IIR Least-Squares EstimateIntroduction
Another lsma estimate, i don't think you are surprised, the lsma is my favorite low-lag filter and i derived it so many times that our relationship became quite intimate. So i already talked about the classical method, the line-rescaling method and many others, but we did not made to many IIR estimate, the only one was made using a general filter estimator and was pretty inaccurate, this is why i wanted to retry the challenge.
Before talking about the formula lets breakdown again what IIR mean, IIR = infinite impulse response, the impulse response of an IIR filter goes on forever, this is why its infinite, such filters use recursion, this mean they use output's as input's, they are extremely efficient.
The Calculation
The calculation is made with only 1 pole, this mean we only use 1 output value with the same index as input, more poles often means a transition band closer to the cutoff frequency.
Our filter is in the form of :
y = a*x+y - a*ema(y,length/2)
where y = x when t = 1 and y(1) when t > 2 and a = 4/(length+2)
This is also an alternate form of exponential moving average but smoothing the last output terms with another exponential moving average reduce the lag.
Comparison
Lets see the accuracy of our estimate.
Sometimes our estimate follow better the trend, there isn't a clear result about the overshoot/undershoot response, sometimes the estimate have less overshoot/undershoot and sometime its the one with the highest.
The estimate behave nicely with short length periods.
Conclusion
Some surprises, the estimate can at least act as a good low-lag filter, sometimes it also behave better than the lsma by smoothing more. IIR estimate are harder to make but this one look really correct.
If you are looking for something or just want to say thanks try to pm me :)
Thank for reading !
Leastsquares
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
Least Squares Moving Average With Overshoot ReductionIntroduction
The ability to reduce lag while keeping a good level of stability has been a major challenge for smoothing filters in technical analysis. Stability involve many parameters, one of them being overshoots. Overshoots are a common effect induced by low-lagging filters, they are defined as the ability of a signal output to exceed a target input. This effect can lead to major drawbacks such as whipsaw and reduction of precision. I propose a modification of the least squares moving average "Reduced Overshoots Moving Average" (ROMA) to reduce overshoots induced by the lsma by using a scaled recursive dispersion coefficient with the purpose of reducing overshoots.
Overshoots - Causes and Effects
Control theory and electronic engineering use step response to measure overshoots, the target signal is defined as an heaviside step function which will be used as input signal for our filter.
In white an input signal, in blue a least squares moving average with the input signal as source, the circle show the overshoot induced by the lsma, the filter exceed drastically the target input. But why low lag filters often induce overshoots ? This is because in order to reduce lag those filter will increase certain frequencies of the input signal, this reduce lag but induce overshoots because the amplitude of those frequencies have been increased, so its normal for the filter to exceed the input target. The increase of frequencies is not a bad process but when those frequencies are already of large amplitudes (high volatility periods) the overshoots can be seen.
Comparison With ROMA
Our method will use the line rescaling technique to estimate the lsma for efficiency sake. This method involve calculating the z-score of a line and multiplying it by the correlation of the line and the target input (price). Then we rescale this result by adding this z-score multiplied by the dispersion coefficient to a simple moving average. Lets compare the step response of our filer and the lsma.
ROMA (in red) need more data to be computed but reduce the mean absolute error in comparison with the classic lsma, it is seen that instead of following increasing, ROMA decrease thus ending with an undershoot.
ROMA in (red) and an lsma (in blue) with both length = 14, ROMA decrease overshoots with the cost of less smoothing, both filter match when there are no overshoots situations.
Both filters with length = 200, large periods increase the amplitude of overshoots, ROMA stabilize early at the cost of some smoothness.
The running Mean Absolute Error of both filters with length = 100, ROMA (in red) is on average closer to the price than the lsma (in blue)
Conclusion
I presented a modification of the least squares moving average with the goal to provide both stability and rapidity, the statistics show that ROMA do a better job when it comes to reduce the mean absolute error. Alternatives methods can involve decreasing the period it take for the filter to be on a steady state (reducing filter period during high volatility periods) , various filters already exploit this method.
Side Project
I'am not that good when it come to make my post easy to read, this is why i'am currently making an article explaining the basis of digital signal processing. This post will help you to understand signals and things such as lag, frequency transform, cycles, overshoots, ringing, FIR/IIR filters, impulse response, convolution, filter topology and many more. I love to post indicators but also making more educational content as well, so stay tuned :)
Thanks for reading, let me know if you need help with something, i would be happy to assist you.
please be kind to notify me if you find errors about the indicator in order for me to update it as fast as possible.
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.
Function for Least Squares Moving AverageThank you to alexgrover for putting me wide to this, after putting up with long conversations and stupid questions. Follow him and behold: www.tradingview.com
What is this?
This is simply the function for a Least Squares Moving Average. You can render this on the chart by using the linreg() function in Pine.
Personally I like to use the slope of the LSMA to help determine what direction to take a trade in, but I'm sure there are other, more exotic ways of using it and, if you know how to get your fingers dirty with Pine, you can create more exotic versions of it by modifying the function provided.
Want to learn?
If you'd like the opportunity to learn Pine but you have difficulty finding resources to guide you, take a look at this rudimentary list: docs.google.com
The list will be updated in the future as more people share the resources that have helped, or continue to help, them. Follow me on Twitter to keep up-to-date with the growing list of resources.
Suggestions or Questions?
Don't even kinda hesitate to forward them to me. My (metaphorical) door is always open.
Adaptive Least SquaresAn adaptive filtering technique allowing permanent re-evaluation of the filter parameters according to price volatility. The construction of this filter is based on the formula of moving ordinary least squares or lsma , the period parameter is estimated by dividing the true range with its highest. The filter will react faster during high volatility periods and slower during low volatility ones.
High smooth parameter will create smoother results, values inferior to 3 are recommended.
You can easily replace the parameter estimation method as long as the one used fluctuate in a range of , for example you can use the efficiency ratio
ER = abs(change(close,length))/sum(abs(change(close)),length)
Or the Fractal Dimension Index , in fact any values will work as long as they are rescaled (stoch(value,value,value,length)/100)
For any suggestions/questions feel free to send me a message :)
B3 Least Squares Regression - "Price Leading MovAvg"B3 Least Squares Regression or "LSR" is very similar to the mid-line at the end of a linear regression channel, except that in a linear regression you cannot see the history of the regression well. There is also the linear regression and least squares curves in some platforms, and this would also be a similar indicator. The smoothness of my indicator and the back-to-basics approach to the mathematics sets it apart from the others. The look of this MA on a chart speaks for itself.
Some people like the flow of this indicator, as it will actually shoot out ahead of price. Most moving averages trail the price action; this one doesn't do that for long before it catches price or begins to lead price. It isn't necessarily a future price predictor; think of it as a slope stylist. The slope of this indicator determines all painting and signals for the strategy. There are two available versions: with or without order placement.
