Student-t Weighted Acceleration & Velocity⚙️ Student-t Weighted Acceleration & Velocity
Author: © GabrielAmadeusLau
Category: Momentum, Smoothing, Divergence Detection
🔍 Overview
Student-t Weighted Acceleration & Velocity is a precision-engineered momentum indicator designed to analyze the rate of price change (velocity) and rate of change of velocity (acceleration). It leverages Student-t weighted smoothing, bandpass filtering, and divergence detection to reveal underlying momentum trends, shifts, and potential reversals with high sensitivity and low noise.
🧠 Key Features
🌀 1. Student-t Weighted Moving Average
Applies Student-t distribution weights to price data.
Controlled by:
ν (Degrees of Freedom): Lower ν increases weight on recent data, improving sensitivity to fast-moving markets.
Window Length: Sets the lookback period for weighted averaging.
🚀 2. Velocity & Acceleration Calculation
Velocity: Measures how fast price is moving over time.
Acceleration: Measures the change in velocity, revealing turning points.
Both are calculated via:
Butterworth High-pass Filter
Super Smoother Low-pass Filter
Fast Root Mean Square (RMS) normalization
Optionally smoothed using a Super Smoother EMA.
🎯 3. Signal Conditions
Strong Up: When smoothed velocity crosses above the overbought threshold and acceleration is positive.
Strong Down: When smoothed velocity crosses below the oversold threshold and acceleration is negative.
Visual cues:
Green & red triangle shapes for signals.
Colored histogram & column plots.
Optional bar coloring based on A/V behavior.
🔎 4. Divergence Detection Engine
Built-in multi-timeframe divergence system with:
Bullish/Bearish Regular Divergence
Bullish/Bearish Hidden Divergence
Customizable settings:
Pivot detection, confirmation logic, lookback limits.
Heikin Ashi mode for smoothed divergence detection.
Configurable line style, width, and color.
Visual plots of divergence lines on price chart.
⚙️ Custom Inputs
A/V Calculation Parameters:
Lookback period, filter lengths (Butterworth, Super Smoother, RMS), EMA smoothing.
Divergence Settings:
Enable/disable confirmation, show last divergence only.
Adjustable pivot period and max lookback bars.
Heikin Ashi Mode:
Option to use Heikin Ashi candles for divergence detection only (without switching chart type).
Thresholds:
Overbought/Oversold Sigma levels for strong signal detection.
🔔 Alerts Included
Strong Up Alert: Momentum and acceleration aligned bullishly.
Strong Down Alert: Momentum and acceleration aligned bearishly.
All Divergence Types:
Bullish/Bearish Regular Divergence
Bullish/Bearish Hidden Divergence
Aggregated Divergence Alerts
📌 Use Cases
Spot momentum bursts and reversals with confirmation from both velocity and acceleration.
Identify divergence-based signals for early entries/exits.
Apply across multiple timeframes or pair with other trend filters.
Student-t
Arbitrary Price Point Probability (APPP)The "Arbitrary Price Point Probability" indicator is designed to calculate the probability of a given price point occurring within a certain range of prices. The indicator uses statistical analysis to determine the likelihood of a specific price point appearing based on the market data.
The indicator works by taking the input price, which is the price point for which the probability is being calculated. The indicator then calculates the mean and standard deviation of the prices over a certain period specified by the user. The length of the period for calculating the mean and standard deviation is also specified by the user.
Once the mean and standard deviation have been calculated, the indicator uses them to calculate the probability of the input price point occurring within the range of prices over the specified period. The indicator does this by calculating the z-score, which is the number of standard deviations between the input price point and the mean price. The z-score is then used to calculate the probability using a t-distribution probability density function.
The t-distribution probability density function used by the indicator is a mathematical function that describes the likelihood of obtaining a particular value from a t-distribution. A t-distribution is a statistical distribution used when the sample size is small, and the population standard deviation is unknown.
The indicator also uses a binary search algorithm to find the t-value for a given confidence level. The t-value is the number of standard deviations from the mean at which the confidence interval is set. The confidence level is set by the user, and the default value is 99%.
Overall, the "Arbitrary Price Point Probability" indicator is a useful tool for traders who want to determine the probability of a particular price point occurring within a certain range of prices. The indicator can be used in conjunction with other technical analysis tools to make more informed trading decisions.
