STD-Filtered, Adaptive Exponential Hull Moving Average [Loxx]STD-Filtered, Adaptive Exponential Hull Moving Average is a Kaufman Efficiency Ratio Adaptive Hull Moving Average that uses EMA instead of WMA for its computation. I've also added standard deviation stepping to further smooth the signal. Using EMA instead of WMA turns the Hull into what's called the AEHMA. You can read more about the EHMA here: eceweb1.rutgers.edu
What is the traditional Hull Moving Average?
The Hull Moving Average (HMA) attempts to minimize the lag of a traditional moving average while retaining the smoothness of the moving average line. Developed by Alan Hull in 2005, this indicator makes use of weighted moving averages to prioritize more recent values and greatly reduce lag. The resulting average is more responsive and well-suited for identifying entry points.
What is Kaufman's Efficiency Ratio?
The Efficiency Ratio (ER) was first presented by Perry Kaufman in his 1995 book ‘Smarter Trading‘. It is calculated by dividing the price change over a period by the absolute sum of the price movements that occurred to achieve that change. The resulting ratio ranges between 0 and 1 with higher values representing a more efficient or trending market.
The value of the ER ranges between 0 and 1. It has the value of 1 when prices move in the same direction for the full time over which the indicator is calculated, e.g. n bars period. It has a value of 0 when prices are unchanged over the n periods. When prices move in wide swings within the interval, the sum of the denominator becomes very large compared to the numerator and ER approaches zero.
Some uses for ER:
A qualifier for a trend following trade; a trend is considered “persistent” only when RE is above a certain value, e.g. 0.3 or 0.4 .
A filter to screen out choppy stocks/markets, where breakouts are frequently “fakeouts”.
In an adaptive trading system, helping to determine whether to apply a trend following algorithm or a mean reversion algorithm.
It is used in the calculation of Kaufman’s Adaptive Moving Average (KAMA).
How to calculate the Hull Adaptive Moving Average (HAMA)
Find Signal to Noise ratio (SNR)
Normalize SNR from 0 to 1
Calculate adaptive alphas
Apply EMAs
Included
Bar coloring
Signals
Alerts
Loxx's Expanded Source Types
Loxx
Ehlers Linear Extrapolation Predictor [Loxx]Ehlers Linear Extrapolation Predictor is a new indicator by John Ehlers. The translation of this indicator into PineScript™ is a collaborative effort between @cheatcountry and I.
The following is an excerpt from "PREDICTION" , by John Ehlers
Niels Bohr said “Prediction is very difficult, especially if it’s about the future.”. Actually, prediction is pretty easy in the context of technical analysis. All you have to do is to assume the market will behave in the immediate future just as it has behaved in the immediate past. In this article we will explore several different techniques that put the philosophy into practice.
LINEAR EXTRAPOLATION
Linear extrapolation takes the philosophical approach quite literally. Linear extrapolation simply takes the difference of the last two bars and adds that difference to the value of the last bar to form the prediction for the next bar. The prediction is extended further into the future by taking the last predicted value as real data and repeating the process of adding the most recent difference to it. The process can be repeated over and over to extend the prediction even further.
Linear extrapolation is an FIR filter, meaning it depends only on the data input rather than on a previously computed value. Since the output of an FIR filter depends only on delayed input data, the resulting lag is somewhat like the delay of water coming out the end of a hose after it supplied at the input. Linear extrapolation has a negative group delay at the longer cycle periods of the spectrum, which means water comes out the end of the hose before it is applied at the input. Of course the analogy breaks down, but it is fun to think of it that way. As shown in Figure 1, the actual group delay varies across the spectrum. For frequency components less than .167 (i.e. a period of 6 bars) the group delay is negative, meaning the filter is predictive. However, the filter has a positive group delay for cycle components whose periods are shorter than 6 bars.
Figure 1
Here’s the practical ramification of the group delay: Suppose we are projecting the prediction 5 bars into the future. This is fine as long as the market is continued to trend up in the same direction. But, when we get a reversal, the prediction continues upward for 5 bars after the reversal. That is, the prediction fails just when you need it the most. An interesting phenomenon is that, regardless of how far the extrapolation extends into the future, the prediction will always cross the signal at the same spot along the time axis. The result is that the prediction will have an overshoot. The amplitude of the overshoot is a function of how far the extrapolation has been carried into the future.
But the overshoot gives us an opportunity to make a useful prediction at the cyclic turning point of band limited signals (i.e. oscillators having a zero mean). If we reduce the overshoot by reducing the gain of the prediction, we then also move the crossing of the prediction and the original signal into the future. Since the group delay varies across the spectrum, the effect will be less effective for the shorter cycles in the data. Nonetheless, the technique is effective for both discretionary trading and automated trading in the majority of cases.
EXPLORING THE CODE
Before we predict, we need to create a band limited indicator from which to make the prediction. I have selected a “roofing filter” consisting of a High Pass Filter followed by a Low Pass Filter. The tunable parameter of the High Pass Filter is HPPeriod. Think of it as a “stone wall filter” where cycle period components longer than HPPeriod are completely rejected and cycle period components shorter than HPPeriod are passed without attenuation. If HPPeriod is set to be a large number (e.g. 250) the indicator will tend to look more like a trending indicator. If HPPeriod is set to be a smaller number (e.g. 20) the indicator will look more like a cycling indicator. The Low Pass Filter is a Hann Windowed FIR filter whose tunable parameter is LPPeriod. Think of it as a “stone wall filter” where cycle period components shorter than LPPeriod are completely rejected and cycle period components longer than LPPeriod are passed without attenuation. The purpose of the Low Pass filter is to smooth the signal. Thus, the combination of these two filters forms a “roofing filter”, named Filt, that passes spectrum components between LPPeriod and HPPeriod.
Since working into the future is not allowed in EasyLanguage variables, we need to convert the Filt variable to the data array XX . The data array is first filled with real data out to “Length”. I selected Length = 10 simply to have a convenient starting point for the prediction. The next block of code is the prediction into the future. It is easiest to understand if we consider the case where count = 0. Then, in English, the next value of the data array is equal to the current value of the data array plus the difference between the current value and the previous value. That makes the prediction one bar into the future. The process is repeated for each value of count until predictions up to 10 bars in the future are contained in the data array. Next, the selected prediction is converted from the data array to the variable “Prediction”. Filt is plotted in Red and Prediction is plotted in yellow.
The Predict Extrapolation indicator is shown above for the Emini S&P Futures contract using the default input parameters. Filt is plotted in red and Predict is plotted in yellow. The crossings of the Predict and Filt lines provide reliable buy and sell timing signals. There is some overshoot for the shorter cycle periods, for example in February and March 2021, but the only effect is a late timing signal. Further reducing the gain and/or reducing the BarsFwd inputs would provide better timing signals during this period.
ADDITIONS
Loxx's Expanded source types:
Library for expanded source types:
Explanation for expanded source types:
Three different signal types: 1) Prediction/Filter crosses; 2) Prediction middle crosses; and, 3) Filter middle crosses.
Bar coloring to color trend.
Signals, both Long and Short.
Alerts, both Long and Short.
STD-Filtered, Gaussian-Kernel-Weighted Moving Average BT [Loxx]STD-Filtered, Gaussian-Kernel-Weighted Moving Average BT is the backtest for the following indicator
Included:
This backtest uses a special implementation of ATR and ATR smoothing called "True Range Double" which is a range calculation that accounts for volatility skew.
You can set the backtest to 1-2 take profits with stop-loss
Signals can't exit on the same candle as the entry, this is coded in a way for 1-candle delay post entry
This should be coupled with the INDICATOR version linked above for the alerts and signals. Strategies won't paint the signal "L" or "S" until the entry actually happens, but indicators allow this, which is repainting on current candle, but this is an FYI if you want to get serious with Pinescript algorithmic botting
You can restrict the backtest by dates
It is advised that you understand what Heikin-Ashi candles do to strategies, the default settings for this backtest is NON Heikin-Ashi candles but you have the ability to change that in the source selection
This is a mathematically heavy, heavy-lifting strategy. Make sure you do your own research so you understand what is happening here.
STD-Filtered, Gaussian-Kernel-Weighted Moving Average is a moving average that weights price by using a Gaussian kernel function to calculate data points. This indicator also allows for filtering both source input price and output signal using a standard deviation filter.
Purpose
This purpose of this indicator is to take the concept of Kernel estimation and apply it in a way where instead of predicting past values, the weighted function predicts the current bar value at each bar to create a moving average that is suitable for trading. Normally this method is used to create an array of past estimators to model past data but this method is not useful for trading as the past values will repaint. This moving average does NOT repaint, however you much allow signals to close on the current bar before taking the signal. You can compare this to Nadaraya-Watson Estimator wherein they use Nadaraya-Watson estimator method with normalized kernel weighted function to model price.
What are Kernel Functions?
A kernel function is used as a weighing function to develop non-parametric regression model is discussed. In the beginning of the article, a brief discussion about properties of kernel functions and steps to build kernels around data points are presented.
Kernel Function
In non-parametric statistics, a kernel is a weighting function which satisfies the following properties.
A kernel function must be symmetrical. Mathematically this property can be expressed as K (-u) = K (+u). The symmetric property of kernel function enables its maximum value (max(K(u)) to lie in the middle of the curve.
The area under the curve of the function must be equal to one. Mathematically, this property is expressed as: integral −∞ + ∞ ∫ K(u)d(u) = 1
Value of kernel function can not be negative i.e. K(u) ≥ 0 for all −∞ < u < ∞.
Kernel Estimation
In this article, Gaussian kernel function is used to calculate kernels for the data points. The equation for Gaussian kernel is:
K(u) = (1 / sqrt(2pi)) * e^(-0.5 *(j / bw )^2)
Where xi is the observed data point. j is the value where kernel function is computed and bw is called the bandwidth. Bandwidth in kernel regression is called the smoothing parameter because it controls variance and bias in the output.
