PA-Adaptive Hull Parabolic [Loxx]The PA-Adaptive Hull Parabolic is not your typical trading indicator. It synthesizes the computational brilliance of two famed technicians: John Ehlers and John Hull. Let's demystify its sophistication.
█ Ehlers' Phase Accumulation
John Ehlers is well-known in the trading community for his digital signal processing approach to market data. One of his standout techniques is phase accumulation. This method identifies the dominant cycle in the market by accumulating the phases of individual cycles. By doing so, it "adapts" to real-time market conditions.
Here's the brilliance of phase accumulation in this code
The indicator doesn't merely use a static look-back period. Instead, it dynamically determines the dominant market cycle through phase accumulation.
The calcComp function, rooted in Ehlers' methodology, provides a complex computation using a digital signal processing approach to filter out market noise and pinpoint the current cycle's frequency.
By measuring and adapting to the instantaneous period of the market, it ensures that the indicator remains relevant, especially in non-stationary market conditions.
Hull's Moving Average
John Hull introduced the Hull Moving Average (HMA) aiming to reduce lag and improve smoothing. The HMA's essence lies in its weighted average computation, prioritizing more recent prices.
This code takes an adaptive twist on the HMA
Instead of a fixed period, the HMA uses the dominant cycle length derived from Ehlers' phase accumulation. This makes the HMA not just fast and smooth, but also adaptive to the dominant market rhythm.
The intricate iLwmp function in the script provides this adaptive HMA computation. It's a weighted moving average, but its length isn't static; it's based on the previously determined dominant market cycle.
█ Trading Insights
The indicator paints the bars to represent the immediate trend: green for bullish and red for bearish.
Entry points, both long ("L") and short ("S"), are presented visually. These are derived from crossovers of the adaptive HMA, a clear indication of a potential shift in the trend.
Additionally, alert conditions are set, ready to notify a trader when these crossovers occur, ensuring real-time actionable insights.
█ Conclusion
The PA-Adaptive Hull Parabolic is a masterclass in advanced technical indicator design. By marrying John Ehlers' adaptive phase accumulation with John Hull's HMA, it creates a dynamic, responsive, and precise tool for traders. It's not just about capturing the trend; it's about understanding the very rhythm of the market.
Paadaptive
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
