 # 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