Market Regime LensMarket Regime Lens
Market Regime Lens reads the market on four independent axes and gives you one honest sentence about the current tape. It is a context descriptor, not a signal — it never tells you which way to trade. It tells you whether the tape is readable, how it moves, how long things take, and how risk is arriving.
WHY FOUR AXES, ONE COMPONENT EACH
Most multi-indicator tools stack measures that secretly say the same thing — three complexity metrics agreeing is not confirmation, it is autocorrelation. This tool deliberately uses one component per independent axis, so each number tells you something the others cannot.
STRUCTURE — Complexity-Entropy plane. Bandt-Pompe permutation entropy paired with Martin-Plastino-Rosso statistical complexity, classifying the tape as structured, mixed, or noise. Thresholds are adaptive by default: the reading is ranked against the instrument's own recent range, so it self-calibrates to any market and timeframe instead of relying on absolute cutoffs that break when you change the window.
PERSISTENCE — Anomalous-diffusion exponent. Fitted from mean-squared-displacement scaling across lags: alpha above 1 means super-diffusive (trending), alpha near 1 is a random walk, alpha below 1 is sub-diffusive (mean-reverting). This describes the character of the motion, not its direction.
TIME — First passage and null odds. Expected bars to reach the target versus the stop under a driftless diffusion, plus the null barrier probability P = b/(a+b) — what a coin flip gives you at your chosen reward-to-risk. At 1.5R that is 40%. That is the breakeven any setup must clear, stated plainly.
TAIL — Extremal index. Measures whether extreme moves cluster (theta below 1) or arrive independently. Clustered tails mean gap risk shows up in bursts, which matters for stop placement.
ON THE CHART
The main line is the diffusion exponent, colored by state and filled against the alpha = 1 random-walk baseline, so deviation from randomness is visible at a glance. Faint guides mark the trending and reverting thresholds. Background tint shows the structure class. The panel adapts to your chart theme and colors each row by meaning — including green or amber on the null-odds row depending on whether your chosen R gives better-than-even odds.
PAIRS WITH RISK & LEVELS COCKPIT
Optionally wire the target and stop sources to the Cockpit's exported levels, and the timing and null-probability rows use your real trade levels instead of internal ATR references.
WORKS ON ANY MARKET AND TIMEFRAME
All lookbacks are in bars with no session, expiry, or clock anchors. Non-repainting: everything uses the current bar's data and confirms at close.
LIMITATIONS
Not a signal and not investment advice — no axis forecasts direction. Permutation entropy and complexity require a window much larger than d factorial; at dimension 4 use at least 300 bars, since short windows are undersampling-biased and pin to a constant. Adaptive thresholds classify relative to the instrument's own recent range, so "structured" means structured for this market lately, not in any absolute sense. First-passage times and the null probability assume driftless diffusion with constant volatility — a deliberate null baseline, not a forecast. The extremal index needs enough exceedances; too short a window pins it at 1.00.
CREDITS
Original implementation. Bandt and Pompe permutation entropy; Martin-Plastino-Rosso and Lopez-Ruiz statistical complexity via Jensen-Shannon divergence; anomalous-diffusion MSD scaling; Ferro-Segers runs estimator for the extremal index; first-passage-time and gambler's-ruin barrier theory. Indicator
Permutation Entropy Complexity OscillatorPermutation Entropy — Complexity Oscillator
What this script does
This is a complexity oscillator: it measures, on a 0–1 scale, how random versus structured recent price action is — not which direction price is going, but whether there is any exploitable order to go on. It reads the order of successive moves (not their size): every three consecutive prices form one of six up/down shapes ("ordinal patterns"), and the oscillator measures how evenly those shapes are spread over a rolling window. Near 1, all shapes are equally likely — the tape is effectively random. Near 0, a few shapes dominate — the tape is structured and, in principle, more predictable.
Why these components are combined (mashup justification)
This is not several indicators shown side by side. There is exactly one plotted value — the normalized ordinal-pattern entropy — and every other element is a decision-support layer built on that single value:
The entropy engine is the core. Conventional price-level oscillators tell you where price is in its range; none of them tell you whether the range is even worth trading. Ordinal-pattern entropy is amplitude-free and noise-robust, so it isolates one orthogonal question — is there structure right now? — that the price-level family cannot answer.
The predictable / random thresholds classify the reading into a regime (structured / mixed / random). They don't add a second indicator; they interpret the one oscillator.
The statistical-complexity measure (complexity–entropy plane) is computed from the same ordinal-pattern counts and answers the question entropy cannot: low entropy alone can be genuinely structured or trivially degenerate (near-periodic). Pairing entropy with complexity separates "richly structured and potentially exploitable" from "low-entropy but trivial," so a signal only treats the tape as structured when both agree.
The momentum sign does nothing on its own — it only sets the direction of an already-armed regime signal. The bet is "a structured tape tends to keep doing what it's doing"; momentum just says which way that is.
The calibration harness is the reason the rest is trustworthy. It logs every signal the oscillator arms and, a fixed horizon later, checks whether price actually extended ≥ k×ATR in that direction — then reports Hit %, the unconditional Base %, and the Edge (Hit − Base).
Every part answers one question about the same entropy reading, which is why they belong in one script rather than as separate studies.
What makes it original
Two things. First, it brings an information-theoretic structure measure — usually seen only in research, not on charts — into a live, bounded oscillator with regime bands and a clean visual. Second, and more importantly, it does not assume the common claim that "low entropy means predictable, tradeable price." It tests that claim, live, on your instrument, with the built-in calibration harness. If low-entropy signals don't actually precede a forward move on your symbol and timeframe, the Edge row shows it plainly — often at or below zero. That honesty layer, not the entropy calculation alone, is the contribution.
How to use it
Add to a chart. Defaults target intraday index futures (e.g. NSE NIFTY); for other markets simply change the chart, or set the Price source input (group 01) — you can even feed it another indicator's output.
Read the regime at a glance from the background tint: green = genuine structure (low entropy and high complexity → the actionable state), amber = low-complexity / trivial low entropy (caution), grey = random / efficient tape (stand aside), no tint = mixed (wait). The line carries the same colour, with a bright line confirming genuine structure; the dashboard "Tape (plane)" chip shows the same state in words.
Optionally enable the statistical-complexity overlay (group 05) to see the complexity–entropy plane directly: it peaks at intermediate entropy where structure is richest and falls toward zero for both pure noise and trivial tapes. The dashboard shows the live complexity value and a ● when it clears the genuine-structure threshold.
Tie-robustness and delay τ (group 02): on discrete / tick-quantised instruments (index futures, where equal consecutive prints are common) equal values bias ordinal-pattern entropy toward false structure. The tie-robust dither (on by default) and an optional delay τ > 1 mitigate this; τ also probes a coarser timescale. Set τ = 1 and tie-robust off to reproduce the plain estimator.
Triangles mark the moment a predictable regime starts, with direction set by recent momentum — points to investigate, not automatic entries. With the complexity gate on (default), a signal only arms when complexity also confirms genuine structure; turn it off to A/B that choice against the entropy-only signal in the Edge row.
Read the Edge row before trusting the signal. A positive Edge means structured starts preceded a forward move more often than chance here; near or below zero means low entropy is not buying you predictability on this instrument.
Window length, smoothing, embedding delay, the two entropy thresholds, the complexity threshold, the momentum length, and the calibration horizon / threshold are all configurable.
Limitations
Entropy describes the tape's structure, not its direction — low entropy can precede a clean trend or a clean oscillation. The momentum-direction bet is one testable interpretation, not a law; the calibration row is there precisely so you don't take it on faith.
Statistics are in-sample, close-to-close, without costs — a study aid, not a backtest.
The reading needs a full window before it is meaningful (the panel shows "warm" until then).
This is an analytical complexity study. It issues no automated buy/sell instructions and is not a strategy.
Concept credit
Permutation entropy / ordinal-pattern analysis — Christoph Bandt and Bernd Pompe (2002).
Information entropy — Claude E. Shannon (1948).
Statistical complexity (the complexity–entropy plane) — the MPR statistical-complexity measure of P. W. Lamberti, M. T. Martín, A. Plastino and O. A. Rosso, applied to markets via the complexity–entropy causality plane of L. Zunino, M. Zanin, B. M. Tabak, D. G. Pérez and O. A. Rosso (2010).
Tie / equal-value bias in ordinal patterns — informed by the work of D. Cuesta-Frau and colleagues (2018).
The implementation, the regime/threshold logic, the complexity gate, the tie-robust dither, the calibration harness and the packaging are original.
Disclaimer
For research and educational purposes only. This script is not financial advice, not a recommendation, and not a guarantee of future results. Indicators describe price behaviour; they do not predict the future. Trading carries risk of loss. Test on out-of-sample data and make your own decisions. The author accepts no liability for any use of this script. Indicator
[GYTS-CE] Pattern Texture Codex (PTC)Pattern Texture Codex (Community Edition)
🌸 Part of GoemonYae Trading System (GYTS) 🌸
🌸 --------- INTRODUCTION --------- 🌸
💮 What is the Pattern Texture Codex?
Standard technical analysis focuses on two dimensions: Amplitude (how far price moves) and Momentum (how fast price moves). The Pattern Texture Codex introduces a third: Structure (how price moves).
This indicator implements Permutation Entropy (PE), a complexity measure from dynamical systems theory that captures whether price evolves in structured patterns or chaotic noise. We call this "Market Texture":
🫧 Smooth Texture (Low Entropy): Price evolves in ordered, predictable patterns. Trends are durable and causality is high. Momentum strategies favoured.
🌵 Rough Texture (High Entropy): Price evolves chaotically. The market is noisy, trends are fragile. Mean reversion or defensive sizing recommended.
💮 Why Use This Indicator?
Most "entropy" indicators on PulseWire fall into common traps:
Shannon entropy of price histograms — measures value distribution but ignores temporal sequence
Approximate Entropy (ApEn) — measures amplitude similarity with O(N²) computational cost
Volatility metrics labelled "entropy" — captures magnitude, not pattern structure
Mathematical errors — normalised values that don't form valid probability distributions
The Pattern Texture Codex provides true ordinal pattern analysis — it examines the sequence of price movements, not just their distribution or magnitude. A smooth uptrend and choppy consolidation may have identical volatility, but their texture is completely different.
↑ Pattern Texture Codex with dynamic threshold bands. Rough Texture (high entropy) often indicates reversals, while Smooth Texture (low entropy) often precedes trend continuation.
🌸 --------- HOW IT WORKS --------- 🌸
💮 Core Concept: Ordinal Patterns
Instead of analysing raw price values, Permutation Entropy converts price into ordinal patterns — the relative ordering of consecutive data points.
For example, with embedding dimension D=3 (three points per pattern):
Pattern "012": first < second < third → ascending
Pattern "210": first > second > third → descending
Pattern "102": middle value smallest → valley shape
The indicator counts how often each pattern appears over a lookback window, then calculates the Shannon entropy of this distribution.
↑ With D=3, three consecutive data points determine each pattern. Left: ascending pattern "012" (first point smallest, second middle, third greatest). Right: descending pattern "210" (first point greatest, second middle, third smallest).
💮 Calculation Overview
The normalised Permutation Entropy is computed as:
H = −∑ p(π) · ln(p(π)) / ln(D!)
Where:
• p(π) is the probability of each ordinal pattern π
• D is the embedding dimension (number of points per pattern)
• D! is the total possible patterns (e.g., 4! = 24 for D=4)
The result ranges from 0 to 1:
• H → 0 : One pattern dominates — highly structured, predictable
• H → 1 : All patterns equally likely — pure randomness
↑ Full calculation example at D=3 showing the lowest entropy point (green vertical line). With 3!=6 possible patterns, the monotonic rising pattern "012" dominates while three other patterns occur only once. The frequency column feeds into the entropy contribution formula, yielding H(3)=1.039. Normalising produces 0.4019 — matching the indicator output exactly.
💮 Theoretical Background
Permutation Entropy has deep theoretical foundations. For piecewise monotone maps, it converges to the Kolmogorov-Sinai entropy — the fundamental measure of chaos in dynamical systems.
Key scientific properties:
• Scale invariance — analyses rank orderings, invariant to monotonic transformations
• Noise robustness — ordinal encoding naturally filters high-frequency noise
• Computational efficiency — O(1) amortised per bar with lookup acceleration
• Micro-structure sensitivity — captures specific sequence patterns, not just distribution
🌸 --------- KEY FEATURES --------- 🌸
💮 Lookup Table Acceleration
Standard PE requires sorting each embedding vector — O(D log D) operations per bar. This implementation uses precomputed transition tables from Unakafova & Keller (2013), reducing complexity to O(D) per bar.
The key insight: successive ordinal patterns in overlapping windows share (D−1) data points. Rather than recomputing from scratch, the algorithm derives the new pattern from the previous one using a single table lookup.
Enabled by default for Delay=1 and Dimension ∈ {3, 4, 5}
Falls back to standard calculation for D=2, D=6
💮 Flexible Threshold Modes
The indicator supports four independent threshold modes for both Smooth and Rough detection:
Static — Fixed threshold values you define
Dynamic — Adaptive bands based on entropy baseline ± standard deviation
Percentile — Threshold at Nth percentile of recent entropy history
Disabled — No threshold for that direction
You can mix modes: for example, Dynamic for Smooth detection while using Percentile for Rough detection.
🌸 --------- CONFIGURATION --------- 🌸
💮 General Settings
• Source — Price series to analyse (default: close)
• Smoothing Critical Period — Smoothing via 2-pole Ultimate Smoother (default: 0 = disabled). Reveals underlying texture by filtering entropy noise.
💮 Entropy Calculation
Dimension (D) — Points per ordinal pattern:
• D=3: 6 patterns — fast, stable. Good for limited lookback.
• D=4: 24 patterns — balanced, captures V-reversals. Recommended.
• D=5: 120 patterns — sensitive, captures W/M patterns. Noisier.
• D=6: 720 patterns — maximum sensitivity. No lookup acceleration.
Lookback — Estimation window size. Hard minimum: D × 5. Statistical recommendation: 5 × D! (e.g., 120 for D=4). Default: 100.
Delay (τ) — Stride between points in each pattern (default: 1). Change only for oversampled data.
Lookup Acceleration — Enables transition tables for D ∈ {3, 4, 5} with Delay=1.
💮 Threshold Management
Rough/Smooth Mode — Static, Dynamic, Percentile, or Disabled for each threshold
Static Values — Fixed threshold when Static mode selected
Std Dev Multiplier — Band width for Dynamic mode (default: 2.0σ)
Baseline/Deviation Length — Lookback for Dynamic mode calculations
Percentile Settings — Lookback and percentile values for Percentile mode
💮 Visualisation & Alerts
Palette — Colour scheme (default: GYTS Purple)
Colouring Bars — Applies texture colours to chart candles
Dark Mode — Optimises colour intensity for dark backgrounds
Alerts — Triggers when entropy crosses above/below thresholds
🌸 --------- USAGE GUIDE --------- 🌸
💮 Getting Started
Apply the indicator with default settings:
• Dimension: 4 (balanced complexity, captures V-shaped reversals)
• Lookback: 100 (responsive; statistical ideal: ≥120 for 5× coverage)
• Smooth Threshold: Dynamic mode with 2.0σ multiplier
Observe how entropy rises during choppy consolidation and falls during clean trends.
💮 Interpretation
Entropy Value (0 to 1):
Below 0.6: Strong pattern dominance — highly ordered
0.7–0.9: Normal complexity — typical market behaviour
Above 0.95: Near-random — patterns uniformly distributed
Transitions:
Watch for regime changes. When entropy rises sharply after a prolonged smooth period, the trend may be losing coherence. When entropy falls from elevated levels, a new trend may be establishing.
↑ Texture transitions during a trend-to-consolidation regime change. During the uptrend, similar patterns (D=3) recur frequently and entropy decreases. As the market transitions to consolidation, entropy rises — signalling the trend is losing structure.
💮 Trading Applications
Trend Filtering — Only take trend-following signals during Smooth texture.
Mean Reversion Timing — Elevated entropy often precedes mean reversion.
Position Sizing — Reduce exposure during Rough texture.
Exit Management — Tighten stops when entropy rises during a position.
💮 Integration with GYTS Suite
The Pattern Texture Codex exports two signals:
PE Continuous — Raw entropy value (0 to 1)
PE Ternary — State signal (+1 = Rough, 0 = Neutral, −1 = Smooth)
These can be read by Flux Composer or used as filter conditions with Market Regime Detector .
🌸 --------- PARAMETER TUNING --------- 🌸
💮 Lookback Selection
Shorter lookbacks react faster but may produce unstable estimates:
50–100: Responsive. Good for intraday regime detection.
100–200: Balanced. Recommended for swing trading.
200–500: Stable. Better for position trading or noisy instruments.
The indicator enforces a hard minimum of D × 5 to prevent meaningless output.
↑ Three dimensions (D=3, D=4, D=5) with their academically recommended minimum lookback periods.
💮 Threshold Tuning
For Smooth Detection:
Dynamic mode with 2.0σ works well across most instruments. Lower multipliers (1.5σ) detect structure earlier but may false-trigger.
For Rough Detection:
Percentile mode at 90th percentile identifies only extreme chaos. Static threshold of 0.95+ focuses on near-random conditions.
Consider disabling Rough detection entirely if your strategy only cares about identifying structured trends.
↑ The three threshold modes on the same PTC calculation. Both upper and lower thresholds are independently configurable.
🌸 --------- LIMITATIONS --------- 🌸
Amplitude Blindness — PE treats all patterns equally regardless of magnitude. A 0.1% drift and a 10% crash produce identical entropy if their ordinal patterns match.
Equal Values (Ties) — Handled via temporal tie-breaking (recent values rank higher), but heavily discretised data may produce edge-case behaviour.
Sample Size Requirements — Very short lookbacks (below D × 5) produce unreliable estimates. Statistical reliability improves with larger samples.
Not Predictive Alone — Low entropy indicates structure exists, not that the trend will continue. Combine with directional analysis for trading decisions.
Lag During Transitions — The sliding window approach introduces inherent lag when market texture changes.
🌸 --------- CREDITS --------- 🌸
💮 Academic Sources
Bandt, C., & Pompe, B. (2002). Permutation entropy: A natural complexity measure for time series. Physical Review Letters, 88 (17), 174102. DOI
Unakafova, V., & Keller, K. (2013). Efficiently measuring complexity on the basis of real-world data. Entropy, 15 (10), 4392-4415. DOI
Ehlers, J. F. (2024). The Ultimate Smoother. Technical Analysis of Stocks & Commodities , 2024-04. TASC
💮 Libraries Used
FiltersToolkit — Ultimate Smoother and other curated filters
PatternTransitionTables — Precomputed lookup tables for O(1) pattern transitions
ColourUtilities — Gradient palette generation and colour management
Indicator
Indicator
PatternTransitionTablesPatternTransitionTables Library
🌸 Part of GoemonYae Trading System (GYTS) 🌸
🌸 --------- 1. INTRODUCTION --------- 🌸
💮 Overview
This library provides precomputed state transition tables to enable ultra-efficient, O(1) computation of Ordinal Patterns. It is designed specifically to support high-performance indicators calculating Permutation Entropy and related complexity measures.
💮 The Problem & Solution
Calculating Permutation Entropy, as introduced by Bandt and Pompe (2002), typically requires computing ordinal patterns within a sliding window at every time step. The standard successive-pattern method (Equations 2+3 in the paper) requires ≤ 4d-1 operations per update.
Unakafova and Keller (2013) demonstrated that successive ordinal patterns "overlap" significantly. By knowing the current pattern index and the relative rank (position l) of just the single new data point, the next pattern index can be determined via a precomputed look-up table. Computing l still requires d comparisons, but the table lookup itself is O(1), eliminating the need for d multiplications and d additions. This reduces total operations from ≤ 4d-1 to ≤ 2d per update (Table 4). This library contains these precomputed tables for orders d = 2 through d = 5.
🌸 --------- 2. THEORETICAL BACKGROUND --------- 🌸
💮 Permutation Entropy
Bandt, C., & Pompe, B. (2002). Permutation entropy: A natural complexity measure for time series.
doi.org
This concept quantifies the complexity of a system by comparing the order of neighbouring values rather than their magnitudes. It is robust against noise and non-linear distortions, making it ideal for financial time series analysis.
💮 Efficient Computation
Unakafova, V. A., & Keller, K. (2013). Efficiently Measuring Complexity on the Basis of Real-World Data.
doi.org
This library implements the transition function φ_d(n, l) described in Equation 5 of the paper. It maps a current pattern index (n) and the position of the new value (l) to the successor pattern, reducing the complexity of updates to constant time O(1).
🌸 --------- 3. LIBRARY FUNCTIONALITY --------- 🌸
💮 Data Structure
The library stores transition matrices as flattened 1D integer arrays. These tables are mathematically rigorous representations of the factorial number system used to enumerate permutations.
💮 Core Function: get_successor()
This is the primary interface for the library for direct pattern updates.
• Input: The current pattern index and the rank position of the incoming price data.
• Process: Routes the request to the specific transition table for the chosen order (d=2 to d=5).
• Output: The integer index of the next ordinal pattern.
💮 Table Access: get_table()
This function returns the entire flattened transition table for a specified dimension. This enables local caching of the table (e.g. in an indicator's init() method), avoiding the overhead of repeated library calls during the calculation loop.
💮 Supported Orders & Terminology
The parameter d is the order of ordinal patterns (following Bandt & Pompe 2002). Each pattern of order d contains (d+1) data points, yielding (d+1)! unique patterns:
• d=2: 3 points → 6 unique patterns, 3 successor positions
• d=3: 4 points → 24 unique patterns, 4 successor positions
• d=4: 5 points → 120 unique patterns, 5 successor positions
• d=5: 6 points → 720 unique patterns, 6 successor positions
Note: d=6 is not implemented. The resulting code size (approx. 191k tokens) exceeds the Pine Script limit of 100k tokens (as of 2025-12). Library
Approximate Entropy Zones [PhenLabs]Version: PineScript™ v6
Description
This indicator identifies periods of market complexity and randomness by calculating the Approximate Entropy (ApEn) of price action. As the movement of the market becomes complex, it means the current trend is losing steam and a reversal or consolidation is likely near. The indicator plots high-entropy periods as zones on your chart, providing a graphical suggestion to anticipate a potential market direction change. This indicator is designed to help traders identify favorable times to get in or out of a trade by highlighting when the market is in a state of disarray.
Points of Innovation
Advanced Complexity Analysis: Instead of relying on traditional momentum or trend indicators, this tool uses Approximate Entropy to quantify the unpredictability of price movements.
Dynamic Zone Creation: It automatically plots zones on the chart during periods of high entropy, providing a clear and intuitive visual guide.
Customizable Sensitivity: Users can fine-tune the ‘Entropy Threshold’ to adjust how frequently zones appear, allowing for calibration to different assets and timeframes.
Time-Based Zone Expiration: Zones can be set to expire after a specific time, keeping the chart clean and relevant.
Built-in Zone Size Filter: Excludes zones that form on excessively large candles, filtering out noise from extreme volatility events.
On-Chart Calibration Guide: A persistent note on the chart provides simple instructions for adjusting the entropy threshold, making it easy for users to optimize the indicator’s performance.
Core Components
Approximate Entropy (ApEn) Calculation: The core of the indicator, which measures the complexity or randomness of the price data.
Zone Plotting: Creates visual boxes on the chart when the calculated ApEn value exceeds a user-defined threshold.
Dynamic Zone Management: Manages the lifecycle of the zones, from creation to expiration, ensuring the chart remains uncluttered.
Customizable Settings: A comprehensive set of inputs that allow users to control the indicator’s sensitivity, appearance, and time-based behavior.
Key Features
Identifies Potential Reversals: The high-entropy zones can signal that a trend is nearing its end, giving traders an early warning.
Works on Any Timeframe: The indicator can be applied to any chart timeframe, from minutes to days.
Customizable Appearance: Users can change the color and transparency of the zones to match their chart’s theme.
Informative Labels: Each zone can display the calculated entropy value and the direction of the candle on which it formed.
Visualization
Entropy Zones: Shaded boxes that appear on the chart, highlighting candles with high complexity.
Zone Labels: Text within each zone that displays the ApEn value and a directional arrow (e.g., “0.525 ↑”).
Calibration Note: A small table in the top-right corner of the chart with instructions for adjusting the indicator’s sensitivity.
Usage Guidelines
Entropy Analysis
Source: The price data used for the ApEn calculation. (Default: close)
Lookback Length: The number of bars used in the ApEn calculation. (Default: 20, Range: 10-50)
Embedding Dimension (m): The length of patterns to be compared; a standard value for financial data. (Default: 2)
Tolerance Multiplier (r): Adjusts the tolerance for pattern matching; a larger value makes matching more lenient. (Default: 0.2)
Entropy Threshold: The ApEn value that must be exceeded to plot a zone. Increase this if too many zones appear; decrease it if too few appear. (Default: 0.525)
Time Settings
Analysis Timeframe: How long a zone remains on the chart after it forms. (Default: 1D)
Custom Period (Bars): The zone’s lifespan in bars if “Analysis Timeframe” is set to “Custom”. (Default: 1000)
Zone Settings
Zone Fill Color: The color of the entropy zones. (Default: #21f38a with 80% transparency)
Maximum Zone Size %: Filters out zones on candles that are larger than this percentage of their low price. (Default: 0.5)
Display Options
Show Entropy Label: Toggles the visibility of the text label inside each zone. (Default: true)
Label Text Position: The horizontal alignment of the text label. (Default: Right)
Show Calibration Note: Toggles the visibility of the calibration note in the corner of the chart. (Default: true)
Best Use Cases
Trend Reversal Trading: Identifying when a strong trend is likely to reverse or pause.
Breakout Confirmation: Using the absence of high entropy to confirm the strength of a breakout.
Ranging Market Identification: Periods of high entropy can indicate that a market is transitioning into a sideways or choppy phase.
Limitations
Not a Standalone Signal: This indicator should be used in conjunction with other forms of analysis to confirm trading signals.
Lagging Nature: Like all indicators based on historical data, ApEn is a lagging measure and does not predict future price movements with certainty.
Calibration Required: The effectiveness of the indicator is highly dependent on the “Entropy Threshold” setting, which needs to be adjusted for different assets and timeframes.
What Makes This Unique
Quantifies Complexity: It provides a numerical measure of market complexity, offering a different perspective than traditional indicators.
Clear Visual Cues: The zones make it easy to see when the market is in a state of high unpredictability.
User-Friendly Design: With features like the on-chart calibration note, the indicator is designed to be easy to use and optimize.
How It Works
Calculate Standard Deviation: The indicator first calculates the standard deviation of the source price data over a specified lookback period.
Calculate Phi: It then calculates a value called “phi” for two different pattern lengths (embedding dimensions ‘m’ and ‘m+1’). This involves comparing sequences of data points to see how many are “similar” within a certain tolerance (determined by the standard deviation and the ‘r’ multiplier).
Calculate ApEn: The Approximate Entropy is the difference between the two phi values. A higher ApEn value indicates greater irregularity and unpredictability in the data.
Plot Zones: If the calculated ApEn exceeds the user-defined ‘Entropy Threshold’, a zone is plotted on the chart.
Note: The “Entropy Threshold” is the most important setting to adjust. If you see too many zones, increase the threshold. If you see too few, decrease it. Indicator
Indicator
Surface Roughness EstimatorIntroduction
Roughness of a signal is often non desired since smooth signals are easier to analyse, its logical to say that anything interacting with rough price is subject to decrease in accuracy/efficiency and can induce non desired effects such as whipsaws. Being able to measure it can give useful information and potentially avoid errors in an analysis.
It is said that roughness appear when a signal have high-frequencies (short wavelengths) components with considerable amplitudes, so its not wrong to say that "estimating roughness" can be derived into "estimating complexity".
Measuring Roughness
There are a lot of way to estimate roughness in a signal, the most well know method being the estimation of fractal dimensions. Here i will use a first order autocorrelation function.
Auto-correlation is defined by the linear relationship between a signal and a delayed version of itself, for exemple if the price goes on the same direction than the price i bars back then the auto-correlation will increase, else decrease. So what this have to do with roughness ? Well when the auto-correlation decrease it means that the dominant frequency is high, and therefore that the signal is rough.
Interpretation Of The Indicator
When the indicator is high it means that price is rough, when its low it indicate that price is smooth. Originally its the inverse way but i found that it was more convenient to do it this way. We can interpret low values of the indicator as a trending market but its not totally true, for example high values dont always indicate that the market is ranging.
Here the comparison with the indicator applied to price (orange) and a moving average (purple)
The average measurement applied to a moving average is way lower than the one using the price, this is because a moving average is smoother than price.
Its also interesting to see that some trend strength estimator like efficiency ratio can treat huge volatility signals as trend as shown below.
Here the efficiency ratio treat this volatile movement as a trending market, our indicator instead indicate that this movement is rough, such indication can avoid situation where price is followed by another huge volatile movement in the opposite direction.
Its important to make the distinction between volatility and trend strength, the trend is defined by low frequencies components of a signal, therefore measuring trend strength can be resumed as measuring the amplitude of such frequencies, but roughness estimation can do a great job as well.
Conclusion
I have showed how to estimate roughness in price and compared how our indicator behaved in comparison with a classic trend strength measurement tool. Filters or any other indicator can be way more efficient if they know how to filter according to a situation, more commonly smoothing more when price is rough and smoothing less when price is smooth. Its good to have a wider view of how market is behaving and not sticking with the binary view of "Trending" and "Ranging" .
I hope you find a use to this script :)
Best Regards
Indicator
