Volume Acceptance Zones [BigBeluga]Volume Acceptance Zones is a market structure tool designed to identify areas of price acceptance and statistically stretched extremes. By modeling market activity as a continuous distribution, the indicator highlights where price is actively accepted versus where it behaves as a statistical outlier.
The goal is not prediction, but context — separating balanced price behavior from structurally stretched conditions.
🔵 CONCEPTS
The indicator calculates a Volume-Weighted Balance Price , representing the center of gravity for participation over a selected range.
Price dispersion around this balance point is measured using volume-weighted standard deviation .
The area within ±1 standard deviation forms the Acceptance Zone , where the majority of activity is concentrated.
Prices beyond this zone are treated as outliers , where participation thins and market reactions become more likely.
These zones do NOT represent guaranteed probabilities — they describe participation density and behavioral extremes.
🔵 STANDARD DEVIATION, BELL CURVE & OUTLIERS
At the core of this indicator lies the concept of standard deviation , which describes how price activity clusters around a central value.
When activity is observed over time, it tends to form a distribution where:
Most activity concentrates near a central balance level.
Fewer observations occur as price moves further away from that balance.
This behavior can be visualized conceptually as a bell-shaped distribution — a practical way to describe market participation density.
Prices that move beyond the Acceptance Zone deviate meaningfully from the balance of participation.
These areas are treated as outliers , where price is statistically stretched relative to recent market behavior.
Outliers do not imply immediate reversals — they signal that price is operating in a low-acceptance environment.
Market responses in these zones often include rejection, consolidation, or strong continuation if acceptance builds.
🔵 NEW: INTEGRATED FREQUENCY PROFILE
While the zones are calculated using volume-weighted math, the visual profile has been updated to a Frequency-Based Distribution . This transition allows you to see "Time at Price" rather than just raw volume.
Frequency Distribution: The profile counts the number of bars (occurrences) spent at each price bin. This highlights levels of high interest where the market finds it easy to trade, effectively acting as a Time-Price Opportunity (TPO) proxy.
Time-Based Sentiment: Each bin is split into Bull/Bear frequency. This shows which side was in control during the time spent at that specific level, identifying where buyers or sellers were more persistent.
Filtering Noise: By using frequency instead of raw volume, the profile avoids being skewed by single high-volume spikes, focusing instead on where the market established a sustained presence.
🔵 FEATURES
Acceptance Zone (±1σ)
Highlights the primary balance area where price is most actively accepted and rotational behavior is common.
Extreme Zones (±2σ)
Marks statistically stretched prices where acceptance weakens and reactions or trend continuation may occur.
Volume-Weighted Balance Line
Acts as a structural fair-value reference similar to an anchored VWAP.
Outlier Detection
Price closing beyond the acceptance zone is flagged as an outlier, helping identify exhaustion or breakout conditions.
Distribution Labels
Displays how price activity is distributed between acceptance and extreme zones, reinforcing the concept visually.
Flexible Anchoring
Calculations can be based on a fixed lookback or the visible chart range.
🔵 HOW TO USE
Treat the Acceptance Zone as a balance area where price is fairly valued and mean-reversion is common.
Observe how price behaves in Extreme Zones — rejection may signal reversion, while sustained acceptance may indicate trend continuation.
Frequency Nodes: Use the Frequency Profile to identify where the market is "stalling." High frequency nodes often act as magnets for price, while low frequency gaps (low time spent) often lead to fast price movement.
Use outlier signals in combination with trend bias, liquidity levels, or momentum tools.
🔵 CONCLUSION
Volume Acceptance Zones reframes market analysis around participation density. By distinguishing accepted price behavior from statistical outliers and providing a frequency-based view of time-at-price, the indicator helps traders understand when the market is balanced—and when it is structurally stretched. Indicator
Harmonic Resonance Field [JOAT]Harmonic Resonance Field
Introduction
The Harmonic Resonance Field is an open-source overlay indicator that combines dynamic range detection, Renko-style trend tracking, harmonic frequency analysis, and magnetic field visualization into a unified system for identifying consolidation zones, trend direction, and potential reversal points. It is designed for traders who want to understand where price is within its current range, how strong the prevailing trend is, and when conditions are ripe for a breakout or mean reversion.
Built with Pine Script v6, the indicator uses custom user-defined types for Renko state management, range detection, reversal signals, harmonic bands, magnetic fields, and resonance points.
Why This Indicator Exists
Range-bound markets account for a significant portion of trading time, yet most indicators are optimized for trending conditions. This indicator fills that gap by providing:
ADX-based range detection: Automatically identifies when the market is ranging versus trending using ADX with a configurable threshold, so traders know which strategy framework to apply
Multi-style band calculation: Offers four band calculation methods (ATR, Percentage, Standard Deviation, Harmonic) so traders can choose the volatility measure that best fits their instrument
Renko trend overlay: A smoothed Renko-style trend line that filters noise and shows the dominant direction without requiring a separate Renko chart
Harmonic frequency analysis: Uses sine-wave modulation to create bands that expand and contract with market rhythm, capturing cyclical behavior that static bands miss
Magnetic field visualization: Plots dynamic attraction/repulsion levels around the mean, helping traders visualize where price is likely to gravitate
Core Components Explained
1. Range Detection Engine
The indicator uses ADX to classify market conditions. When ADX falls below the configurable threshold (default 25), the market is classified as ranging, and the indicator highlights the range boundaries. When ADX rises above the threshold, the market is trending, and the indicator shifts focus to the Renko trend line and harmonic bands.
adxSmoothed = ta.rma(dx, adxLength)
isRanging = adxSmoothed < adxThreshold
During ranging conditions, the indicator calculates the highest high and lowest low over the range lookback period and draws a dynamic range box with upper, lower, and midline levels. This gives traders clear boundaries for mean reversion strategies.
2. Harmonic Band System
The band system supports four calculation styles:
ATR: Bands based on Average True Range multiplied by a configurable factor
Percentage: Bands at a fixed percentage distance from the mean
Standard Deviation: Bollinger-style bands using standard deviation
Harmonic: Bands modulated by a sine wave that creates rhythmic expansion and contraction
The harmonic mode is unique to this indicator. It calculates a phase and amplitude based on bar position and ATR, then modulates the band width with a sine function:
harmonicPhase = math.sin(bar_index * 2 * math.pi / bandLength) * 0.5 + 0.5
harmonicAmplitude = atrVal * bandMultiplier
bandWidth = harmonicAmplitude * (0.5 + harmonicPhase * 0.5)
This creates bands that breathe with the market's natural rhythm rather than remaining static or purely reactive.
Chart showing the Harmonic Resonance Field with harmonic bands expanding and contracting around price, Renko trend line, and range detection box during a consolidation period
3. Renko Trend Engine
Rather than requiring traders to switch to a Renko chart, this indicator calculates a Renko-style trend directly on the standard candlestick chart. The brick size can be set using ATR, a fixed percentage, or a static value. The Renko state is managed as a custom type that tracks the current level, direction, and brick boundaries.
When price moves by one brick size in the trend direction, the Renko level advances. When price reverses by the configurable reversal multiplier (default 2 bricks), the trend flips. The result is a stepped trend line overlaid on the chart that filters minor fluctuations and shows only significant directional changes.
4. Magnetic Field Visualization
The magnetic field creates a set of attraction levels around the mean price. These levels represent zones where price tends to gravitate based on the configurable field strength parameter. The field is calculated using the distance from the mean and the current ATR:
Strong attraction zone: Within 0.5x ATR of the mean — price tends to consolidate here
Moderate zone: 0.5x to 1.0x ATR from the mean — normal trading range
Weak zone: Beyond 1.0x ATR — price is extended and may revert
The magnetic field lines are drawn with gradient transparency, becoming more transparent as they move away from the mean, visually communicating the decreasing "pull" of the mean at greater distances.
5. Reversal and Resonance Detection
The indicator generates two types of signals:
Reversal signals: Triggered when price reaches the outer bands with momentum showing signs of exhaustion (RSI-based or rate-of-change based). These are plotted as directional markers on the chart.
Resonance signals: Triggered when multiple conditions align — price at a band extreme, ranging market detected, and volume above average. Resonance points represent higher-conviction mean reversion opportunities.
Visual Elements
Harmonic Bands: Upper and lower bands with gradient fill between them
Renko Trend Line: Stepped line showing the dominant trend direction
Range Box: Dynamic box highlighting the current consolidation range
Magnetic Field Lines: Gradient-colored attraction levels around the mean
Reversal Markers: Directional signals at potential turning points
Resonance Points: High-confluence mean reversion signals
Candle Coloring: Optional trend-based candle coloring
Dashboard: Displays trend direction, range status, band width, Renko state, and resonance count
Input Parameters
Range Detection:
Range Lookback (default 50)
ADX Length (default 14) and ADX Threshold (default 25)
Band Settings:
Band Style: ATR, Percentage, Standard Dev, or Harmonic
Band Length (default 20) and Band Multiplier (default 2.0)
Renko Settings:
Brick Size Style: ATR, Percentage, or Static
Brick Size (default 1.0) and Reversal Multiplier (default 2)
Magnetic Field:
Field Strength (0.1-2.0, default 1.0)
Visual Settings:
Show Candle Coloring, Gradient Fill, Dashboard, Glow Effects, Pulse Effects
How to Use This Indicator
Step 1: Check the dashboard for the current market regime. If the market is ranging, focus on the range box boundaries and magnetic field levels for mean reversion setups.
Step 2: In trending conditions, follow the Renko trend line. Stay with the trend as long as the Renko direction holds. A Renko reversal (direction flip) is a significant event that suggests the trend may be changing.
Step 3: Watch for price reaching the outer harmonic bands. In ranging markets, these represent potential reversal zones. In trending markets, they may indicate overextension.
Step 4: Look for resonance signals. These combine multiple conditions (band extreme + ranging + volume) and represent the highest-conviction mean reversion setups.
Step 5: Use the magnetic field levels as dynamic support and resistance. Price tends to gravitate toward the strong attraction zone near the mean.
Close-up showing reversal markers at band extremes with resonance signals highlighted during a ranging market, with the magnetic field gradient visible around the mean
Indicator Limitations
ADX-based range detection has an inherent lag. The transition from trending to ranging (and vice versa) is identified after it has already begun.
Harmonic bands use a fixed-frequency sine wave. Real market cycles are not perfectly periodic, so the harmonic modulation is an approximation.
Renko trend calculations on a candlestick chart are a simulation. They will not match a true Renko chart exactly due to differences in bar construction.
Reversal signals at band extremes do not guarantee reversals. In strong trends, price can ride the outer band for extended periods.
The magnetic field visualization is a conceptual tool for understanding mean reversion tendency, not a precise prediction of where price will go.
Performance may be affected on very low timeframes with many visual elements enabled. Consider reducing visual effects on sub-minute charts.
Originality Statement
This indicator is original in its synthesis of range detection, harmonic frequency analysis, and magnetic field visualization. While individual components (ADX range detection, Renko trends, Bollinger-style bands) are established concepts, this indicator is justified because:
The harmonic band mode introduces sine-wave modulation to create bands that rhythmically expand and contract, a method not found in standard band indicators
The magnetic field visualization provides a novel way to represent mean reversion tendency using gradient-based attraction zones
Combining Renko trend tracking with ADX range detection on a standard chart gives traders both trend-following and mean-reversion frameworks simultaneously
Resonance detection creates a multi-factor confluence signal by combining band position, range status, and volume conditions
The four-style band system (ATR, Percentage, StdDev, Harmonic) allows traders to adapt the indicator to different instruments and market conditions
Disclaimer
This indicator is provided for educational and informational purposes only. It is not financial advice or a recommendation to buy or sell any financial instrument. Trading involves substantial risk of loss. Range detection and band analysis are tools for understanding market structure, not guarantees of future price movement. Always use proper risk management. The author is not responsible for any losses incurred from using this indicator.
-Made with passion by officialjackofalltrades
Indicator
Rolling SSA Oscillator [LuxAlgo]The Rolling SSA Oscillator indicator is a cycle-analysis tool that utilizes Singular Spectrum Analysis (SSA) to decompose price action into its most significant periodic components, providing a real-time view of underlying market rhythms. Unlike traditional lagging oscillators, this script uses eigendecomposition to isolate dominant trends and noise-reduced oscillations for better market timing.
🔶 USAGE
The indicator provides two primary components derived from the price's spectral signature: a Long-Term Periodic component and a Short-Term Periodic component. These can be used to identify trend direction, cyclical reversals, and momentum exhaustion.
🔹 Trading Signals
Trend Direction: When the Long-Term Periodic component (solid line) is above the zero level and colored green, the primary underlying cycle is in an upward phase. Conversely, a red line below zero indicates a downward phase.
Cycle Crosses: Traders can look for the Short-Term Periodic component (dotted line) crossing the Long-Term component or the zero line to anticipate shorter-term shifts in momentum.
Normalization: When the "Normalize" setting is enabled, the components are scaled relative to their combined absolute magnitude. This is particularly useful for identifying extreme cycle peaks regardless of absolute price volatility.
🔶 DETAILS
Singular Spectrum Analysis (SSA) is a powerful non-parametric technique used in time-series analysis. This indicator implements a rolling version of SSA through the following mathematical steps:
Embedding: The price data is mapped into a trajectory matrix using the "Window" length defined in the settings.
Decomposition: A covariance matrix is computed, followed by eigendecomposition to find the eigenvalues and eigenvectors.
Grouping & Reconstruction: The eigenvectors are sorted by their energy (eigenvalues). The script specifically reconstructs the first two components to form the Long-Term trend/cycle and the subsequent two components to form the Short-Term cycle.
Because this script uses matrix.eigenvalues() and matrix.eigenvectors() , it requires significant computation. The "Window" input determines the "resolution" of the cycles; a larger window can capture longer-term rhythms but increases the lag and computational load.
🔶 SETTINGS
Window: Controls the embedding dimension (L). This defines the maximum cycle length the indicator can effectively resolve.
Long Term Periodic: Toggles the visibility of the primary trend-following cycle (Components 1 & 2).
Short Term Periodic: Toggles the visibility of the faster, more reactive cycle (Components 3 & 4).
Normalize: If enabled, adjusts the output so that the combined amplitude of both components stays within a consistent range, making it easier to spot cyclical extremes.
🔹 Dashboard
Dashboard: Toggles the on-screen statistics table.
Position: Determines where the dashboard is displayed (Top Right, Bottom Right, or Bottom Left).
Size: Adjusts the text size within the dashboard.
Indicator
HTF Frequency Zone [BigBeluga]🔵 OVERVIEW
HTF Frequency Zone highlights the dominant price level (Point of Control) and the full high–low expansion of any higher timeframe — Daily, Weekly, or Monthly. It captures the frequency of closes inside each HTF candle and plots the most traded “frequency zone”, allowing traders to easily see where price spent the most time and where buy/sell pressure accumulated.
This tool transforms each higher-timeframe bar into a fully visualized structure:
• Top = HTF high
• Bottom = HTF low
• Midline = HTF Frequency POC
• Color-coded zones = bullish or bearish bias
• Labels = counts of bullish and bearish candles inside the HTF range
It is designed to give traders an immediate understanding of high-timeframe balance, imbalance, and price attraction zones.
🔵 CONCEPTS
HTF Partitioning — Each Weekly/Daily/Monthly candle is converted into a dedicated zone with its own High, Low, and Frequency Point of Control.
Frequency POC (Most Touched Price) — The indicator divides the HTF range into 100 bins and counts how many times price closed near each level.
Dominant Zone — The level with the highest frequency becomes the HTF “Value Zone,” plotted as a bold central line.
Directional Bias —
• Bullish HTF zone
• Bearish HTF zone
Internal Candle Counting — Within each HTF period the indicator counts:
• Buy candles (close > open)
• Sell candles (close < open)
This reveals whether intraperiod flow was bullish or bearish.
HTF Structure Blocks — High, Low, and POC are connected across the entire higher-timeframe duration, showing the real shape of HTF balance.
🔵 FEATURES
Automatic HTF Zone Construction — Generates a complete price zone every time the selected timeframe flips (Daily / Weekly / Monthly).
Dynamic High & Low Extraction — The indicator scans every bar inside the HTF window to find true extremes of the range.
100-Level Frequency Scan — Each close within the period is assigned to a bin, creating a detailed distribution of price interaction.
HTF POC Highlighting — The most frequent price level is plotted with a bold red line for immediate visual clarity.
Bull/Bear Coloring —
• Green → Bullish HTF zone.
• Orange → Bearish HTF zone.
Zone Shading — High–Low range is filled with a semi-transparent color matching trend direction.
Buy/Sell Candle Counters — Printed at the top and bottom of each HTF block, showing how many internal candles were bullish or bearish.
POC Label — Displays frequency count (how many touches) at the POC level.
Adaptive Threshold Warning — If bars inside the HTF window are too few (<10), the indicator warns the trader to switch timeframe.
🔵 HOW TO USE
Higher-Timeframe Biasing — Read the zone color to determine if the HTF candle leaned bullish or bearish.
Value Zone Reactions — Price often reacts to the Frequency POC; use it as support/resistance or liquidity magnet.
Range Context — Identify when price is trading near HTF highs (breakout potential) or lows (reversal potential).
Momentum Evaluation — More bullish internal candles = internal buying pressure; more bearish = internal selling pressure.
Swing Trading — Use HTF zones as the “macro map,” then execute trades on lower timeframes aligned with the zone structure.
Liquidity Awareness — The HTF POC often aligns with algorithmic liquidity levels, making it a strong reaction point.
🔵 CONCLUSION
HTF Frequency Zone transforms raw higher-timeframe candles into detailed distribution zones that reveal true market behavior inside the HTF structure. By showing highs, lows, buying/selling activity, and the most interacted price level (Frequency POC), this tool becomes invaluable for traders who want to align executions with powerful HTF levels, liquidity magnets, and structural zones. Indicator
Frequency Momentum Oscillator [QuantAlgo]🟢 Overview
The Frequency Momentum Oscillator applies Fourier-based spectral analysis principles to price action to identify regime shifts and directional momentum. It calculates Fourier coefficients for selected harmonic frequencies on detrended price data, then measures the distribution of power across low, mid, and high frequency bands to distinguish between persistent directional trends and transient market noise. This approach provides traders with a quantitative framework for assessing whether current price action represents meaningful momentum or merely random fluctuations, enabling more informed entry and exit decisions across various asset classes and timeframes.
🟢 How It Works
The calculation process removes the dominant trend from price data by subtracting a simple moving average, isolating cyclical components for frequency analysis:
detrendedPrice = close - ta.sma(close , frequencyPeriod)
The detrended price series undergoes frequency decomposition through Fourier coefficient calculation across the first 8 harmonics. For each harmonic frequency, the algorithm computes sine and cosine components across the lookback window, then derives power as the sum of squared coefficients:
for k = 1 to 8
cosSum = 0.0
sinSum = 0.0
for n = 0 to frequencyPeriod - 1
angle = 2 * math.pi * k * n / frequencyPeriod
cosSum := cosSum + detrendedPrice * math.cos(angle)
sinSum := sinSum + detrendedPrice * math.sin(angle)
power = (cosSum * cosSum + sinSum * sinSum) / frequencyPeriod
Power measurements are aggregated into three frequency bands: low frequencies (harmonics 1-2) capturing persistent cycles, mid frequencies (harmonics 3-4), and high frequencies (harmonics 5-8) representing noise. Each band's power normalizes against total spectral power to create percentage distributions:
lowFreqNorm = totalPower > 0 ? (lowFreqPower / totalPower) * 100 : 33.33
highFreqNorm = totalPower > 0 ? (highFreqPower / totalPower) * 100 : 33.33
The normalized frequency components undergo exponential smoothing before calculating spectral balance as the difference between low and high frequency power:
smoothLow = ta.ema(lowFreqNorm, smoothingPeriod)
smoothHigh = ta.ema(highFreqNorm, smoothingPeriod)
spectralBalance = smoothLow - smoothHigh
Spectral balance combines with price momentum through directional multiplication, producing a composite signal that integrates frequency characteristics with price direction:
momentum = ta.change(close , frequencyPeriod/2)
compositeSignal = spectralBalance * math.sign(momentum)
finalSignal = ta.ema(compositeSignal, smoothingPeriod)
The final signal oscillates around zero, with positive values indicating low-frequency dominance coupled with upward momentum (trending up), and negative values indicating either high-frequency dominance (choppy market) or downward momentum (trending down).
🟢 How to Use This Indicator
→ Long/Short Signals: the indicator generates long signals when the smoothed composite signal crosses above zero (indicating low-frequency directional strength dominates) and short signals when it crosses below zero (indicating bearish momentum persistence).
→ Upper and Lower Reference Lines: the +25 and -25 reference lines serve as threshold markers for momentum strength. Readings beyond these levels indicate strong directional conviction, while oscillations between them suggest consolidation or weakening momentum. These references help traders distinguish between strong trending regimes and choppy transitional periods.
→ Preconfigured Presets: three optimized configurations are available with Default (32, 3) offering balanced responsiveness, Fast Response (24, 2) designed for scalping and intraday trading, and Smooth Trend (40, 5) calibrated for swing trading and position trading with enhanced noise filtration.
→ Built-in Alerts: the indicator includes three alert conditions for automated monitoring - Long Signal (momentum shifts bullish), Short Signal (momentum shifts bearish), and Signal Change (any directional transition). These alerts enable traders to receive real-time notifications without continuous chart monitoring.
→ Color Customization: four visual themes (Classic green/red, Aqua blue/orange, Cosmic aqua/purple, Custom) allow chart customization for different display environments and personal preferences.
Indicator
Count█ OVERVIEW
A library of functions for counting the number of times (frequency) that elements occur in an array or matrix.
█ USAGE
Import the Count library.
import joebaus/count/1 as c
Create an array or matrix that is a `float`, `int`, `string`, or `bool` type to count elements from, then call the count function on the array or matrix.
id = array.from(1.00, 1.50, 1.25, 1.00, 0.75, 1.25, 1.75, 1.25)
countMap = id.count() // Alternatively: countMap = c.count(id)
The "count map" will return a map with keys for each unique element in the array or matrix, and with respective values representing the number of times the unique element was counted. The keys will be the same type as the array or matrix counted. The values will always be an `int` type.
array mapKeys = countMap.keys() // Returns unique keys
array mapValues = countMap.values() // Returns counts
If an array is in ascending or descending order, then the keys of the map will also generate in the same order.
intArray = array.from(2, 2, 2, 3, 4, 4, 4, 4, 4, 6, 6) // Ascending order
map countMap = intArray.count() // Creates a "count map" of all unique elements
array mapKeys = countMap.keys() // Returns // Ascending order
array mapValues = countMap.values() // Returns count
Include a value to get the count of only that value in an array or matrix.
floatMatrix = matrix.new(3, 3, 0.0)
floatMatrix.set(0, 0, 1.0), floatMatrix.set(1, 0, 1.0), floatMatrix.set(2, 0, 1.0)
floatMatrix.set(0, 1, 1.5), floatMatrix.set(1, 1, 2.0), floatMatrix.set(2, 1, 2.5)
floatMatrix.set(0, 2, 1.0), floatMatrix.set(1, 2, 2.5), floatMatrix.set(2, 2, 1.5)
int countFloatMatrix = floatMatrix.count(1.0) // Counts all 1.0 elements, returns 5
// Alternatively: int countFloatMatrix = c.count(floatMatrix, 1.0)
The string method of count() can use strings or regular expressions like "bull*" to count all matching occurrences in a string array.
stringArray = array.from('bullish', 'bull', 'bullish', 'bear', 'bull', 'bearish', 'bearish')
int countString = stringArray.count('bullish') // Returns 2
int countStringRegex = stringArray.count('bull*') // Returns 4
To count multiple values, use an array of values instead of a single value. Returning a count map only of elements in the array.
countArray = array.from(1.0, 2.5)
map countMap = floatMatrix.count(countArray)
array mapKeys = countMap.keys() // Returns keys
array mapValues = countMap.values() // Returns counts
Multiple regex patterns or strings can be counted as well.
stringMatrix = matrix.new(3, 3, '')
stringMatrix.set(0, 0, 'a'), stringMatrix.set(1, 0, 'a'), stringMatrix.set(2, 0, 'a')
stringMatrix.set(0, 1, 'b'), stringMatrix.set(1, 1, 'c'), stringMatrix.set(2, 1, 'd')
stringMatrix.set(0, 2, 'a'), stringMatrix.set(1, 2, 'd'), stringMatrix.set(2, 2, 'b')
// Count the number of times the regex patterns `'^(a|c)$'` and `'^(b|d)$'` occur
array regexes = array.from('^(a|c)$', '^(b|d)$')
map countMap = stringMatrix.count(regexes)
array mapKeys = countMap.keys() // Returns
array mapValues = countMap.values() // Returns
An optional comparison operator can be specified to count the number of times an equality was satisfied for `float`, `int`, and `bool` methods of `count()`.
intArray = array.from(2, 2, 2, 3, 4, 4, 4, 4, 4, 6, 6)
// Count the number of times an element is greater than 4
countInt = intArray.count(4, '>') // Returns 2
When passing an array of values to count and a comparison operator, the operator will apply to each value.
intArray = array.from(2, 2, 2, 3, 4, 4, 4, 4, 4, 6, 6)
values = array.from(3, 4)
// Count the number of times and element is greater than 3 and 4
map countMap = intArray.count(values, '>')
array mapKeys = countMap.keys() // Returns
array mapValues = countMap.values() // Returns
Multiple comparison operators can be applied when counting multiple values.
intMatrix = matrix.new(3, 3, 0)
intMatrix.set(0, 0, 2), intMatrix.set(1, 0, 3), intMatrix.set(2, 0, 5)
intMatrix.set(0, 1, 2), intMatrix.set(1, 1, 4), intMatrix.set(2, 1, 2)
intMatrix.set(0, 2, 5), intMatrix.set(1, 2, 2), intMatrix.set(2, 2, 3)
values = array.from(3, 4)
comparisons = array.from('<', '>')
// Count the number of times an element is less than 3 and greater than 4
map countMap = intMatrix.count(values, comparisons)
array mapKeys = countMap.keys() // Returns
array mapValues = countMap.values() // Returns
Library
Indicator
Adaptive Resonance Oscillator [AlgoAlpha]Introducing the Adaptive Resonance Oscillator , an advanced momentum-based oscillator designed to dynamically adjust to changing market conditions. This innovative indicator detects market frequency through a Hilbert Transform approach, adapting in real-time to identify overbought and oversold conditions with improved accuracy. With built-in divergence detection, trend analysis, and customizable smoothing, this tool is perfect for traders looking to refine their entries and exits based on adaptive oscillation mechanics.
🚀 Key Features :
🔹 Adaptive Frequency Detection – Uses Hilbert Transform principles to dynamically determine market cycle length for precise oscillator calculation.
⚙️ Customizable Smoothing – Option to apply a Hull Moving Average (HMA) for enhanced signal clarity.
📈 Divergence Detection – Identifies bullish and bearish divergences with visual markers, helping traders spot early trend reversals.
🟢 Overbought & Oversold Signals – Highlights extreme momentum conditions with adjustable thresholds.
🔔 Real-Time Alerts – Get notified for crossovers, divergences, and strong trend shifts directly on your PulseWire chart.
🎨 Fully Customizable Appearance – Modify colors, divergence sensitivity, and smoothing options to fit your trading style.
🛠 How to Use :
Add the Adaptive Resonance Oscillator to your PulseWire chart by clicking the ★ to favorite it.
Monitor the Charts , switch between smoothed and I smoothed modes to identify trend and price swings, use divergences and reversal signals for potential entry/exits.
Set alerts for bullish/bearish crossovers and divergence signals to stay ahead of market moves.
⚙ How It Works :
The indicator begins by applying a Hilbert Transform frequency estimation to the price series, identifying the dominant market cycle length. This is used to calculate a period for the RSI that matches its resonant frequency with the dominant market frequency, dynamically adjusting the Oscillator. The oscillator then applies an optional Hull Moving Average (HMA) smoothing for signal refinement. Additionally, the indicator scans for bullish and bearish divergences by comparing oscillator movements against price action, plotting signals accordingly. When overbought/oversold conditions or divergence events occur, alerts are triggered to notify the trader in real time. Indicator
High/Low Location Frequency [LuxAlgo]The High/Low Location Frequency tool provides users with probabilities of tops and bottoms at user-defined periods, along with advanced filters that offer deep and objective market information about the likelihood of a top or bottom in the market.
🔶 USAGE
There are four different time periods that traders can select for analysis of probabilities:
HOUR OF DAY: Probability of occurrence of top and bottom prices for each hour of the day
DAY OF WEEK: Probability of occurrence of top and bottom prices for each day of the week
DAY OF MONTH: Probability of occurrence of top and bottom prices for each day of the month
MONTH OF YEAR: Probability of occurrence of top and bottom prices for each month
The data is displayed as a dashboard, which users can position according to their preferences. The dashboard includes useful information in the header, such as the number of periods and the date from which the data is gathered. Additionally, users can enable active filters to customize their view. The probabilities are displayed in one, two, or three columns, depending on the number of elements.
🔹 Advanced Filters
Advanced Filters allow traders to exclude specific data from the results. They can choose to use none or all filters simultaneously, inputting a list of numbers separated by spaces or commas. However, it is not possible to use both separators on the same filter.
The tool is equipped with five advanced filters:
HOURS OF DAY: The permitted range is from 0 to 23.
DAYS OF WEEK: The permitted range is from 1 to 7.
DAYS OF MONTH: The permitted range is from 1 to 31.
MONTHS: The permitted range is from 1 to 12.
YEARS: The permitted range is from 1000 to 2999.
It should be noted that the DAYS OF WEEK advanced filter has been designed for use with tickers that trade every day, such as those trading in the crypto market. In such cases, the numbers displayed will range from 1 (Sunday) to 7 (Saturday). Conversely, for tickers that do not trade over the weekend, the numbers will range from 1 (Monday) to 5 (Friday).
To illustrate the application of this filter, we will exclude results for Mondays and Tuesdays, the first five days of each month, January and February, and the years 2020, 2021, and 2022. Let us review the results:
DAYS OF WEEK: `2,3` or `2 3` (for crypto) or `1,2` or `1 2` (for the rest)
DAYS OF MONTH: `1,2,3,4,5` or `1 2 3 4 5`
MONTHS: `1,2` or `1 2`
YEARS: `2020,2021,2022` or `2020 2021 2022`
🔹 High Probability Lines
The tool enables traders to identify the next period with the highest probability of a top (red) and/or bottom (green) on the chart, marked with two horizontal lines indicating the location of these periods.
🔹 Top/Bottom Labels and Periods Highlight
The tool is capable of indicating on the chart the upper and lower limits of each selected period, as well as the commencement of each new period, thus providing traders with a convenient reference point.
🔶 SETTINGS
Period: Select how many bars (hours, days, or months) will be used to gather data from, max value as default.
Execution Window: Select how many bars (hours, days, or months) will be used to gather data from
🔹 Advanced Filters
Hours of day: Filter which hours of the day are excluded from the data, it accepts a list of hours from 0 to 23 separated by commas or spaces, users can not mix commas or spaces as a separator, must choose one
Days of week: Filter which days of the week are excluded from the data, it accepts a list of days from 1 to 5 for tickers not trading weekends, or from 1 to 7 for tickers trading all week, users can choose between commas or spaces as a separator, but can not mix them on the same filter.
Days of month: Filter which days of the month are excluded from the data, it accepts a list of days from 1 to 31, users can choose between commas or spaces as separator, but can not mix them on the same filter.
Months: Filter months to exclude from data. Accepts months from 1 to 12. Choose one separator: comma or space.
Years: Filter years to exclude from data. Accepts years from 1000 to 2999. Choose one separator: comma or space.
🔹 Dashboard
Dashboard Location: Select both the vertical and horizontal parameters for the desired location of the dashboard.
Dashboard Size: Select size for dashboard.
🔹 Style
High Probability Top Line: Enable/disable `High Probability Top` vertical line and choose color
High Probability Bottom Line: Enable/disable `High Probability Bottom` vertical line and choose color
Top Label: Enable/disable period top labels, choose color and size.
Bottom Label: Enable/disable period bottom labels, choose color and size.
Highlight Period Changes: Enable/disable vertical highlight at start of period
Indicator
Advanced Keltner Channel/Oscillator [MyTradingCoder]This indicator combines a traditional Keltner Channel overlay with an oscillator, providing a comprehensive view of price action, trend, and momentum. The core of this indicator is its advanced ATR calculation, which uses statistical methods to provide a more robust measure of volatility.
Starting with the overlay component, the center line is created using a biquad low-pass filter applied to the chosen price source. This provides a smoother representation of price than a simple moving average. The upper and lower channel lines are then calculated using the statistically derived ATR, with an additional set of mid-lines between the center and outer lines. This creates a more nuanced view of price action within the channel.
The color coding of the center line provides an immediate visual cue of the current price momentum. As the price moves up relative to the ATR, the line shifts towards the bullish color, and vice versa for downward moves. This color gradient allows for quick assessment of the current market sentiment.
The oscillator component transforms the channel into a different perspective. It takes the price's position within the channel and maps it to either a normalized -100 to +100 scale or displays it in price units, depending on your settings. This oscillator essentially shows where the current price is in relation to the channel boundaries.
The oscillator includes two key lines: the main oscillator line and a signal line. The main line represents the current position within the channel, smoothed by an exponential moving average (EMA). The signal line is a further smoothed version of the oscillator line. The interaction between these two lines can provide trading signals, similar to how MACD is often used.
When the oscillator line crosses above the signal line, it might indicate bullish momentum, especially if this occurs in the lower half of the oscillator range. Conversely, the oscillator line crossing below the signal line could signal bearish momentum, particularly if it happens in the upper half of the range.
The oscillator's position relative to its own range is also informative. Values near the top of the range (close to 100 if normalized) suggest that price is near the upper Keltner Channel band, indicating potential overbought conditions. Values near the bottom of the range (close to -100 if normalized) suggest proximity to the lower band, potentially indicating oversold conditions.
One of the strengths of this indicator is how the overlay and oscillator work together. For example, if the price is touching the upper band on the overlay, you'd see the oscillator at or near its maximum value. This confluence of signals can provide stronger evidence of overbought conditions. Similarly, the oscillator hitting extremes can draw your attention to price action at the channel boundaries on the overlay.
The mid-lines on both the overlay and oscillator provide additional nuance. On the overlay, price action between the mid-line and outer line might suggest strong but not extreme momentum. On the oscillator, this would correspond to readings in the outer quartiles of the range.
The customizable visual settings allow you to adjust the indicator to your preferences. The glow effects and color coding can make it easier to quickly interpret the current market conditions at a glance.
Overlay Component:
The overlay displays Keltner Channel bands dynamically adapting to market conditions, providing clear visual cues for potential trend reversals, breakouts, and overbought/oversold zones.
The center line is a biquad low-pass filter applied to the chosen price source.
Upper and lower channel lines are calculated using a statistically derived ATR.
Includes mid-lines between the center and outer channel lines.
Color-coded based on price movement relative to the ATR.
Oscillator Component:
The oscillator component complements the overlay, highlighting momentum and potential turning points.
Normalized values make it easy to compare across different assets and timeframes.
Signal line crossovers generate potential buy/sell signals.
Advanced ATR Calculation:
Uses a unique method to compute ATR, incorporating concepts like root mean square (RMS) and z-score clamping.
Provides both an average and mode-based ATR value.
Customizable Visual Settings:
Adjustable colors for bullish and bearish moves, oscillator lines, and channel components.
Options for line width, transparency, and glow effects.
Ability to display overlay, oscillator, or both simultaneously.
Flexible Parameters:
Customizable inputs for channel width multiplier, ATR period, smoothing factors, and oscillator settings.
Adjustable Q factor for the biquad filter.
Key Advantages:
Advanced ATR Calculation: Utilizes a statistical method to generate ATR, ensuring greater responsiveness and accuracy in volatile markets.
Overlay and Oscillator: Provides a comprehensive view of price action, combining trend and momentum analysis.
Customizable: Adjust settings to fine-tune the indicator to your specific needs and trading style.
Visually Appealing: Clear and concise design for easy interpretation.
The ATR (Average True Range) in this indicator is derived using a sophisticated statistical method that differs from the traditional ATR calculation. It begins by calculating the True Range (TR) as the difference between the high and low of each bar. Instead of a simple moving average, it computes the Root Mean Square (RMS) of the TR over the specified period, giving more weight to larger price movements. The indicator then calculates a Z-score by dividing the TR by the RMS, which standardizes the TR relative to recent volatility. This Z-score is clamped to a maximum value (10 in this case) to prevent extreme outliers from skewing the results, and then rounded to a specified number of decimal places (2 in this script).
These rounded Z-scores are collected in an array, keeping track of how many times each value occurs. From this array, two key values are derived: the mode, which is the most frequently occurring Z-score, and the average, which is the weighted average of all Z-scores. These values are then scaled back to price units by multiplying by the RMS.
Now, let's examine how these values are used in the indicator. For the Keltner Channel lines, the mid lines (top and bottom) use the mode of the ATR, representing the most common volatility state. The max lines (top and bottom) use the average of the ATR, incorporating all volatility states, including less common but larger moves. By using the mode for the mid lines and the average for the max lines, the indicator provides a nuanced view of volatility. The mid lines represent the "typical" market state, while the max lines account for less frequent but significant price movements.
For the color coding of the center line, the mode of the ATR is used to normalize the price movement. The script calculates the difference between the current price and the price 'degree' bars ago (default is 2), and then divides this difference by the mode of the ATR. The resulting value is passed through an arctangent function and scaled to a 0-1 range. This scaled value is used to create a color gradient between the bearish and bullish colors.
Using the mode of the ATR for this color coding ensures that the color changes are based on the most typical volatility state of the market. This means that the color will change more quickly in low volatility environments and more slowly in high volatility environments, providing a consistent visual representation of price momentum relative to current market conditions.
Using a good IIR (Infinite Impulse Response) low-pass filter, such as the biquad filter implemented in this indicator, offers significant advantages over simpler moving averages like the EMA (Exponential Moving Average) or other basic moving averages.
At its core, an EMA is indeed a simple, single-pole IIR filter, but it has limitations in terms of its frequency response and phase delay characteristics. The biquad filter, on the other hand, is a two-pole, two-zero filter that provides superior control over the frequency response curve. This allows for a much sharper cutoff between the passband and stopband, meaning it can more effectively separate the signal (in this case, the underlying price trend) from the noise (short-term price fluctuations).
The improved frequency response of a well-designed biquad filter means it can achieve a better balance between smoothness and responsiveness. While an EMA might need a longer period to sufficiently smooth out price noise, potentially leading to more lag, a biquad filter can achieve similar or better smoothing with less lag. This is crucial in financial markets where timely information is vital for making trading decisions.
Moreover, the biquad filter allows for independent control of the cutoff frequency and the Q factor. The Q factor, in particular, is a powerful parameter that affects the filter's resonance at the cutoff frequency. By adjusting the Q factor, users can fine-tune the filter's behavior to suit different market conditions or trading styles. This level of control is simply not available with basic moving averages.
Another advantage of the biquad filter is its superior phase response. In the context of financial data, this translates to more consistent lag across different frequency components of the price action. This can lead to more reliable signals, especially when it comes to identifying trend changes or price reversals.
The computational efficiency of biquad filters is also worth noting. Despite their more complex mathematical foundation, biquad filters can be implemented very efficiently, often requiring only a few operations per sample. This makes them suitable for real-time applications and high-frequency trading scenarios.
Furthermore, the use of a more sophisticated filter like the biquad can help in reducing false signals. The improved noise rejection capabilities mean that minor price fluctuations are less likely to cause unnecessary crossovers or indicator movements, potentially leading to fewer false breakouts or reversal signals.
In the specific context of a Keltner Channel, using a biquad filter for the center line can provide a more stable and reliable basis for the entire indicator. It can help in better defining the overall trend, which is crucial since the Keltner Channel is often used for trend-following strategies. The smoother, yet more responsive center line can lead to more accurate channel boundaries, potentially improving the reliability of overbought/oversold signals and breakout indications.
In conclusion, this advanced Keltner Channel indicator represents a significant evolution in technical analysis tools, combining the power of traditional Keltner Channels with modern statistical methods and signal processing techniques. By integrating a sophisticated ATR calculation, a biquad low-pass filter, and a complementary oscillator component, this indicator offers traders a comprehensive and nuanced view of market dynamics.
The indicator's strength lies in its ability to adapt to varying market conditions, providing clear visual cues for trend identification, momentum assessment, and potential reversal points. The use of statistically derived ATR values for channel construction and the implementation of a biquad filter for the center line result in a more responsive and accurate representation of price action compared to traditional methods.
Furthermore, the dual nature of this indicator – functioning as both an overlay and an oscillator – allows traders to simultaneously analyze price trends and momentum from different perspectives. This multifaceted approach can lead to more informed decision-making and potentially more reliable trading signals.
The high degree of customization available in the indicator's settings enables traders to fine-tune its performance to suit their specific trading styles and market preferences. From adjustable visual elements to flexible parameter inputs, users can optimize the indicator for various trading scenarios and time frames.
Ultimately, while no indicator can predict market movements with certainty, this advanced Keltner Channel provides traders with a powerful tool for market analysis. By offering a more sophisticated approach to measuring volatility, trend, and momentum, it equips traders with valuable insights to navigate the complex world of financial markets. As with any trading tool, it should be used in conjunction with other forms of analysis and within a well-defined risk management framework to maximize its potential benefits.
Indicator
SpectrumLibrary "Spectrum"
This library includes spectrum analysis tools such as the Fast Fourier Transform (FFT).
method toComplex(data, polar)
Creates an array of complex type objects from a float type array.
Namespace types: array
Parameters:
data (array) : The float type array of input data.
polar (bool) : Initialization coordinates; the default is false (cartesian).
Returns: The complex type array of converted data.
method sAdd(data, value, end, start, step)
Performs scalar addition of a given float type array and a simple float value.
Namespace types: array
Parameters:
data (array) : The float type array of input data.
value (float) : The simple float type value to be added.
end (int) : The last index of the input array (exclusive) on which the operation is performed.
start (int) : The first index of the input array (inclusive) on which the operation is performed; the default value is 0.
step (int) : The step by which the function iterates over the input data array between the specified boundaries; the default value is 1.
Returns: The modified input array.
method sMult(data, value, end, start, step)
Performs scalar multiplication of a given float type array and a simple float value.
Namespace types: array
Parameters:
data (array) : The float type array of input data.
value (float) : The simple float type value to be added.
end (int) : The last index of the input array (exclusive) on which the operation is performed.
start (int) : The first index of the input array (inclusive) on which the operation is performed; the default value is 0.
step (int) : The step by which the function iterates over the input data array between the specified boundaries; the default value is 1.
Returns: The modified input array.
method eMult(data, data02, end, start, step)
Performs elementwise multiplication of two given complex type arrays.
Namespace types: array
Parameters:
data (array type from RezzaHmt/Complex/1) : the first complex type array of input data.
data02 (array type from RezzaHmt/Complex/1) : The second complex type array of input data.
end (int) : The last index of the input arrays (exclusive) on which the operation is performed.
start (int) : The first index of the input arrays (inclusive) on which the operation is performed; the default value is 0.
step (int) : The step by which the function iterates over the input data array between the specified boundaries; the default value is 1.
Returns: The modified first input array.
method eCon(data, end, start, step)
Performs elementwise conjugation on a given complex type array.
Namespace types: array
Parameters:
data (array type from RezzaHmt/Complex/1) : The complex type array of input data.
end (int) : The last index of the input array (exclusive) on which the operation is performed.
start (int) : The first index of the input array (inclusive) on which the operation is performed; the default value is 0.
step (int) : The step by which the function iterates over the input data array between the specified boundaries; the default value is 1.
Returns: The modified input array.
method zeros(length)
Creates a complex type array of zeros.
Namespace types: series int, simple int, input int, const int
Parameters:
length (int) : The size of array to be created.
method bitReverse(data)
Rearranges a complex type array based on the bit-reverse permutations of its size after zero-padding.
Namespace types: array
Parameters:
data (array type from RezzaHmt/Complex/1) : The complex type array of input data.
Returns: The modified input array.
method R2FFT(data, inverse)
Calculates Fourier Transform of a time series using Cooley-Tukey Radix-2 Decimation in Time FFT algorithm, wikipedia.org
Namespace types: array
Parameters:
data (array type from RezzaHmt/Complex/1) : The complex type array of input data.
inverse (int) : Set to -1 for FFT and to 1 for iFFT.
Returns: The modified input array containing the FFT result.
method LBFFT(data, inverse)
Calculates Fourier Transform of a time series using Leo Bluestein's FFT algorithm, wikipedia.org This function is nearly 4 times slower than the R2FFT function in practice.
Namespace types: array
Parameters:
data (array type from RezzaHmt/Complex/1) : The complex type array of input data.
inverse (int) : Set to -1 for FFT and to 1 for iFFT.
Returns: The modified input array containing the FFT result.
method DFT(data, inverse)
This is the original DFT algorithm. It is not suggested to be used regularly.
Namespace types: array
Parameters:
data (array type from RezzaHmt/Complex/1) : The complex type array of input data.
inverse (int) : Set to -1 for DFT and to 1 for iDFT.
Returns: The complex type array of DFT result. Library
Indicator
Indicator
FunctionPatternFrequencyLibrary "FunctionPatternFrequency"
Counts the word or integer number pattern frequency on a array.
reference:
rosettacode.org
count(pattern)
counts the number a pattern is repeated.
Parameters:
pattern : : array : array with patterns to be counted.
Returns:
array : list of unique patterns.
array : list of counters per pattern.
usage:
count(array.from('a','b','c','a','b','a'))
count(pattern)
counts the number a pattern is repeated.
Parameters:
pattern : : array : array with patterns to be counted.
Returns:
array : list of unique patterns.
array : list of counters per pattern.
usage:
count(array.from(1,2,3,1,2,1)) Library
Fourier Extrapolator of Price w/ Projection Forecast [Loxx]Due to popular demand, I'm pusblishing Fourier Extrapolator of Price w/ Projection Forecast.. As stated in it's twin indicator, this one is also multi-harmonic (or multi-tone) trigonometric model of a price series xi, i=1..n, is given by:
xi = m + Sum( a*Cos(w*i) + b*Sin(w*i), h=1..H )
Where:
xi - past price at i-th bar, total n past prices;
m - bias;
a and b - scaling coefficients of harmonics;
w - frequency of a harmonic ;
h - harmonic number;
H - total number of fitted harmonics.
Fitting this model means finding m, a, b, and w that make the modeled values to be close to real values. Finding the harmonic frequencies w is the most difficult part of fitting a trigonometric model. In the case of a Fourier series, these frequencies are set at 2*pi*h/n. But, the Fourier series extrapolation means simply repeating the n past prices into the future.
This indicator uses the Quinn-Fernandes algorithm to find the harmonic frequencies. It fits harmonics of the trigonometric series one by one until the specified total number of harmonics H is reached. After fitting a new harmonic , the coded algorithm computes the residue between the updated model and the real values and fits a new harmonic to the residue.
see here: A Fast Efficient Technique for the Estimation of Frequency , B. G. Quinn and J. M. Fernandes, Biometrika, Vol. 78, No. 3 (Sep., 1991), pp . 489-497 (9 pages) Published By: Oxford University Press
The indicator has the following input parameters:
src - input source
npast - number of past bars, to which trigonometric series is fitted;
Nfut - number of predicted future bars;
nharm - total number of harmonics in model;
frqtol - tolerance of frequency calculations.
The indicator plots two curves: the green/red curve indicates modeled past values and the yellow/fuchsia curve indicates the modeled future values.
The purpose of this indicator is to showcase the Fourier Extrapolator method to be used in future indicators.
Indicator
Fourier Extrapolator of Price [Loxx]Fourier Extrapolator of Price is a multi-harmonic (or multi-tone) trigonometric model of a price series xi, i=1..n, is given by:
xi = m + Sum( a *Cos(w *i) + b *Sin(w *i), h=1..H )
Where:
xi - past price at i-th bar, total n past prices;
m - bias;
a and b - scaling coefficients of harmonics;
w - frequency of a harmonic;
h - harmonic number;
H - total number of fitted harmonics.
Fitting this model means finding m, a , b , and w that make the modeled values to be close to real values. Finding the harmonic frequencies w is the most difficult part of fitting a trigonometric model. In the case of a Fourier series, these frequencies are set at 2*pi*h/n. But, the Fourier series extrapolation means simply repeating the n past prices into the future.
This indicator uses the Quinn-Fernandes algorithm to find the harmonic frequencies. It fits harmonics of the trigonometric series one by one until the specified total number of harmonics H is reached. After fitting a new harmonic, the coded algorithm computes the residue between the updated model and the real values and fits a new harmonic to the residue.
see here: A Fast Efficient Technique for the Estimation of Frequency , B. G. Quinn and J. M. Fernandes, Biometrika, Vol. 78, No. 3 (Sep., 1991), pp. 489-497 (9 pages) Published By: Oxford University Press
The indicator has the following input parameters:
src - input source
npast - number of past bars, to which trigonometric series is fitted;
nharm - total number of harmonics in model;
frqtol - tolerance of frequency calculations.
The indicator plots the modeled past values
The purpose of this indicator is to showcase the Fourier Extrapolator method to be used in future indicators. While this method can also prediction future price movements, for our purpose here we will avoid doing. Indicator
FunctionBestFitFrequencyLibrary "FunctionBestFitFrequency"
TODO: add library description here
array_moving_average(sample, length, ommit_initial, fillna) Moving Average values for selected data.
Parameters:
sample : float array, sample data values.
length : int, length to smooth the data.
ommit_initial : bool, default=true, ommit values at the start of the data under the length.
fillna : string, default='na', options='na', '0', 'avg'
Returns: float array
errors:
length > sample size "Canot call array methods when id of array is na."
best_fit_frequency(sample, start, end) Search a frequency range for the fairest moving average frequency.
Parameters:
sample : float array, sample data to based the moving averages.
start : int lowest frequency.
end : int highest frequency.
Returns: tuple with (int frequency, float percentage) Library
Indicator
Indicator
Fourier Analysis and Filtering [tbiktag]This tool uses Fourier transform to decompose the input time series into its periodic constituents and seasonalities , in other words, its frequency components . It also can reconstruct the time-domain data while using only the frequency components within a user-defined range (band-pass filtering). Thereby, this tool can reveal the cyclical characteristics of the studied market.
USAGE
The source and the size of the input data can be chosen by the “ Dataset Source ” and “ Dataset Size ” options. Price, volume, or some technical indicator (e.g., RSI, MACD, etc.) can serve as a source of the input data.
“ Action ” defines the type of the plot that will be displayed. Two options are available:
- Fourier Analysis
If selected, the frequency spectrum of the squares of the Fourier coefficient magnitudes is displayed. The zero-frequency component is on the right. Since the magnitudes of half of the coefficients are repeated, the graph displays only half of the frequency components.
The squared magnitude of a given frequency component is a measure of its power , that is, its contribution to the total variance of the dataset. Thus, by analyzing the frequency-domain spectrum, one can identify the most prominent seasonalities and then visualize them by using the " Band-pass Filtering " option (see below). Note that the zero component stores information about the amount of data, so it is naturally higher when the data is not centered at zero.
By activating the " Info about Frequency Component " option, the user can display information about the power and frequency of the selected Fourier component.
- Band-pass Filter
This option reconstructs and plots the dataset in the time domain, blocking frequency components outside of the cutoff frequencies (defined by the input parameters “ Upper Cutoff ” and “ Lower Cutoff ” input parameters in the “ Band-pass Filter Properties ” section).
FURTHER READING
In general, Fourier analysis has a long history of attempted applications for analyzing price data and estimating market cycles. For example, see the paper by John Ehlers
www.mesasoftware.com
and also some tools available here on PulseWire, such as:
“Function: Discrete Fourier Transform” by @RicardoSantos
“Fourier series Model Of The Market” by @e2e4mfck
“Ehlers Discrete Fourier Transform” by @cheatcountry
Thus, I tried to make this tool versatile and user-friendly so you all can experiment with your own analysis.
Enjoy and don't hesitate to leave your feedback in the comments below! Indicator
Particle Physics Moving AverageThis indicator simulates the physics of a particle attracted by a distance-dependent force towards the evolving value of the series it's applied to.
Its parameters include:
The mass of the particle
The exponent of the force function f=d^x
A "medium damping factor" (viscosity of the universe)
Compression/extension damping factors (for simulating spring-damping functions)
This implementation also adds a second set of all of these parameters, and tracks 16 particles evenly interpolated between the two sets.
It's a kind of Swiss Army Knife of Moving Average-type functions; For instance, because the position and velocity of the particle include a "historical knowlege" of the series, it turns out that the Exponential Moving Average function simply "falls out" of the algorithm in certain configurations; instead of being configured by defining a period of samples over which to calculate an Exponential Moving Average, in this derivation, it is tuned by changing the mass and/or medium damping parameters.
But the algorithm can do much more than simply replicate an EMA... A particle acted on by a force that is a linear function of distance (force exponent=1) simulates the physics of a sprung-mass system, with a mass-dependent resonant frequency. By altering the particle mass and damping parameters, you can simulate something like an automobile suspension, letting your particle track a stock's price like a Cadillac or a Corvette (or both, including intermediates) depending on your setup. Particles will have a natural resonance with a frequency that depends on its mass... A higher mass particle (i.e. higher inertia) will resonate at a lower frequency than one with a lower mass (and of course, in this indicator, you can display particles that interpolate through a range of masses.)
The real beauty of this general-purpose algorithm is that the force function can be extended with other components, affecting the trajectory of the particle; For instance "volume" could be factored into the current distance-based force function, strengthening or weakening the impulse accordingly. (I'll probably provide updates to the script that incoroprate different ideas I come up with.)
As currently pictured above, the indicator is interpolating between a medium-damped EMA-like configuration (red) and a more extension-damped suspension-like configuration (blue).
This indicator is merely a tool that provides a space to explore such a simulation, to let you see how tweaking parameters affects the simulations. It doesn't provide buy or sell signals, although you might find that it could be adapted into an MACD-like signal generator... But you're on your own for that. Indicator
Filter Amplitude Response Estimator - A Simple CalculationIn digital signal processing knowing how a system interact with the frequency content of an input signal is extremely important, the mathematical tool that give you this information is called "frequency response". The frequency response regroup two elements, the amplitude response, and the phase response. The amplitude response tells you how the system modify the amplitude of the frequency components in the input signal, the phase response tells you how the system modify the phase of the frequency components in the signal, each being a function of the frequency.
The today proposed tool aim to give a low resolution representation of the amplitude response of any filter.
What Is The Amplitude Response Of A Filter ?
Remember that filters allow to interact with the frequency content of a signal by amplifying, attenuating and/or removing certain frequency components in the input signal, the amplitude (also called magnitude) response of a filter let you know exactly how your filter change the amplitude of the frequency components in the input signal, another way to see the amplitude response is as a tool that tell you what is the peak amplitude of a filter using a sinusoid of a certain frequency as input signal.
For example if the amplitude response of a filter give you a value of 0.9 at frequency 0.5, it means that the filter peak amplitude using a sinusoid of frequency 0.5 is equal to 0.9.
There are several ways to calculate the frequency response of a filter, when our filter is a FIR filter (the filter impulse response is finite), the frequency response of the filter is the absolute value of the discrete Fourier transform (DFT) of the filter impulse response.
If you are curious about this process, know that the DFT of a N samples signal return N values, so if our FIR filter coefficients are composed of only 5 values we would get a frequency response of 5 values...which would not be useful, this is why we "pad" our coefficients with zeros, that is we add zeros to the start and end of our series of coefficients, this process is called "zero-padding", so if our series of coefficients is: (1,2,3,4,5), applying zero padding would give (0,0...1,2,3,4,5,...0,0) while keeping a certain symmetry. This is related to the concept of resolution, a low resolution amplitude response would be composed of a low number of values and would not be useful, this is why we use zero-padding to add more values thus increasing the resolution.
Making a Fourier transform in Pinescript is not doable, as you need the complex number i for computing a DFT, but thats not even the only problem, a DFT would not be that useful anyway (as the processes to make it useful in a trading context would be way too complex) . So how can we calculate a filter amplitude response without using a DFT ? The simple answer is by taking the peak amplitude of a filter using a sinusoid of a certain frequency as input, this is what the proposed tool do.
Using The Tool
The proposed tool give you a 50 point amplitude response from frequency 0.005 to 0.25 by default. the setting "Range Divisor" allow you to see the amplitude response by using a different range of frequency, for example if the range divisor is equal to 2 the filter amplitude response will be evaluated from frequency 0.0025 to 0.125.
In the script, filt hold the filter you want to see the frequency response, by default a simple moving average.
The position of the frequency response is defined by the "Show Amplitude Response At Bar Number" setting, if you want the frequency response to start at bar number 5000 then enter 5000, by default 10000. If you are not a premium set the number at 4000 and it should work.
amplitude response of a simple moving average of period 14, res = 2.
By default the amplitude response use an amplitude scale, a value of 1 represent an unchanged amplitude. You can use Dbfs (decibel full scale) instead by checking the "To Decibels (Full Scale)" setting.
Dbfs amplitude response, a value of 0 represent an unchanged amplitude.
Some Amplitude Responses
In order to prove the accuracy of the proposed tool we can compare the amplitude response given by the proposed tool with the mathematical function of the amplitude response of a simple moving average, that is:
abs(sin(pi*f*length)/(length*sin(pi*f)))
In cyan the amplitude response given by the proposed tool and in blue the above function. Below are the amplitude responses of some moving averages with period 14.
Amplitude response of an EMA, the EMA is a IIR filter, therefore the amplitude response can't be made by taking the DFT of the impulse response (as this ones has infinite length), however our tool can give its frequency response.
Amplitude response of the Hull MA, as you can see some frequencies are amplified, this is common with low-lag filters.
Gaussian moving average (ALMA), with offset = 0.5 and sigma = 6.
Simple moving average high-pass filter amplitude response
Center of gravity bandpass filter amplitude response
Center of gravity bandreject filter.
IMPORTANT!: The amplitude response of adaptive moving averages is not stationary and might change over time.
Conclusion
A tool giving the amplitude response of any filter has been presented, of course this method is not efficient at all and has a low resolution of 50 points (the common resolution is of 512 points) and is difficult to work with, but has the merit to work on Tradingview and can give the frequency response of IIR filters, if you really need to see the frequency response of a filter then i recommend you to use the function freqz from the scipy package.
I still hope you will enjoy using this tool to have a look at the amplitude responses of your favorite moving averages.
I'am aware of the current situation, however i'am somehow feeling left out from the pinescript community, let me know via PM if i have done something to you and i'll do my best to fix any problems i might have caused (or i might be being parano xD)
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