energy. Natural Gas also weakened (-32% to -42%), and Oil Brent barely changed.

👉 Overall: ROC works much better on fractionally differenced data in most markets — especially stocks, currencies, and farm commodities. But in chaotic markets like oil and gas, those wild swings are part of the story, and smoothing them away makes ROC less useful.

Bollinger Bands: Volatility Insights with Fractional Differencing

Legend:

✅ Improvement  |  ⚠️ Weak  |  🔁 Mixed  |  🌟 Flip 

The results show that fractional differencing provides a clear benefit for Bollinger Bands, making volatility-based signals far more robust across most markets.

Key Highlights

BB Upper:

• Biggest gains: Copper, GBP/JPY, Palladium, and USD/JPY jumped 70–90%. Even in markets that are usually messy, the signals turned much clearer.
• Defensive plays: Gold and Silver only improved 10–30%. That makes sense since these assets naturally bounce around a set range — there wasn’t as much “junk” to filter out.
• Weak spot: EUR/GBP slipped a little (-6% at the 480-bar horizon). Likely the long-term cycles here got over-smoothed, so some useful context was lost.

BB Lower:

• Breakthrough flips: Palladium and Copper went from negative (hurting predictions) to positive (helping) — flipping completely into useful signals, with gains over 100%.
• Solid gains: US500, Cocoa, and USD/SEK posted 50–70% boosts, showing fractional differencing works really well in big liquid markets.
• Outlier: Coffee Arabica fell (-59% at 96). It looks like fractional differencing may have smoothed out the big swings that actually carry predictive weight for this commodity.

👉 Overall: Fractional differencing makes Bollinger Bands cleaner, more stable, and way more predictive. In some markets it even turns a “bad signal” into a “good one,” which makes a strong case for using fractional differencing before running volatility-based indicators.

Z-Score: Detecting Price Deviations After Fractional Differencing

Legend:

✅ Improvement  |  ⚠️ Weak  |  🔁 Mixed  |  🌟 Flip 

The analysis shows that fractional differencing drives some of the biggest transformations in Z-Score, which measures how far prices deviate from their average.

Key Highlights

• Standout flips: Coffee Arabica, Corn, Cocoa, and UK Sugar moved from negative (hurting accuracy) to positive (adding value), with gains above 100%. This shows that once the “dead weight” of long-term memory is removed, Z-Score can suddenly become a clear and powerful signal.
• Strong improvements: Copper, DXY, GBP/JPY, Palladium, US500, USD/JPY, and USD/SEK recorded 60–85% gains, suggesting that fractional differencing makes deviations much cleaner to interpret in highly liquid and trend-sensitive markets.
• Moderate gains: Gold, Silver, Platinum, and USD/CHF improved by 20–50%, reflecting that these markets already had fairly stable mean-reverting behavior, so the extra cleaning helped but didn’t change the picture dramatically.
• Weaker or negative cases: Oil Crude slipped (-20% at 96) and EUR/GBP dipped slightly (-8% at 480). In these cases, fractional differencing may have removed longer-term cycles that actually carried useful predictive context.

👉 Overall: Z-Score comes out as one of the biggest beneficiaries of fractional differencing. It often flips from noisy and misleading to highly predictive, especially in commodities and equity indices where raw deviations are otherwise harder to trust.