Liquidity-Weighted Business Cycle (Satoshi Global Base)🌍 BTC-Affinity Global Liquidity Business Cycle (MACD Model)
This indicator models Bitcoin’s macroeconomic business cycle using a BTC-weighted global liquidity index as its foundation. It adapts a MACD-based framework to visualize expansions and contractions in fiat liquidity across major economies with high Bitcoin affinity.
🔍 What It Does:
🧠 Constructs a Global M2 Liquidity Index from the top 10 most BTC-relevant fiat currencies
(USD, EUR, JPY, GBP, INR, CNY, KRW, BRL, CAD, AUD)
— each weighted by its Bitcoin adoption score and FX-converted into USD.
📊 Applies a MACD (Moving Average Convergence Divergence) signal to the index to detect macro liquidity trends.
🟢 Plots a histogram of business cycle momentum (red = expansion, green = contraction).
🔴 Marks potential cycle peaks, useful for macro trading alignment.
⚖️ BTC Affinity-Weighted Countries:
🇺🇸 United States
🇪🇺 Eurozone
🇯🇵 Japan
🇬🇧 United Kingdom
🇮🇳 India
🇨🇳 China
🇰🇷 South Korea
🇧🇷 Brazil
🇨🇦 Canada
🇦🇺 Australia
Weights are user-adjustable to reflect evolving capital controls, regulation, and real-world BTC adoption trends.
✅ Use Cases:
Confirm macro risk-on vs risk-off regimes for BTC and crypto.
Identify ideal entry and exit zones in macro pair trades (e.g., MSTR vs MSTY).
Monitor how global monetary expansion feeds into BTC valuations.
週期
US Liquidity-Weighted Business Cycle📈 BTC Liquidity-Weighted Business Cycle
This indicator models the Bitcoin macro cycle by comparing its logarithmic price against a log-transformed liquidity proxy (e.g., US M2 Money Supply). It helps visualize cyclical tops and bottoms by measuring the relative expansion of Bitcoin price versus fiat liquidity.
🧠 How It Works:
Transforms both BTC and M2 using natural logarithms.
Computes a liquidity ratio: log(BTC) – log(M2) (i.e., log(BTC/M2)).
Runs MACD on this ratio to extract business cycle momentum.
Plots:
🔴 Histogram bars showing cyclical growth or contraction.
🟢 Top line to track the relative price-to-liquidity trend.
🔴 Cycle peak markers to flag historical market tops.
⚙️ Inputs:
Adjustable MACD lengths
Toggle for liquidity trend line overlay
🔍 Use Cases:
Identifying macro cycle tops and bottoms
Timing long-term Bitcoin accumulation or de-risking
Confirming global liquidity's influence on BTC price movement
Note: This version currently uses US M2 (FRED:M2SL) as the liquidity base. You can easily expand it with other global M2 sources or adjust the weights.
[blackcat] L1 Dual Ehlers Bandpass FilterOVERVIEW
The Dual Ehlers Bandpass Filter combines two bandpass filters tuned to the dominant and subdominant market cycles, creating a powerful signal extraction tool. This indicator uses John Ehlers' advanced digital signal processing techniques to isolate specific frequency components from price data. By mixing the outputs of two bandpass filters, it provides a smoother, more responsive signal that captures both primary and secondary market cycles. The indicator includes divergence detection capabilities and multiple mixing methods for customizable signal extraction.
FEATURES
- Dual bandpass filtering with dominant and subdominant cycle detection
- Multiple dominant cycle calculation methods (HoDyDC, PhAcDC, DuDiDC, CycPer, BPZC)
- Flexible mixing options: weighted, sum, difference, dominant-only, or subdominant-only
- Adjustable bandwidth parameters for both filters
- Built-in divergence detection with customizable lookback periods
- Optional display of individual filter components
- Color-coded signals and alerts for bullish/bearish divergences
HOW TO USE
1. Select your preferred price source (close, high, low, etc.)
2. Choose the dominant cycle calculation method from the available options
3. Set the subdominant cycle ratio (typically 0.1-0.9 of the dominant cycle)
4. Adjust bandwidth parameters for both filters (0.1-1.0 range)
5. Select your preferred mixing method:
- Weighted: Mix based on adjustable weights
- Sum: Add both filter outputs
- Difference: Subtract subdominant from dominant
- Dominant: Show only the dominant filter
- Subdominant: Show only the subdominant filter
6. Enable divergence detection to identify potential trend reversals
7. Optionally enable individual filter plots for analysis
LIMITATIONS
- The indicator requires sufficient historical data for accurate cycle detection
- Dominant cycle calculations may vary significantly during low volatility periods
- Divergence signals are lagging indicators and should be used with confirmation
- Bandpass filters may produce false signals during choppy market conditions
- The indicator is not suitable for all trading styles and timeframes
NOTES
- The indicator uses the blackcat1402/dc_ta library for advanced cycle calculations
- Zero line crossing can indicate potential trend changes
- Positive values typically suggest bullish momentum, negative values bearish momentum
- Divergence signals appear as colored dots and labels on the chart
- Alert conditions are available for both bullish and bearish divergences
THANKS
Special thanks to John Ehlers for his pioneering work in digital signal processing for financial markets.
Ludvig Indicator PROThe Ludvig Indicator is designed to identify high-probability breakout setups by combining trend, volume, volatility, and relative strength filters. It helps you enter stocks (or ETFs/crypto) when institutional money is likely flowing in, while avoiding false breakouts and weak trends.
🔑 Core Features
Zero-Lag EMA (ZLEMA)
Faster, less lagging trend detection compared to traditional EMAs.
Used as the basis for dynamic ATR bands.
ATR Volatility Bands
Adaptive bands based on the Average True Range (ATR).
Define the zone where price must close outside to confirm trend strength.
Breakout Confirmation
Requires price to close above recent highs (lookback configurable).
Ensures signals are “true breakouts,” not just noise around moving averages.
Volume Filter (Relative Volume)
Validates breakouts with significantly higher volume than average.
Prevents low-liquidity signals from triggering.
Trend Strength (ADX)
Built-in ADX calculation ensures only strong, trending moves are considered.
Default filter: ADX ≥ 18 (configurable).
Relative Strength vs. Benchmark
Compares the asset’s momentum against a benchmark (default: SPY).
Only signals when the asset is outperforming the benchmark.
Useful for sector rotation and picking leaders instead of laggards.
Alerts & Signals
Breakout entries are marked with small green triangles.
Built-in alerts for automated notifications (TradingView alerts).
Sweep2Trade Pro [CHE]Sweep2Trade Pro \ — Liquidity Sweep → Trend → Confirmation
Sweep2Trade Pro \ helps you catch high-probability reversals or continuations that start with a liquidity sweep, align with the T3 trend, and finalize with a structure confirmation (BOS). It’s designed to reduce noise, time your entries, and keep you out of weak, chop-driven signals.
What’s a “sweep”?
A liquidity sweep happens when price briefly breaks a prior swing high/low (where many stops sit), triggers those stops, and then snaps back. This “stop-hunt” creates liquidity for bigger players and often precedes a sharp move in the opposite direction if the break fails, or fuels continuation if structure actually shifts.
What’s a BOS (Break of Structure)?
A BOS is a price action event where the market takes out a recent swing level in the trend’s direction, signaling continuation and confirming that structure has shifted (bullish BOS through a recent swing high, bearish BOS through a recent swing low).
How the indicator works (at a glance)
1. Regime Filter (T3 + R²)
T3 Moving Average: A smoother, faster-responding moving average that aims to reduce lag while filtering noise, so trend direction changes are clearer.
R² (Coefficient of Determination): Measures how “linear” the recent price path is (0→1). Higher values = stronger, cleaner trend; lower values = more chop. Used here to allow trades only when trend quality exceeds a user-set threshold.
2. Sweep Detection
Bullish sweep: price pokes below a prior swing low and closes back above it.
Bearish sweep: price pokes above a prior swing high and closes back below it.
Lookback length is configurable.
3. Sequence Lock (built-in FSM)
The script manages state in phases so you don’t jump the gun:
Phase 1: Sweep detected → wait for T3 to turn in the corresponding direction.
Phase 2: T3 direction confirmed → show “SWEEP OK” and wait for final confirmation.
Trade Signal: Only fires if confirmation arrives before a timeout.
4. Confirmation Layer
BOS via wick or close (you choose),
Strong close toward the signal (top/bottom quartile of the candle),
Optional “close above/below T3” condition.
These checks help avoid weak sweeps that immediately fade.
5. Alerts & Visuals
“SWEEP OK” markers show when the sweep + T3 direction align.
Final BUY/SELL arrows appear only when the confirmation layer passes.
Ready-made alert conditions for automation.
What you can do with it
Time reversals after sweeps: Enter when a stop-hunt fades and structure confirms.
Ride continuations: Use BOS with the T3 trend to pyramid or re-enter with structure on your side.
Filter chop: Let R² gate entries to periods with cleaner directional drift.
Automate: Use the included alerts with your platform or webhook setup.
Inputs (key settings)
Regime Filter
T3 Length / Volume Factor: Controls smoothness and responsiveness. Smaller length → faster, more sensitive; higher volume factor → smoother curve.
R² Lookback & Threshold: Length of the linear fit window and the minimum “trend quality” required. Higher thresholds mean fewer, cleaner signals.
Sweep / Sequence
Swing Lookback: How far back to define the “reference” high/low for sweeps.
Timeout: Maximum bars allowed between phases to keep signals fresh.
Restart timeout on Phase 2: Optional safety so entries don’t go stale.
Confirmation
BOS Lookback: Micro-pivot window for structure breaks.
Wick vs Close BOS: Conservative traders may prefer close.
Require close above/below T3: Tightens confirmation with trend alignment.
Practical guide (quick start)
1. Timeframe & markets: Works across majors, indices, and crypto. Start with 5m–1h intraday or 1h–4h swing; adjust R² threshold upward on noisier pairs.
2. Entry recipe (Long):
Bullish sweep of a prior low → T3 turns up → BOS/strong close.
Optional: enable “close above T3” for extra confirmation.
3. Entry recipe (Short): Mirror the above.
4. Stops: Common choices are just beyond the sweep wick (tighter) or past the BOS invalidation (safer).
5. Targets: Previous structural levels, measured move, or a T3 trail (exit when price closes back through T3).
6. Avoid low-quality contexts: If R² is very low, market is likely ranging erratically—skip or widen filters.
Tips & best practices
Context first: The same sweep means different things in a strong trend vs. flat regime; that’s why the T3+R² filter exists.
BOS choice: Wick-based BOS is earlier but noisier; close-based BOS is slower but cleaner. Tune per market.
Backtest -> Forward test: Validate settings per symbol/timeframe; then paper trade before going live.
Risk: Fixed fractional risk with asymmetric R\:R (e.g., 1:1.5–1:3) generally performs better than “all-in” discretionary sizing.
Behind the scenes (for the curious)
T3 is a multi-stage EMA construction that produces a smooth curve with reduced lag versus simple/standard EMAs.
R² is the square of correlation (0–1). Here it’s used as a moving gauge of how well price aligns to a linear path—our “trend quality” dial.
Stop-hunts / sweeps are a recognized microstructure phenomenon where clustered stops provide the liquidity that fuels the next move.
Disclaimer
No indicator guarantees profits. Sweep2Trade Pro \ is a decision aid; always combine with solid risk management and your own judgment. Backtest, forward test, and size responsibly.
The content provided, including all code and materials, is strictly for educational and informational purposes only. It is not intended as, and should not be interpreted as, financial advice, a recommendation to buy or sell any financial instrument, or an offer of any financial product or service. All strategies, tools, and examples discussed are provided for illustrative purposes to demonstrate coding techniques and the functionality of Pine Script within a trading context.
Any results from strategies or tools provided are hypothetical, and past performance is not indicative of future results. Trading and investing involve high risk, including the potential loss of principal, and may not be suitable for all individuals. Before making any trading decisions, please consult with a qualified financial professional to understand the risks involved.
By using this script, you acknowledge and agree that any trading decisions are made solely at your discretion and risk.
Enhance your trading precision and confidence 🚀
Happy trading
Chervolino
Custom Support & Resistance Levels (Manual Input)This indicator lets you plot your own support levels (and can be extended for resistance) directly on the chart by entering them as comma-separated values.
📌 Supports manual input for multiple price levels.
📊 Lines are extended across the chart for clear visualization.
🎨 Dynamic coloring:
Green if the current price is above the level.
Red if the current price is below the level.
🧹 Old lines are automatically cleared to avoid clutter.
This tool is ideal if you:
Prefer to mark your own key zones instead of relying only on auto-detected levels.
Want clean and simple visualization of critical price areas.
👉 Coming soon: Resistance levels input (commented in the code, can be enabled).
Same Day Past CandlesSame-Day Past Candles
This indicator is a tool that plots the shapes of the candles from the same date one and two years ago directly on the current chart. By visually comparing past price movements, it can help you analyze seasonality and cyclical patterns.
Key Features
Plots Past Candles: Displays candles from the same date one and two years ago on your current chart.
Toggle Visibility: You can individually turn the display of the "1 year ago candle" and "2 years ago candle" on or off in the indicator's settings.
Candle Shape: The open, high, low, and close prices of the past candles are plotted, scaled to the current price range.
How to Use
Add this indicator to a daily chart for best results. The plotted candles are slightly offset upwards so they don't overlap with the current price, making it easier to compare the shape of the past candles with the current chart movement.
Visually checking how specific past price changes are reflected on the same day this year can provide insights for your trading strategy.
I do not speak English at all. Please understand that if you send me a message, I may not be able to reply, or my reply may have a different meaning. Thank you for your understanding.
SHHHHHHH“Round Numbers — 100/50/25”
lines… endless lines… they whisper in 25s, scream in 50s, collapse in 100s.
price dances on the grid, you don’t trade it, it trades you.
blue for the void. orange for the in-between. green for the fracture.
extend both. never stop. above and below. above and below.
do not ask why 25. do not ask why 50. the 100s already know.
quarter. half. whole. repeat until delirium.
add it to chart → stare too long → numbers start staring back.
Path of the Planets🪐 Path of the Planets
Path of the Planets is an open-source Pine Script™ v6 indicator. It is inspired by W.D. Gann’s Path of Planets chart, specifically the Chart 5-9 artistic replica by Patrick Mikula "shown below". The script visualizes planetary positions so you can explore possible correlations with price. It overlays geocentric and heliocentric longitudes and declinations using the AstroLib library and includes an optional positions table that shows, at a glance, each body’s geocentric longitude, heliocentric longitude, and declination. This is an educational tool only and not trading advice.
Key Features
Start point: Choose a date and time to begin plotting so studies can align with market events.
Adjustments: Mirror longitudes and shift by 360° multiples to re-frame cycles.
Planets: Toggle geocentric and heliocentric longitudes and declinations for Sun, Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune, and Pluto. Moon declination is available.
Positions table: Optional color-coded table (bottom-right) with three columns labeled Geo, Helio, and Dec. Values show degrees with the zodiac sign for the longitudes and degrees for declinations.
Visualization: Solid lines for geocentric longitudes, circles for heliocentric longitudes, and columns for declinations. Includes a zero-declination reference line.
How It Works
Converts bar timestamps to Julian days via AstroLib.
Fetches positions with AstroLib types: geocentric (0), heliocentric (1), and declination (3).
Normalizes longitudes to the −180° to +180° range, applies optional mirroring and 360° shifts, and converts longitudes to zodiac sign labels for the table.
Plots and the table update only on and after the selected start time.
Usage Tips
Apply on daily or higher timeframes when studying broader cycles. For degrees, use the left scale.
Limitations at the moment: default latitude, longitude, and timezone are set to 0; aspects and retrogrades are not included; the focus is on raw paths.
License and Credits
Dependency: @BarefootJoey Astrolib
Contributions and observations are welcome.
Ichimoku Trading Signals 2Swing Trading (Strategy 1, H4+ timeframes)
Use the Kumo Cloud to identify the trend: price above a green cloud = uptrend; price below a red cloud = downtrend.
Entry signals occur when price or the Tenkan-sen line crosses the Kijun-sen line, confirmed by Chikou Span momentum.
Exit triggers when price crosses back through the Kijun-sen or when Tenkan-sen crosses back below (for long positions) or above (for short positions).
Place stop-loss orders just beyond the nearest swing low/high candle cluster to manage risk tightly.
Market Sessions [odnac]
This indicator highlights the three main global market sessions (USA, Europe, Asia) and their overlaps directly on the chart.
It helps traders quickly identify active trading periods and potential high-liquidity overlaps.
Features:
Customizable start and end times for each session
Optional daily dividers with weekday labels
Session markers displayed as circles above the candles
Overlap sessions displayed in distinct colors
Adjustable opacity for better chart visibility
Option to hide weekends
Sessions included:
USA Market Session (default 13:30–20:00 UTC)
Europe Market Session (default 07:00–16:00 UTC)
Asia Market Session (default 00:00–09:00 UTC)
Overlaps: USA + Europe, USA + Asia, Europe + Asia
This tool is designed for intraday timeframes (1m–60m) and can be useful for scalping, day trading, or session-based strategies.
DMI MTF Color Table v5DMI Multi-Timeframe Color Table v5
A comprehensive DMI (Directional Movement Index) table that displays trend direction and strength across multiple timeframes simultaneously. This indicator helps traders quickly assess market conditions and identify confluence across different time horizons.
Features:
Multi-timeframe analysis (7 configurable timeframes)
Color-coded cells based on trend strength and direction
Real-time current market condition display
Customizable strength thresholds and color schemes
Multiple display modes (All, DI+ Only, DI- Only, ADX Only)
Text-based strength classifications (STRONG/MEDIUM/WEAK)
Directional bias indicators (BULL/BEAR)
How It Works:
The table shows DI+, DI-, and ADX values across your chosen timeframes with intelligent color coding:
Green shades indicate bullish momentum (DI+ > DI-)
Red shades indicate bearish momentum (DI- > DI+)
Color intensity reflects trend strength based on ADX values
Current market condition appears in top-right corner
Display Options:
Toggle numerical values, strength text, and timeframe labels
Adjustable table size and transparency
Customizable color schemes for all conditions
Optional current timeframe DMI plot overlay
Educational Use:
This tool is designed for educational purposes to help understand multi-timeframe analysis and DMI interpretation. All trading decisions should be based on your own analysis and risk management.
Credits:
Original concept and development by Profitgang. If you use or modify this script, please provide appropriate credit to the original author.
Note: This indicator is for analysis purposes only. Past performance does not guarantee future results. Always conduct your own research and consider your risk tolerance before making trading decisions.
Daily Distribution Range - Amplitude Probability DashboardSummary
This indicator provides a powerful statistical deep-dive into an asset's daily distribution range, amplitude and volatility. It moves beyond simple range indicators by calculating the historical probability of a trading day reaching certain amplitude levels.
The results are presented in a clean, interactive dashboard that highlights the current day's performance in real-time, allowing traders to instantly gauge if the current volatility is normal, unusually high, or unusually low compared to history.
This tool is designed to help traders answer a critical question: "Based on past behavior, what is the likelihood that today's range will be at least X%?"
Key Concepts Explained
1. Daily Amplitude (%)
The indicator first calculates the amplitude (or range) of every historical daily candle and expresses it as a percentage of that day's opening price.
Formula: (Daily High - Daily Low) / Daily Open * 100
This normalization allows for a consistent volatility comparison across different price levels and time periods.
2. Cumulative Probability Distribution
Instead of showing the probability of a day's final range falling into a small, exclusive bin (e.g., "exactly between 1.0% and 1.5%"), this indicator uses a cumulative model. It answers the question, "What is the probability that the daily range will be at least a certain value?"
For example, if the row for "≥ 2%" shows a probability of 12.22%, it means that historically, 12.22% of all trading days have had a total range of 2% or more. This is incredibly useful for risk management and setting realistic expectations.
Core Features
Statistical Dashboard: Presents all data in a clear, easy-to-read table on your chart.
Cumulative Probability Model: Instantly see the historical probability of the daily range reaching or exceeding key percentage levels.
Real-Time Highlight & Arrow (→): The dashboard isn't just historical. It actively tracks the current, unfinished day's amplitude and highlights the corresponding row with a color and an arrow (→). This provides immediate context for the current session's price action.
Timeframe Independent: You can use this indicator on any chart timeframe (e.g., 5-minute, 1-hour, 4-hour), and it will always fetch and calculate using the correct daily data.
Clean & Professional UI: Features a monospace font for perfect alignment and a simple, readable design.
Fully Customizable: Easily adjust the dashboard's position, text size, and the amount of historical data used for the analysis.
How to Use & Interpret the Data
This indicator is not a trading signal but a powerful tool for statistical context and decision-making.
Risk Management: If you see that an asset has only a 5% historical probability of moving more than 3% in a day, you can set stop-losses more intelligently and avoid being overly aggressive with your targets on a typical day.
Setting Profit Targets: Gauge realistic intra-day profit targets. If a stock is already up 2.5% and has historically only moved more than 3% on rare occasions, you might consider taking profits.
Options Trading: Volatility is paramount for options. This tool helps you visualize the expected range of movement, which can inform decisions on strike selection for strategies like iron condors or straddles.
Identifying Volatility Regimes: Quickly see if the current day is a "normal" low-volatility day or an "abnormal" high-volatility day that could signal a major market event or trend initiation.
Dashboard Breakdown
→ (Arrow): Points to the bin corresponding to the current, live day's amplitude.
Amplitude Level: The minimum amplitude threshold. The format "≥ 1.5%" means "greater than or equal to 1.5%".
Days Reaching Level: The raw number of historical days that had an amplitude equal to or greater than the level in the first column.
Prob. of Reaching Level (%): The percentage of total days that reached that amplitude level (Days Reaching Level / Total Days Analyzed).
Settings
Position: Choose where the dashboard appears on your chart.
Text Size: Adjust the font size for better readability on your screen resolution.
Max Historical Days to Analyze: Set the lookback period for the statistical analysis. A larger number provides a more robust statistical sample but may take slightly longer to load initially.
Enjoy this tool and use it to add a new layer of statistical depth to your trading analysis.
ICT Structure Levels (ST/IT/LT) - v7 (by Jonas E)ICT Structure Levels (ST/IT/LT) – Neighbor-Wick Pivots
This indicator is designed for traders following ICT-style market structure analysis. It identifies Short-Term (ST), Intermediary (IT), and Long-Term (LT) swing highs and lows, but with a stricter filter that reduces false signals.
Unlike standard pivot indicators, this script requires not only that a bar makes a structural high/low, but also that the neighboring bars’ extremes are formed by wicks rather than flat-bodied candles. This wick condition helps confirm that the level is a true liquidity sweep and not just random price action.
How it works (conceptual):
Detects pivots based on user-defined left/right bars.
Validates that extremes on both sides of the pivot are wick-driven (high > body for highs, low < body for lows).
Marks valid STH/STL, ITH/ITL, and LTH/LTL directly on the chart with optional price labels.
Uses ATR offset for better label readability.
Alerts can be enabled to notify when a new structural level is confirmed.
How to use it:
Map market structure across multiple layers (ST/IT/LT).
Identify true liquidity grabs and avoid false highs/lows.
Integrate with Break of Structure (BOS) and Change of Character (CHoCH) strategies.
Combine with other ICT concepts (Order Blocks, Fair Value Gaps, Liquidity Pools).
What makes it unique:
Most pivot indicators mark every high/low indiscriminately. This script filters pivots using wick validation, which significantly reduces noise and focuses only on the levels most relevant to liquidity-based trading strategies.
Auto-Fit Growth Trendline# **Theoretical Algorithmic Principles of the Auto-Fit Growth Trendline (AFGT)**
## **🎯 What Does This Algorithm Do?**
The Auto-Fit Growth Trendline is an advanced technical analysis system that **automates the identification of long-term growth trends** and **projects future price levels** based on historical cyclical patterns.
### **Primary Functionality:**
- **Automatically detects** the most significant lows in regular periods (monthly, quarterly, semi-annually, annually)
- **Constructs a dynamic trendline** that connects these historical lows
- **Projects the trend into the future** with high mathematical precision
- **Generates Fibonacci bands** that act as dynamic support and resistance levels
- **Automatically adapts** to different timeframes and market conditions
### **Strategic Purpose:**
The algorithm is designed to identify **fundamental value zones** where price has historically found support, enabling traders to:
- Identify optimal entry points for long positions
- Establish realistic price targets based on mathematical projections
- Recognize dynamic support and resistance levels
- Anticipate long-term price movements
---
## **🧮 Core Mathematical Foundations**
### **Adaptive Temporal Segmentation Theory**
The algorithm is based on **dynamic temporal partition theory**, where time is divided into mathematically coherent uniform intervals. It uses modular transformations to create bijective mappings between continuous timestamps and discrete periods, ensuring each temporal point belongs uniquely to a specific period.
**What does this achieve?** It allows the algorithm to automatically identify natural market cycles (annual, quarterly, etc.) without manual intervention, adapting to the inherent periodicity of each asset.
The temporal mapping function implements a **discrete affine transformation** that normalizes different frequencies (monthly, quarterly, semi-annual, annual) to a space of unique identifiers, enabling consistent cross-temporal comparative analysis.
---
## **📊 Local Extrema Detection Theory**
### **Multi-Point Retrospective Validation Principle**
Local minima detection is founded on **relative extrema theory with sliding window**. Instead of using a simple minimum finder, it implements a cross-validation system that examines the persistence of the extremum across multiple historical periods.
**What problem does this solve?** It eliminates false minima caused by temporal volatility, identifying only those points that represent true historical support levels with statistical significance.
This approach is based on the **statistical confirmation principle**, where a minimum is only considered valid if it maintains its extremum condition during a defined observation period, significantly reducing false positives caused by transitory volatility.
---
## **🔬 Robust Interpolation Theory with Outlier Control**
### **Contextual Adaptive Interpolation Model**
The mathematical core uses **piecewise linear interpolation with adaptive outlier correction**. The key innovation lies in implementing a **contextual anomaly detector** that identifies not only absolute extreme values, but relative deviations to the local context.
**Why is this important?** Financial markets contain extreme events (crashes, bubbles) that can distort projections. This system identifies and appropriately weights them without completely eliminating them, preserving directional information while attenuating distortions.
### **Implicit Bayesian Smoothing Algorithm**
When an outlier is detected (deviation >300% of local average), the system applies a **simplified Kalman filter** that combines the current observation with a local trend estimation, using a weight factor that preserves directional information while attenuating extreme fluctuations.
---
## **📈 Stabilized Extrapolation Theory**
### **Exponential Growth Model with Dampening**
Extrapolation is based on a **modified exponential growth model with progressive dampening**. It uses multiple historical points to calculate local growth ratios, implements statistical filtering to eliminate outliers, and applies a dampening factor that increases with extrapolation distance.
**What advantage does this offer?** Long-term projections in finance tend to be exponentially unrealistic. This system maintains short-to-medium term accuracy while converging toward realistic long-term projections, avoiding the typical "exponential explosions" of other methods.
### **Asymptotic Convergence Principle**
For long-term projections, the algorithm implements **controlled asymptotic convergence**, where growth ratios gradually converge toward pre-established limits, avoiding unrealistic exponential projections while preserving short-to-medium term accuracy.
---
## **🌟 Dynamic Fibonacci Projection Theory**
### **Continuous Proportional Scaling Model**
Fibonacci bands are constructed through **uniform proportional scaling** of the base curve, where each level represents a linear transformation of the main curve by a constant factor derived from the Fibonacci sequence.
**What is its practical utility?** It provides dynamic resistance and support levels that move with the trend, offering price targets and profit-taking points that automatically adapt to market evolution.
### **Topological Preservation Principle**
The system maintains the **topological properties** of the base curve in all Fibonacci projections, ensuring that spatial and temporal relationships are consistently preserved across all resistance/support levels.
---
## **⚡ Adaptive Computational Optimization**
### **Multi-Scale Resolution Theory**
It implements **automatic multi-resolution analysis** where data granularity is dynamically adjusted according to the analysis timeframe. It uses the **adaptive Nyquist principle** to optimize the signal-to-noise ratio according to the temporal observation scale.
**Why is this necessary?** Different timeframes require different levels of detail. A 1-minute chart needs more granularity than a monthly one. This system automatically optimizes resolution for each case.
### **Adaptive Density Algorithm**
Calculation point density is optimized through **adaptive sampling theory**, where calculation frequency is adjusted according to local trend curvature and analysis timeframe, balancing visual precision with computational efficiency.
---
## **🛡️ Robustness and Fault Tolerance**
### **Graceful Degradation Theory**
The system implements **multi-level graceful degradation**, where under error conditions or insufficient data, the algorithm progressively falls back to simpler but reliable methods, maintaining basic functionality under any condition.
**What does this guarantee?** That the indicator functions consistently even with incomplete data, new symbols with limited history, or extreme market conditions.
### **State Consistency Principle**
It uses **mathematical invariants** to guarantee that the algorithm's internal state remains consistent between executions, implementing consistency checks that validate data structure integrity in each iteration.
---
## **🔍 Key Theoretical Innovations**
### **A. Contextual vs. Absolute Outlier Detection**
It revolutionizes traditional outlier detection by considering not only the absolute magnitude of deviations, but their relative significance within the local context of the time series.
**Practical impact:** It distinguishes between legitimate market movements and technical anomalies, preserving important events like breakouts while filtering noise.
### **B. Extrapolation with Weighted Historical Memory**
It implements a memory system that weights different historical periods according to their relevance for current prediction, creating projections more adaptable to market regime changes.
**Competitive advantage:** It automatically adapts to fundamental changes in asset dynamics without requiring manual recalibration.
### **C. Automatic Multi-Timeframe Adaptation**
It develops an automatic temporal resolution selection system that optimizes signal extraction according to the intrinsic characteristics of the analysis timeframe.
**Result:** A single indicator that functions optimally from 1-minute to monthly charts without manual adjustments.
### **D. Intelligent Asymptotic Convergence**
It introduces the concept of controlled asymptotic convergence in financial extrapolations, where long-term projections converge toward realistic limits based on historical fundamentals.
**Added value:** Mathematically sound long-term projections that avoid the unrealistic extremes typical of other extrapolation methods.
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## **📊 Complexity and Scalability Theory**
### **Optimized Linear Complexity Model**
The algorithm maintains **linear computational complexity** O(n) in the number of historical data points, guaranteeing scalability for extensive time series analysis without performance degradation.
### **Temporal Locality Principle**
It implements **temporal locality**, where the most expensive operations are concentrated in the most relevant temporal regions (recent periods and near projections), optimizing computational resource usage.
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## **🎯 Convergence and Stability**
### **Probabilistic Convergence Theory**
The system guarantees **probabilistic convergence** toward the real underlying trend, where projection accuracy increases with the amount of available historical data, following **law of large numbers** principles.
**Practical implication:** The more history an asset has, the more accurate the algorithm's projections will be.
### **Guaranteed Numerical Stability**
It implements **intrinsic numerical stability** through the use of robust floating-point arithmetic and validations that prevent overflow, underflow, and numerical error propagation.
**Result:** Reliable operation even with extreme-priced assets (from satoshis to thousand-dollar stocks).
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## **💼 Comprehensive Practical Application**
**The algorithm functions as a "financial GPS"** that:
1. **Identifies where we've been** (significant historical lows)
2. **Determines where we are** (current position relative to the trend)
3. **Projects where we're going** (future trend with specific price levels)
4. **Provides alternative routes** (Fibonacci bands as alternative targets)
This theoretical framework represents an innovative synthesis of time series analysis, approximation theory, and computational optimization, specifically designed for long-term financial trend analysis with robust and mathematically grounded projections.
MMA, Mid-Price Moving Averages (Open + Close Based MAs)📝 Script Description
This script introduces a custom set of moving averages based on the mid-price, calculated as the average of the open and close prices:
Mid Price = (Open + Close) / 2
Instead of traditional close-based MAs, this approach reflects the average sentiment throughout the trading session, offering a smoother and more realistic view of price action.
🔍 Key Features:
✅ Gap-aware smoothing
Captures opening gaps, offering a better representation of intraday shifts.
✅ Reduced noise
Less vulnerable to sharp closing moves or one-off spikes, making it easier to identify true trend breaks or supports.
✅ Closer to actual flow
Reflects a more natural midline of price movement, ideal for traders who prioritize clean, sustained trends.
✅ Better support/resistance alignment
Especially useful for identifying stable uptrends and minimizing false breakout signals.
📐 Included Moving Averages:
MA 5
MA 10
MA 20
MA 60
MA 120
MA 200
(All based on mid-price, not close)
🎯 Recommended For:
Traders seeking smoother and more reliable trendlines
Those who want a more realistic depiction of support and resistance
Ideal for filtering out noisy movements while focusing on clean, straight-moving charts
Daily Seasonality Strength + Prediction TableDaily Seasonality Strength + Prediction Table
Return Estimates:
This indicator uses historical price data to calculate average returns for each day (of the week or month) and uses these to predict the next day’s return.
Seasonality Strength:
It measures seasonality strength by comparing predicted returns with actual returns, using the inverse of MSE (higher values mean stronger seasonality).
supports up to 10 assets
This script is for informational and educational purposes only. It does not constitute financial, investment, or trading advice. I am not a financial advisor. Any decisions you make based on this indicator are your own responsibility. Always do your own research and consult with a qualified financial professional before making any investment decisions.
Past performance is no guarantee of future results. The value of the instruments may fluctuate and is not guaranteed
Transfer Function Filter [theUltimator5]The Transfer Function Filter is an engineering style approach to transform the price action on a chart into a frequency, then filter out unwanted signals using Butterworth-style filter approach.
This indicator allows you to analyze market structure by isolating or removing different frequency components of price movement—similar to how engineers filter signals in control systems and electrical circuits.
🔎 Features
Four Filter Types
1) Low Pass Filter – Smooths price data, highlighting long-term trends while filtering out short-term noise. This filter acts similar to an EMA, removing noisy signals, resulting in a smooth curve that follows the price of the stock relative to the filter cutoff settings.
Real world application for low pass filter - Used in power supplies to provide a clean, stable power level.
2) High Pass Filter – Removes slow-moving trends to emphasize short-term volatility and rapid fluctuations. The high pass filter removes the "DC" level of the chart, removing the average price moves and only outputting volatility.
Real world application for high pass filter - Used in audio equalizers to remove low-frequency noise (like rumble) while allowing higher frequencies to pass through, improving sound clarity.
3) Band Pass Filter – Allows signals to plot only within a band of bar ranges. This filter removes the low pass "DC" level and the high pass "high frequency noise spikes" and shows a signal that is effectively a smoothed volatility curve. This acts like a moving average for volatility.
Real world application for band pass filter - Radio stations only allow certain frequency bands so you can change your radio channel by switching which frequency band your filter is set to.
4) Band Stop Filter – Suppresses specific frequency bands (cycles between two cutoffs). This filter allows through the base price moving average, but keeps the high frequency volatility spikes. It allows you to filter out specific time interval price action.
Real world application for band stop filter - If there is prominent frequency signal in the area which can cause unnecessary noise in your system, a band stop filter can cancel out just that frequency so you get everything else
Configurable Parameters
• Cutoff Periods – Define the cycle lengths (in bars) to filter. This is a bit counter-intuitive with the numbering since the higher the bar count on the low-pass filter, the lower the frequency cutoff is. The opposite holds true for the high pass filter.
• Filter Order – Adjust steepness and responsiveness (higher order = sharper filtering, but with more delay).
• Overlay Option – Display Low Pass & Band Stop outputs directly on the price chart, or in a separate pane. This is enabled by default, plotting the filters that mimic moving averages directly onto the chart.
• Source Selection – Apply filters to close, open, high, low, or custom sources.
Histograms for Comparison
• BS–LP Histogram – Shows distance between Band Stop and Low Pass filters.
• BP–HP Histogram – Highlights differences between Band Pass and High Pass filters.
Histograms give the visualization of a pseudo-MACD style indicator
Visual & Informational Aids
• Customizable colors for each filter line.
• Optional zero-line for histogram reference.
• On-chart info table summarizing active filters, cutoff settings, histograms, and filter order.
📊 Use Cases
Trend Detection – Use the Low Pass filter to smooth noise and follow underlying market direction.
Volatility & Cycle Analysis – Apply High Pass or Band Pass to capture shorter-term patterns.
Noise Suppression – Deploy Band Stop to remove specific choppy frequencies.
Momentum Insight – Watch the histograms to spot divergences and relative filter strength.
Elliott Wave Detector with FibonacciDetermines what timeframe (if any) the underlying asset displays congruence with Elliot Waves, validated by examining the congruence of the waves with fibonacci patterns. Like all backwards-looking indicators, any actual match will be a very pretty coincidence rather than any kind of indicator of potential future behaviour,
BTC Power Law Valuation BandsBTC Power Law Rainbow
A long-term valuation framework for Bitcoin based on Power Law growth — designed to help identify macro accumulation and distribution zones, aligned with long-term investor behavior.
🔍 What Is a Power Law?
A Power Law is a mathematical relationship where one quantity varies as a power of another. In this model:
Price ≈ a × (Time)^b
It captures the non-linear, exponentially slowing growth of Bitcoin over time. Rather than using linear or cyclical models, this approach aligns with how complex systems, such as networks or monetary adoption curves, often grow — rapidly at first, and then more slowly, but persistently.
🧠 Why Power Law for BTC?
Bitcoin:
Has finite supply and increasing adoption.
Operates as a monetary network , where Metcalfe’s Law and power laws naturally emerge.
Exhibits exponential growth over logarithmic time when viewed on a log-log chart .
This makes it uniquely well-suited for power law modeling.
🌈 How to Use the Valuation Bands
The central white line represents the modeled fair value according to the power law.
Colored bands represent deviations from the model in logarithmic space, acting as macro zones:
🔵 Lower Bands: Deep value / Accumulation zones.
🟡 Mid Bands: Fair value.
🔴 Upper Bands: Euphoria / Risk of macro tops.
📐 Smart Money Concepts (SMC) Alignment
Accumulation: Occurs when price consolidates near lower bands — often aligning with institutional positioning.
Markup: As price re-enters or ascends the bands, we often see breakout behavior and trend expansion.
Distribution: When price extends above upper bands, potential for exit liquidity creation and distribution events.
Reversion: Historically, price mean-reverts toward the model — rarely staying outside the bands for long.
This makes the model useful for:
Cycle timing
Long-term DCA strategy zones
Identifying value dislocations
Filtering short-term noise
⚠️ Disclaimer
This tool is for educational and informational purposes only . It is not financial advice. The power law model is a non-predictive, mathematical framework and does not guarantee future price movements .
Always use additional tools, risk management, and your own judgment before making trading or investment decisions.
Lanzadera)The Lanzadera Indicator is designed to identify market momentum and potential breakout opportunities. It works as a dynamic tool that helps traders detect price acceleration zones, providing clear signals for possible entries and exits. With customizable settings and a user-friendly design, this indicator is suitable for both beginners and experienced traders.
Use it to:
Spot momentum shifts before major price movements.
Enhance your breakout trading strategies.
Gain a clearer view of market dynamics with visual alerts.
This indicator is built for traders who want precision, discipline, and a professional edge in their decision-making process.
GEXStrik BarS EUR USDGEX strike bars on the left side measure the prevailing amount of positive or negative gamma. On the right side, the volume of calls and puts traded in the region.
