Polynomial Regression Derivatives [Loxx]Polynomial Regression Derivatives is an indicator that explores the different derivatives of polynomial position. This indicator also includes a signal line. In a later release, alerts with signal markings will be added.
Polynomial Derivatives are as follows
1rst Derivative - Velocity: Velocity is the directional speed of a object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time (e.g. 60 km/h northbound). Velocity is a fundamental concept in kinematics, the branch of classical mechanics that describes the motion of bodies.
2nd Derivative - Acceleration: In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by the orientation of the net force acting on that object.
3rd Derivative - Jerk: In physics, jerk or jolt is the rate at which an object's acceleration changes with respect to time. It is a vector quantity (having both magnitude and direction). Jerk is most commonly denoted by the symbol j and expressed in m/s3 (SI units) or standard gravities per second (g0/s).
4th Derivative - Snap: Snap, or jounce, is the fourth derivative of the position vector with respect to time, or the rate of change of the jerk with respect to time. Equivalently, it is the second derivative of acceleration or the third derivative of velocity.
5th Derivative - Crackle: The fifth derivative of the position vector with respect to time is sometimes referred to as crackle. It is the rate of change of snap with respect to time.
6nd Derivative - Pop: The sixth derivative of the position vector with respect to time is sometimes referred to as pop. It is the rate of change of crackle with respect to time.
Included:
Loxx's Expanded Source Types
Loxx's Moving Averages
Polynomialregression
Polynomial Regression Bands w/ Extrapolation of Price [Loxx]Polynomial Regression Bands w/ Extrapolation of Price is a moving average built on Polynomial Regression. This indicator paints both a non-repainting moving average and also a projection forecast based on the Polynomial Regression. I've included 33 source types and 38 moving average types to smooth the price input before it's run through the Polynomial Regression algorithm. This indicator only paints X many bars back so as to increase on screen calculation speed. Make sure to read the tooltips to answer any questions you have.
What is Polynomial Regression?
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 modeled as an nth degree polynomial in x. Polynomial regression fits a nonlinear relationship between the value of x and the corresponding conditional mean of y, denoted E(y |x). Although polynomial regression fits a nonlinear model to the data, as a statistical estimation problem it is linear, in the sense that the regression function E(y | x) is linear in the unknown parameters that are estimated from the data. For this reason, polynomial regression is considered to be a special case of multiple linear regression .
Related indicators
Polynomial-Regression-Fitted Oscillator
Polynomial-Regression-Fitted RSI
PA-Adaptive Polynomial Regression Fitted Moving Average
Poly Cycle
Fourier Extrapolator of Price w/ Projection Forecast
PA-Adaptive Polynomial Regression Fitted Moving Average [Loxx]PA-Adaptive Polynomial Regression Fitted Moving Average is a moving average that is calculated using Polynomial Regression Analysis. The purpose of this indicator is to introduce polynomial fitting that is to be used in future indicators. This indicator also has Phase Accumulation adaptive period inputs. Even though this first indicator is for demonstration purposes only, its still one of the only viable implementations of Polynomial Regression Analysis on TradingView is suitable for trading, and while this same method can be used to project prices forward, I won't be doing that since forecasting is generally worthless and causes unavoidable repainting. This indicator only repaints on the current bar. Once the bar closes, any signal on that bar won't change.
For other similar Polynomial Regression Fitted methodologies, see here
Poly Cycle
What is the Phase Accumulation Cycle?
The phase accumulation method of computing the dominant cycle is perhaps the easiest to comprehend. In this technique, we measure the phase at each sample by taking the arctangent of the ratio of the quadrature component to the in-phase component. A delta phase is generated by taking the difference of the phase between successive samples. At each sample we can then look backwards, adding up the delta phases.When the sum of the delta phases reaches 360 degrees, we must have passed through one full cycle, on average.The process is repeated for each new sample.
The phase accumulation method of cycle measurement always uses one full cycle’s worth of historical data.This is both an advantage and a disadvantage.The advantage is the lag in obtaining the answer scales directly with the cycle period.That is, the measurement of a short cycle period has less lag than the measurement of a longer cycle period. However, the number of samples used in making the measurement means the averaging period is variable with cycle period. longer averaging reduces the noise level compared to the signal.Therefore, shorter cycle periods necessarily have a higher out- put signal-to-noise ratio.
What is Polynomial Regression?
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. Polynomial regression fits a nonlinear relationship between the value of x and the corresponding conditional mean of y, denoted E(y |x). Although polynomial regression fits a nonlinear model to the data, as a statistical estimation problem it is linear, in the sense that the regression function E(y | x) is linear in the unknown parameters that are estimated from the data. For this reason, polynomial regression is considered to be a special case of multiple linear regression.
Things to know
You can select from 33 source types
The source is smoothed before being injected into the Polynomial fitting algorithm, there are 35+ moving averages to choose from for smoothing
The output of the Polynomial fitting algorithm is then smoothed to create the signal, there are 35+ moving averages to choose from for smoothing
Included
Alerts
Signals
Bar coloring
