FIT

Daily Polynomial Regressions [LuxAlgo]The Daily Polynomial Regressions indicator uses matrix calculations to solve polynomial regression (degrees 1-4) on a daily basis, providing a dynamic visualization of intraday trends and price distribution. By fitting a curved line to price action throughout the trading session, it helps traders identify the underlying momentum and strength of the daily trend. The fit for the current day may be subject to repainting 🔶 USAGE The indicator highlights each trading day with a dynamic box that expands as the daily high and low are updated. Inside this box, a polynomial regression curve is plotted using a polyline to represent the best-fit path of price action for that specific day. The tool is particularly useful for identifying: Intraday Trend Direction: The background and curve color change based on whether the current regression endpoint is higher (bullish) or lower (bearish) than its daily starting point. Trend Strength: A higher R² value indicates that the price action is following the regression curve more closely, suggesting a more "orderly" or predictable trend. Mean Reversion: The regression curve acts as a dynamic moving average that adapts to the specific curvature of the day's price movement, highlighting potential overextensions. 🔶 DETAILS 🔹 Polynomial Degrees The indicator allows users to select between different regression complexities: Degree 1 (Linear): Fits a straight line. Best for identifying simple linear trends. Degree 2 (Quadratic): Fits a simple curve (parabola). Useful for identifying trend exhaustion or rounding tops/bottoms. Degree 3 (Cubic) & 4 (Quartic): Provides a highly flexible curve that can account for multiple shifts in momentum within a single day. 🔹 Matrix Calculations Unlike standard moving averages, this script solves the Normal Equation (X'X)B = X'Y using matrix inversion to find the coefficients for the selected polynomial degree. All accumulators reset at the start of each new day to ensure the analysis remains strictly intraday. 🔹 R-Squared (R²) The R² statistic is calculated as 1 - (SSres / SStot). It represents the proportion of variance for the price that's explained by the polynomial model. A value of 1.0 would mean the price is perfectly following the curve. 🔶 SETTINGS Polynomial Degree: Determines the complexity of the regression curve (1: Linear, 2: Quadratic, 3: Cubic, 4: Quartic). Show Median Line: Toggles the visibility of a dashed line representing the midpoint (HL2) of the daily high-low range. Show R² Label: Displays the R-squared statistic at the top of the daily box to indicate how well the curve fits the price data. Bullish Color: The color used for the curve and box background when the trend is positive. Bearish Color: The color used for the curve and box background when the trend is negative. Fill Transparency: Adjusts the opacity of the daily background highlighting.

Indicator

by LuxAlgo

Gaussian Volume Profile [LuxAlgo]The Gaussian Volume Profile indicator is a sophisticated volume analysis tool that uses the Levenberg-Marquardt optimization algorithm to fit a Sum of Gaussians model to historical volume distribution. This approach transcends traditional discrete volume profiles by providing a continuous, noise-reduced representation of liquidity clusters, allowing for the precise identification of high-volume nodes and their respective price boundaries. 🔶 USAGE The indicator projects a lateral volume density map to the right of the current price action. Users can utilize this tool to identify "fair value" zones where the Gaussian peaks are most concentrated. Unlike standard profiles that show jagged horizontal bars, this tool provides a smooth "fit" line that highlights the true center of gravity for volume at specific price levels. 🔹 Identifying High-Volume Nodes The script automatically detects local maxima (peaks) within the fitted Gaussian model. These peaks represent the most significant price levels where the highest density of trading occurred. Horizontal dashed lines are drawn at these apexes, color-coded to match the specific Gaussian component that is most dominant at that price. 🔹 Zone Width and Volatility By observing the width (standard deviation) of the individual Gaussian components (the dotted curves), traders can gauge the "breadth" of a value area. A narrow, sharp peak suggests a very specific price level of agreement, while a wide, shallow curve indicates a broad range where volume was distributed less precisely. 🔶 DETAILS This tool represents a scientific advancement over regular Volume Profiles by applying a Gaussian Density model to market data: Noise Reduction: Discrete profiles are often "noisy," with small volume gaps between price ticks. The Sum of Gaussians model acts as a sophisticated filter, smoothing out insignificant variances to reveal the underlying structural liquidity. Levenberg-Marquardt Optimization: The script utilizes the LM algorithm, a standard in non-linear least squares problems, to iteratively refine the fit of multiple Gaussian pulses. This ensures the model converges on the most mathematically accurate representation of the volume data. Precise Liquidity Centers: While a standard profile bin might be several ticks wide, the Gaussian apex provides a mathematically derived "center" ($\mu$) for liquidity, often offering more precise support and resistance levels. Continuous Distribution: Because it models volume as a continuous function, it can estimate volume density between discrete price bins, providing a more fluid view of market interest. The visual output combines a lateral histogram with a bold Gaussian density curve, color-coded components, and auto-detected peak levels for a comprehensive view of institutional interest. 🔶 SETTINGS 🔹 Profile Settings Lookback Window: The number of historical bars used to calculate the volume profile distribution. Number of Bins: Determines the vertical resolution of the profile. More bins provide more detail but require more computation. 🔹 Gaussian Settings Max Potential Peaks: The maximum number of Gaussian components (nodes) the algorithm will attempt to fit to the data. Max Iterations: Controls how many times the LM optimizer refines the fit. Higher values improve accuracy but may impact performance. Initial Lambda: The damping factor for the optimization algorithm, affecting the early steps of the fitting process. 🔹 Visuals Histogram Resolution: The maximum horizontal length of the projected histogram and fit line, measured in bar widths. Highlight Window Range: Toggles a visual background box covering the historical lookback area for context. Highlight Detected Peaks: Detects local maxima in the final fit and draws horizontal dashed levels at those price points. Fit Color: Sets the static color for the main density curve. Auto: When enabled, the fit color automatically adapts to your chart's foreground color (e.g., white on dark backgrounds).

Indicator

by LuxAlgo

FunctionMatrixSolve Library "FunctionMatrixSolve" Matrix Equation solution for Ax = B, finds the value of x. solve(A, B) Solves Matrix Equation for Ax = B, finds value for x. Parameters: A : matrix, Square matrix with data values. B : matrix, One column matrix with data values. Returns: matrix with X, x = A^-1 b, assuming A is square and has full rank introcs.cs.princeton.edu

Library

by RicardoSantos

FunctionPolynomialFit Library "FunctionPolynomialFit" Performs Polynomial Regression fit to data. In statistics, polynomial regression is a form of regression analysis in which the relationship between the independent variable x and the dependent variable y is modelled as an nth degree polynomial in x. reference: en.wikipedia.org www.bragitoff.com gauss_elimination(A, m, n) Perform Gauss-Elimination and returns the Upper triangular matrix and solution of equations. Parameters: A : float matrix, data samples. m : int, defval=na, number of rows. n : int, defval=na, number of columns. Returns: float array with coefficients. polyfit(X, Y, degree) Fits a polynomial of a degree to (x, y) points. Parameters: X : float array, data sample x point. Y : float array, data sample y point. degree : int, defval=2, degree of the polynomial. Returns: float array with coefficients. note: p(x) = p * x**deg + ... + p interpolate(coeffs, x) interpolate the y position at the provided x. Parameters: coeffs : float array, coefficients of the polynomial. x : float, position x to estimate y. Returns: float.

Library

by RicardoSantos