R2-Adaptive RegressionIntroduction
I already mentioned various problems associated with the lsma, one of them being overshoots, so here i propose to use an lsma using a developed and adaptive form of 1st order polynomial to provide several improvements to the lsma. This indicator will adapt to various coefficient of determinations while also using various recursions.
More In Depth
A 1st order polynomial is in the form : y = ax + b , our indicator however will use : y = a*x + a1*x1 + (1 - (a + a1))*y , where a is the coefficient of determination of a simple lsma and a1 the coefficient of determination of an lsma who try to best fit y to the price.
In some cases the coefficient of determination or r-squared is simply the squared correlation between the input and the lsma. The r-squared can tell you if something is trending or not because its the correlation between the rough price containing noise and an estimate of the trend (lsma) . Therefore the filter give more weight to x or x1 based on their respective r-squared, when both r-squared is low the filter give more weight to its precedent output value.
Comparison
lsma and R2 with both length = 100
The result of the R2 is rougher, faster, have less overshoot than the lsma and also adapt to market conditions.
Longer/Shorter terms period can increase the error compared to the lsma because of the R2 trying to adapt to the r-squared. The R2 can also provide good fits when there is an edge, this is due to the part where the lsma fit the filter output to the input (y2)
Conclusion
I presented a new kind of lsma that adapt itself to various coefficient of determination. The indicator can reduce the sum of squares because of its ability to reduce overshoot as well as remaining stationary when price is not trending. It can be interesting to apply exponential averaging with various smoothing constant as long as you use : (1- (alpha+alpha1)) at the end.
Thanks for reading
Regression
Pseudo Polynomial ChannelIntroduction
Back when i started using pine i made a script called periodic channel who aimed to rescale an average correlated sine wave to the price...don't worked very well. So i tried to fix problems induced by the indicator without much success, i had to redo it from scratch while abandoning the idea of rescaling correlated smooth functions to the price, at that time i also received requests regarding polynomial channel, some plateformes included this indicator, this led me to the idea to estimate it in order to both respond to the periodic channel problems and the requests i received, i have tried many many things and recently i tweaked a linear extrapolation to have an approximation.
Linear Extrapolation To Pseudo Polynomial Regression
I could be wrong but a polynomial regression must use constant parameters in order to provide a really smooth output, at least constant for a set of time. The moving averages forms (Savitzky-Golay moving average) who smooth polynomials across a window to the data don't have such smoothness, so how to estimate a polynomial regression while having a parameter providing control over the smoothness, a response to this is by using a recursive linear extrapolation. I posted a linear extrapolation indicator long ago, i used the same formula while adding a function to morph the output and the input in the form of :
morph * output + (1-morph) * input
How can this provide an estimate of a polynomial regression ? Well i'm not even sure myself but if you use the output as input (morph = 1) for the linear extrapolation function you should get a rough estimate of a line, this is what i thought at first and it proved to be right
Based on this observation i thought that it would be possible to get polynomial results by lowering morph, and as expected it worked well but showed a periodic pattern, this is why i smooth k in line 10.
0.9 for morph work well, higher values create sometimes smoother results but damage heavily the estimation.
Parameters
Morph have been introduced earlier, it control the amount of output and input the linear extrapolation should process, lower values create rougher but more stables results, if you see that the estimation is going nuts lower morph or change length, also lower length if you increase morph .
High overshoot, morph to 0.8 can help have a better estimation at the cost of less smoothness.
Length control the indicator smoothing, this parameter differ heavily from other filters, therefore low values can create mid/long term smoothing, it can also depend on which market instrument you are applying it, so there are no fixed optimal length.
Mult control how spread the bands are, to do so mult multiply the cumulative mean error, you can change this error measurement by anything you want like standard deviation/atr/range but take into account that you may create a separate parameter to control the error instead of length . Mult can be a float and like length can have different optimal values depending on the market the indicator is applied to.
Flatten do exactly what is name imply, it flatten the overall output to have a better estimation, can be a float. The result is less smooth.
Flatten = 2
More Exemples
BTCUSD length = 25 and mult = 4
XPDUSD length = 25 and mult = 1
ALPHABET length = 6 and morph = 0.99
Conclusion
I tried to estimate a polynomial channel by using recursion in the linear extrapolation function. This build is way more stable than the periodic channel but its still a bit inaccurate in my opinion. I hope this code can still help someone build something really nice, if so share your results :)
I apologize for those expecting a legit polynomial channel build but i really don't know how to do that, as i said parameters for the regression must be constants, i hope it still fine :)
Thanks for reading !
Fast Z-ScoreIntroduction
The ability of the least squares moving average to provide a great low lag filter is something i always liked, however the least squares moving average can have other uses, one of them is using it with the z-score to provide a fast smoothing oscillator.
The Indicator
The indicator aim to provide fast and smooth results. length control the smoothness.
The calculation is inspired from my sample correlation coefficient estimation described here
Instead of using the difference between a moving average of period length/2 and a moving average of period length , we use the difference between a lsma of period length/2 and a lsma of period length , this difference is then divided by the standard deviation. All those calculations use the price smoothed by a moving average as source.
The yellow version don't divide the difference by a standard deviation, you can that it is less reactive. Both version have length = 200
Conclusion
I presented a smooth and responsive version of a z-score, the result could be used to estimate an even faster lsma by using the line rescaling technique and our indicator as correlation coefficient.
Hope you like it, feel free to modify it and share your results ! :)
Notes
I have been requested a lot of indicators lately, from mt4 translations to more complex time series analysis methods, this accumulation of work made that it is impossible for me to publish those within a short period of time, also some are really complex. I apologize in advance for the inconvenience, i will try to do my best !
Robust Weighting OscillatorIntroduction
A simple oscillator using a modified lowess architecture, good in term of smoothness and reactivity.
Lowess Regression
Lowess or local regression is a non-parametric (can be used with data not fitting a normal distribution) smoothing method. This method fit a curve to the data using least squares.
In order to have a lowess regression one must use tricube kernel for the weightings w , the weightings are determined using a k-nearest-neighbor model.
lowess is then calculated like so :
Σ (wG(y-a-bx)^2)
Our indicator use G , a , b and remove the square as well as replacing x by y
Conclusion
The oscillator is simple and nothing revolutionary but its still interesting to have new indicators.
Lowess would be a great method to be made on pinescript, i have an estimate but its not that good. Some codes use a simple line equation in order to estimate a lowess smoother, i can describe it as ax + b where a is a smooth oscillator, b some kind of filter defined by lp + bp with lp a smooth low pass filter and bp a bandpass filter, x is a variable dependent of the smoothing span.
Dorsey InertiaThis indicator was originally developed by Donald Dorsey (Stocks & Commodities, V.13:9 (September, 1995): "Refining the Relative Volatility Index").
Inertia is based on Relative Volatility Index (RVI) smoothed using linear regression.
In physics, inertia is the tendency of an object to resist to acceleration. Dorsey chose this name because he believes that trend and inertia are related and that it takes more effort and energy to reverse the direction of a stock or market than to keep it in the same direction. He argues that the volatility is the simplest and most accurate measure of inertia.
When the indicator is below 50, it signals bearish market sentiment and when the indicator is above 50 it signals a bullish trend.
Good luck!
Kirshenbaum BandsThis indicator was originally developed by Paul Kirshenbaum, a mathematician with a Ph.D. in economics from New York University.
It uses the standard error of linear regression lines of the closing price to determine band width. This has the effect of measuring volatility around the current trend, rather than measuring volatility for changes in trend.
Good luck!
Quadratic Regression Slope [DW]This is a study geared toward identifying price trends using Quadratic regression.
Quadratic regression is the process of finding the equation of a parabola that best fits the set of data being analyzed.
In this study, first a quadratic regression curve is calculated, then the slope of the curve is calculated and plotted.
Custom bar colors are included. The color scheme is based on whether the slope is positive or negative, and whether it is increasing or decreasing.
Quadratic RegressionA quadratic regression is the process of finding the equation that best fits a set of data.This form of regression is mainly used for smoothing data shaped like a parabola.
Because we can use short/midterm/longterm periods we can say that we use a Quadratic Least Squares Moving Average or a Moving Quadratic Regression.
Like the Linear Regression (LSMA) a Quadratic regression attempt to minimize the sum of squares (sum of the squared difference between a set of data and an estimator), this is why
those kinds of filters have low lag .
Here the difference between a Least Squared Moving Average ( green ) and a Quadratic Regression ( red ) of both period 500
Here it look like the Quadratic Regression have a best fit than the LSMA
Regression OscillatorRegression Oscillator indicator script.
This indicator was originally developed by Richard Goedde (Stocks & Commodities V.15:3, Timing A Stock Using The Regression Oscillator).
Line Regression Intercept Linear Regression Intercept is one of the indicators calculated by using the
Linear Regression technique. Linear regression indicates the value of the Y
(generally the price) when the value of X (the time series) is 0. Linear
Regression Intercept is used along with the Linear Regression Slope to create
the Linear Regression Line. The Linear Regression Intercept along with the Slope
creates the Regression line.
LinearRegressionChannelBreakoutMy first idea about the linear regression channel... It is free and available for everybody.
Fractal Regression Bands [DW]This study is an experimental regression curve built around fractal and ATR calculations.
First, Williams Fractals are calculated, and used as anchoring points.
Next, high anchor points are connected to negative sloping lines, and low anchor points to positive sloping lines. The slope is a specified percentage of the current ATR over the sampling period.
The median between the positive and negative sloping lines is then calculated, then the best fit line (linear regression) of the median is calculated to generate the basis line.
Lastly, a Golden Mean ATR is taken of price over the sampling period and multiplied by 1/2, 1, 2, and 3. The results are added and subtracted from the basis line to generate the bands.
Williams Fractals are included in the plots. The color scheme indicated whether each fractal is engulfing or non-engulfing.
Custom bar color scheme is included.
Momentum Linear RegressionThe original script was posted on ProRealCode by user Nicolas.
This is an indicator made of the linear regression applied to the rate of change of price (or momentum). I made a simple signal line just by duplicating the first one within a period decay in the past, to make those 2 lines cross. You can add more periods decay to made signal smoother with less false entry.
Function 2 Point Line using UNIX TIMESTAMP V1experimental:
draws a line from 2 vectors(price, time)
update:
reformatted the function,
added automatic detection of the period multiplier by approximation(gets a bit goofy with stocks/week time),
example using timestamp() function.
offsetting is still bugged, i cant find a way around it atm.
ORDINARY LEAST SQUARES Slope by @XeL_ArjonaORDINARY LEAST SQUARES Slope by @XeL_Arjona
Ver. 1 by Ricardo M Arjona @XeL_Arjona
DISCLAIMER:
The Following indicator/code IS NOT intended to be a formal investment advice or recommendation by the author, nor should be construed as such. Users will be fully responsible by their use regarding their own trading vehicles/assets.
The embedded code and ideas within this work are FREELY AND PUBLICLY available on the Web for NON LUCRATIVE ACTIVITIES and must remain as is.
WHAT'S THIS?
This is a REAL mathematically approach of an ORDINARY LEAST SQUARES LINE FITTING SLOPE as TradingView currently don't have a native one embedded, neither as a pine function. Other "Sope" indicators from this linear regression model I found on public library are currently based on "momentum" rather tan slope.
Any modifications or additions are quite welcome!
Cheers!
@XeL_Arjona
BUY & SELL PRESSURE XeLMod V2BUY & SELL PRESSURE Oscillator
Ver. 2.0 XelMod
WHAT'S THIS?
This is an UPDATED version of a previous script already posted.
List of changes from previous script:
Separated as Column Histogram just the Regressive (Rate-Of-Change) Force of the indicator which gives a faster response of the trend.
Default period is now set to 81, as better Oscillator swing lagging.
This is an excelent momentum indicator very similar to ADX but in a candle weighting distribution rather than ranges.
For additional reference:
Karthik Marar BUY AND SELL PRESSURE INDICATORS.
Cheers!
Any feedback will be welcome...
@XeL_Arjona
Standard Error of the Estimate -Composite Bands-Standard Error of the Estimate - Code and adaptation by @glaz & @XeL_arjona
Ver. 2.00.a
Original implementation idea of bands by:
Traders issue: Stocks & Commodities V. 14:9 (375-379):
Standard Error Bands by Jon Andersen
This code is a former update to previous "Standard Error Bands" that was wrongly applied given that previous version in reality use the Standard Error OF THE MEAN, not THE ESTIMATE as it should be used by Jon Andersen original idea and corrected in this version.
As always I am very Thankfully with the support at the Pine Script Editor chat room, with special mention to user @glaz in order to help me adequate the alpha-beta (y-y') algorithm, as well to give him full credit to implement the "wide" version of the former bands.
For a quick and publicly open explanation of this truly statistical (regression analysis) indicator, you can refer at Here!
Extract from the former URL:
Standard Error Bands are quite different than Bollinger's. First, they are bands constructed around a linear regression curve. Second, the bands are based on two standard errors above and below this regression line. The error bands measure the standard error of the estimate around the linear regression line. Therefore, as a price series follows the course of the regression line the bands will narrow, showing little error in the estimate. As the market gets noisy and random, the error will be greater resulting in wider bands.
[STRATEGY] Follow the Janet YellenIn the era of central bank's helicopter money, the market will always be skyrocketing up and up given enough time.
What's the strategy to profit from indices?
Only short the market when its in a state of euphoria /irrational exuberance bubble, or sell when it is confirmed (20% drawdown). Otherwise, you really have no reason not to long at every chance.
Conclusion:
Follow the printing press like a sheep.
[RS]Decay Channel Candles V0EXPERIMENTAL: Experiment using Linear Regression based on %atr for decay(decay option is a mutiplier for the atr).
[RS]Linear Regression Bands V1experiment with linear regression, the purpose was to catch break outs early, but it creates to much visual noise
same as version 0 but with added margin filter and signal to mark entrys
