Blackman Filter - The Smoother The BetterIntroduction
Who doesn't like smooth things? I'd like a smooth market price for christmas! But i can't get it, instead its so noisy...so you apply a filter to smooth it, such filters are called low-pass filters, they smooth and its great but they have lag, so nobody really use them, but they are pretty to look at.
Its on a childish note that i will introduce this indicator, so what it is all about? I propose a new FIR filter using a blackman function as filter kernel for financial time-series smoothing, do you prefer the childish tone ? Fear not its surprisingly easy!
The Blackman Function
The blackman function look like a bell shaped curve, look:
The blackman function will produce such curve. This function is called a cosine sum function because she is based on the sum of cosine functions, here only 2.
0.42 - 0.5 * cos(2 * pi * k) + 0.08 * cos(4 * pi * k)
Originally you use this function for windowing , what does it means? In signal processing you have a function called sync function , if you use this function as filter kernel you would get the ideal frequency domain response filter, sometime called brickwall filter, it would be extremely smooth.
Above the optimal low pass filter frequency response.
However the sync function has no ending values and goes on forever, therefore we can't use it for convolution, expect if we apply windowing. Filters using windowing are called windowed-sinc filters, i will describe the procedure below :
1 - Create a sync function = sin(pi*n)/(pi*n)
2 - Truncate it = I only keep the first length points of the sync function.
This create a abrupt end, the frequency of a filter using step 1 as kernel would contain ripples in the pass band and stop band, this is bad! The frequency response would look like this :
3 - I multiply my values of step 2 by a window function, it can the blackman window, i no longer have an abrupt end, its smooth!
The frequency response of the filter using this kernel would no longer have ripples! This is the power of windowing functions.
Here we are not using such thing, but we could in the future. Here instead we use the blackman function as filter kernel, because this function is bell shaped this mean that the filter will certainly be smooth (symmetrical weighting is a rule of thumb for kernels when we want really smooth filters).
The Filter
This filter is quite smooth, unlike the gaussian filter this filter give less weights to recent and past values, this is because the blackman function has fatter tails than the gaussian one. I could make a comparison of both, however they are quite alike, if you often use a gaussian filter its up to you to decide which one you prefer.
The filter can do a better job than the moving average when it comes to preserve the frequency components that constitute the cycles/trend.
We can see that the filter has a greater performance when it comes to keep the shape of the market price, thus it has a slightly better fit.
Conclusion
Ok so in this post you learned a bit about the sync function and windowing, those are basic subjects in signal processing, they allow us to approximate the filter with the ideal frequency response, i also showed you that those windowing function could be used as kernel and that they where pretty smooth on their own, there are many others, but the one i prefer is the blackman windowing function.
I know what you are thinking, "we want trailing stops, alerts, colors, arrows!", and i understand you pal, but sometimes its cool to take a break from all this stuff. However i can tell that i'am working on a side project that aim to estimate rolling maximum/minimum as fast as possible, any experiments will be published here, and i can ensure you that those indicators will make your day quite brighter, we will see that soon.
I hope you learned something from this post! I'am a bit tired (look i'am disappearing !)
Thanks for reading !
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Kaufman Adaptive Correlation OscillatorIntroduction
The correlation oscillator is a technical indicator that measure the linear relationship between the market closing price and a simple increasing line, the indicator is in a (-1,1) range and rise when price is up-trending and fall when price is down-trending. Another characteristic of the indicator is its inherent smoothing which provide a noise free (to some extent) oscillator.
Such indicator use simple moving averages as well as estimates of the standard deviation for its calculation, but we can easily make it adaptive, this is why i propose this new technical indicator that create an adaptive correlation oscillator based on the Kaufman adaptive moving average.
The Indicator
The length parameter control the period window of the moving average, larger periods return smoother results while having a low kurtosis, which mean that values will remain around 1 or -1 a longer period of time. Pre-filtering apply a Kaufman adaptive moving average to the input, which allow for a smoother output.
No pre-filtering in orange, pre-filtering in yellow, period = 100 for both oscillators.
If you are not aware of the Kaufman adaptive moving average, such moving average return more reactive results when price is trending and smoother results when price is ranging, this also apply for the proposed indicator.
Conclusion
Classical correlation coefficients could use this approach, therefore the linear relationships between any variables could be measured. The fact that the indicator is adaptive add a certain potential, however such combination make the indicator have the drawback of kama + the correlation oscillator, which might appear at certain points.
Thanks for reading ! Indicator
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Turbo Scaler - The Art Of Being (too) EarlyIntroduction
Fast smooth indicators that produce early signals can sound utopic but mathematically its not a huge deal, the effect of early outputs based on smooth inputs can be seen on differentiators crosses, this is why i propose this indicator that aim to return extra fast signals based on a slightly modified max-min normalization method. The indicator introduce inherent smoothing without having an huge impact on the indicator reactivity.
The Indicator
The indicator is based on max-min normalization (like the stochastic oscillator) however instead of using the highest/lowest of the input we use the highest and lowest of the moving average of the input. This process using as input the closing price and the moving average closing price will return two lines, and because of the nature of max-min normalization we can see that the trigger line (in orange) produce earlier crosses. length control the highest/lowest period while smooth control the output lines smoothness (50 by default).
alpha control the scaling amount, with higher values of alpha creating more constrained scale, when alpha = 1 the scale is in a range of (0,1) while lower values of alpha can make the output move more freely.
alpha = 0.25
alpha = 1
Higher values of alpha create earlier signals.
Downsides Of Early Crosses
Of course such indicator make us exposed to the trend as seen below.
We can nonetheless protect ourselves against such cases scenarios by lowering alpha.
lowering alpha allow to catch movements of the trend without loosing much reactivity at the cost of an increased umber of trades.
Possible Uses
The proposed indicator allow for an high number of uses because of its scale, reactive nature...etc. A method that allow us to go with the main trend is by taking into account the crosses between the lines and the sign of the lines, for example :
The first signal (green) happen when the main line (in blue) crossover the trigger (orange) while both are > 0, the same happen with the second signal however both lines are < 0. This method can use certain levels instead of the sign (main line crossover trigger while both > 0.7...etc).
This method is great for the indicator because such cases scenarios does not happen a lot with ranging markets, we can clearly that when trending the trigger can have the tendency to be flat and higher than 0 thus allowing for the main line to produce those signals.
Conclusion
I have presented a super reactive crosses indicator based on max-min normalization with the ability to both be smooth and produce early entries/exits signals, different methods have been presented in order to allow for different setups using this indicator.
The introduction of the alpha parameter allow for more control which is what those kind of indicators needs. I hope you find an use to it :)
Support Me
Making indicators sure is hard, it takes time and it can be quite lonely to, so i would love talking with you guys while making them :) There isn't better support than the one provided by your friends so drop me a message.
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Motion Smoothness Index Introduction
Its holiday time for me, i have been working here a lot. But no leaving before publishing. Telling when market price is smooth or rough is not the easiest task, so today i present a trend metric indicator that allow you to give you this kind of information.
The Indicator
The indicator is in an approximate range of (0,1) with mean x̄ decaying for higher length's, when the indicator is below 0.5 the market is smooth, else rough, this is the simple interpretation. The indicator is simply the ratio of the price residual standard deviation and the price standard deviation.
Higher value of length will make the indicator less accurate when it comes to detect rough market price, you can still use the indicator direction or its running mean to give you insights but 0.5 is still the recommended detection threshold.
In More Depth
Even tho market is random by nature there can still be structures in the price (cycles and trends), the fractional BM model will tell you that market price is sometimes auto-correlated (trending) or non auto-correlated (ranging), knowing what is the current market state is therefore important, when price is rough it can means an excess in noise thus exhibiting an uncorrelated market at the contrary of a smoother price that can allow for auto-correlation.
Now, market is infected by noise, and thats really unfortunate but the noise posses various properties that can allow for all the structures we see in market price. So thinking about the market allowing for possible profits during auto-correlated states is encouraging.
Conclusion
Although the indicator measure smoothness/roughness it can still be interpreted as a trend/range state detector. I hope it provide to be useful.
I wish you all good holidays and see you next time ! Thanks for reading !
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Bilateral Stochastic Oscillator - For The Sake Of EfficiencyIntroduction
The stochastic oscillator is a feature scaling method commonly used in technical analysis, this method is the same as the running min-max normalization method except that the stochastic oscillator is in a range of (0,100) while min-max normalization is in a range of (0,1). The stochastic oscillator in itself is efficient since it tell's us when the price reached its highest/lowest or crossed this average, however there could be ways to further develop the stochastic oscillator, this is why i propose this new indicator that aim to show all the information a classical stochastic oscillator would give with some additional features.
Min-Max Derivation
The min-max normalization of the price is calculated as follow : (price - min)/(max - min) , this calculation is efficient but there is alternates forms such as :
price - (max - min) - min/(max - min)
This alternate form is the one i chosen to make the indicator except that both range (max - min) are smoothed with a simple moving average, there are also additional modifications that you can see on the code.
The Indicator
The indicator return two main lines, in blue the bull line who show the buying force and in red the bear line who show the selling force.
An orange line show the signal line who represent the moving average of the max(bull,bear), this line aim to show possible exit/reversals points for the current trend.
Length control the highest/lowest period as well as the smoothing amount, signal length control the moving average period of the signal line, the pre-filtering setting indicate which smoothing method will be used to smooth the input source before applying normalization.
The default pre-filtering method is the sma.
The ema method is slightly faster as you can see above.
The triangular moving average is the moving average of another moving average, the impulse response of this filter is a triangular function hence its name. This moving average is really smooth.
The lsma or least squares moving average is the fastest moving average used in this indicator, this filter try to best fit a linear function to the data in a certain window by using the least squares method.
No filtering will use the source price without prior smoothing for the indicator calculation.
Relationship With The Stochastic Oscillator
The crosses between the bull and bear line mean that the stochastic oscillator crossed the 50 level. When the Bull line is equal to 0 this mean that the stochastic oscillator is equal to 0 while a bear line equal to 0 mean a stochastic oscillator equal to 100.
The indicator and below a stochastic oscillator of both period 100
Using Levels
Unlike a stochastic oscillator who would clip at the 0 and 100 level the proposed indicator is not heavily constrained in a range like the stochastic oscillator, this mean that you can apply levels to trigger signals
Possible levels could be 1,2,3... even if the indicator rarely go over 3.
Its then possible to create strategies using such levels as support or resistance one.
Conclusion
I've showed a modified stochastic oscillator who aim to show additional information to the user while keeping all the information a classical stochastic oscillator would give. The proposed indicator is no longer constrained in an hard range and posses more liberty to exploit its scale which in return allow to create strategies based on levels.
For pinescript users what you can learn from this is that alternates forms of specific formulas can be extremely interesting to modify, changes can be really surprising so if you are feeling stuck, modifying alternates forms of know indicators can give great results, use tools such as sympy gamma to get alternates forms of formulas.
Thanks for reading !
If you are looking for something or just want to say thanks try to pm me :)
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Fisher Least Squares Moving AverageIntroduction
I already estimated the least-squares moving average numerous times, one of the most elegant ways was by rescaling a linear function to the price by using the z-score, today i will propose a new smoother (FLSMA) based on the line rescaling approach and the inverse fisher transform of a scaled moving average error with the goal to provide an alternative least-squares smoother, the indicator won't use the correlation coefficient and will try to adresses problems such as overshoots and lag reduction.
Line Rescaling Method
For those who did not see my least squares moving average estimation using the line rescaling method here is a resume, we want to fit a polynomial function of degree 1 to the price by reducing the sum of squares between the price and the filter, squares is a term meaning the squared difference between the price and its estimation. The line rescaling technique work as follow :
1 - get the z-score of a line.
2 - multiply this z-score with the correlation between the price and a line.
3 - multiply the precedent result with the standard deviation of the price, then sum that to a simple moving average.
This process is shorter than the classical least-squares moving average method.
Z-Score Derivation And The Inverse Fisher Transform
The FLSMA will use a similar approach to the line rescaling technique but instead of using the correlation during step 2 we will use an alternative calculated from the error between the estimate and the price.
In order to do so we must use the inverse fisher transform, the inverse fisher transform can take a z-score and scale it in a range of (1,-1), it is possible to estimate the correlation with it. First lets create our modified z-score in the form of : Z = ma((y - Y)/e) where y is the price, Y our output estimate and e the moving average absolute error between the price and Y and lets call it scaled smoothed error , then apply the inverse fisher transform : r = IFT(Z) = tanh(Z) , we then multiply the z-score of the line with it.
Performance
The FLSMA greatly reduce the overshoots, this mean that the maximas of abs(r) are lower than the maxima's of the absolute correlation, such case is not "bad" but we can see that the filter is not closer to the price than the LSMA during trending periods, we can assume the filter don't reduce least-squares as well as the LSMA.
The image above is the running mean of the absolute error of each the FLSMA (in red) and the LSMA (in blue), we could fix this problem by multiplying the smooth scaled error by p where p can be any number, for example :
z = sma(src - nz(b ,src),length)/e * p where p = 2
In red the FLSMA and in blue the FLSMA with p = 2 , the greater p is the less lag the FLSMA will have.
Conclusion
It could be possible to get better results than the LSMA with such design, the presented indicator use its own correlation replacement but it is possible to use anything in a range of (1,-1) to multiply the line z-score. Although the proposed filter only reduce overshoots without keeping the accuracy of the LSMA i believe the code can be useful for others.
Thanks for reading.
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Adaptive Autonomous Recursive Moving AverageIntroduction
Using conditions in filters is a way to make them adapt to those, i already used this methodology in one of my proposed indicators ARMA which gave a really promising adaptive filter, ARMA tried to have a flat response when dealing with ranging market while following the price when the market where trending or exhibiting volatile movements, the filter was terribly simple which is one of its plus points but its down points where clearly affecting its performance thus making it almost impractical.
Today i propose a new filter A2ARMA which aim to correct all the bad behaviours of ARMA while having a good performance on various markets thanks to the added adaptivity.
Fixes And Changes
ARMA was dealing with terribles over/under-shoots which affected its performance, adding a zero-lag option made the thing even worse, in order to fix those mistakes i first cleaned the code, then i removed the offset for src in d , this choice is optional but the filter is sometimes more accurate this way.
The major change is the use of an adaptive moving average instead of the triangular moving average that smoothed the output, this adaptive moving average is calculated using exponential averaging while using the efficiency ratio as smoothing variable, this choice surprisingly removed the majority of overshoots while adding more adaptivity to the filter.
The Indicator
The Indicator work the same way as ARMA, not reacting during flat market periods while following the price when this one is volatile or trending. length control the smoothing amount while gamma determine how the filter is affected during flat market periods, gamma = 0 is just a double smoothed adaptive moving average, higher values of gamma will filter flat markets with a certain degree.
On Intel Corp with gamma = 0, i want to filter the flat period starting at July 10, gamma = 3 will certainly help us on this task.
Hooray, the problem appear to be solved ! Lower values of gamma also produce desirable effect as shown below :
gamma = 2
So far so good, but gamma or length might have different optimal values depending on the market, also problems still exists as shown here :
Seagate is tricky, gamma at 2.4 might help
The relationship between length and gamma is somewhat complicated.
On Different Markets
While some filters will process market price the same way no matter the market they are affected, A2ARMA will change drastically depending of the market.
On AMD
On EURUSD
On BTCUSD
Comparison With ARMA
ARMA with parameters roughly matching A2RMA, overall most of the problems i wanted to fix where indeed fixed.
Conclusion
A huge thanks for the support i received during this "Blank Page" period i'am suffering, ARMA was an indicator i really wanted to further develop without giving up on the code simplicity and i think this version might provide useful results, we can also notice that the decision making is easier with this version of the indicator thanks to the added coloring (which would have been impossible with ARMA).
My work don't have license attached to it, feel free to modify and share your findings, mentioning is appreciated :)
Thanks for reading !
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Modular Filter - Spot Trends And Smooth PriceIntroduction
This indicator can have a wide variety of usages, and since it is based on exponential averaging then the whole indicator can be made adaptive, thus ending up with a really promising tool. This indicator who can both smooth price and act as a trailing stop depending on user preferences, i tried to make it as reactive, stable and efficient as possible in order to both smooth and spot trends, lets view it more in depth.
The Indicator
line 8 and 9 create two bands, one upper and one lower, then based on certain conditions the indicator will only return a certain band or an average of both with different weights, this weight is controlled by the beta parameter, values of 1 will return a simple filter while values of 0 will return a classical trailing stop.
beta = 0
The indicator can use output values as input, thus using smoother values as input, in order to do so just check "Feedback", this help the overall output to be smoother as well as giving more long terms signals
The amount of feedback is controlled by the feedback weighting parameter, lower values will weight more the output values thus creating smoother results.
Feedback weighting of 0.2
Using beta = 0 thus having the indicator act as a trailing stop while having the feedback option activated return more long terms signals. Notes that the colors are based on the initial conditions of the indicator.
Conclusion
You can replace length and change alpha for any smoothing variable such as the efficiency ratio or anything with scale (1,0), same goes for beta and the feedback weighting parameter, this is why the indicator is "Modular" in addition of providing different usages. This indicator can look like cluster filters (smooth price monarch, forexguru) , filters with the ability to follow the price quite fine while being stables. I really hope you find an use to it.
Thanks for reading !
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Inverse Fisher Fast Z-scoreIntroduction
The fast z-score is a modification of the classic z-score that allow for smoother and faster results by using two least squares moving averages, however oscillators of this kind can be hard to read and modifying its shape to allow a better interpretation can be an interesting thing to do.
The Indicator
I already talked about the fisher transform, this statistical transform is originally applied to the correlation coefficient, the normal transform allow to get a result similar to a smooth z-score if applied to the correlation coefficient, the inverse transform allow to take the z-score and rescale it in a range of (1,-1), therefore the inverse fisher transform of the fast z-score can rescale it in a range of (1,-1).
inverse = (exp(k*fz) - 1)/(exp(k*fz) + 1)
Here k will control the squareness of the output, an higher k will return heavy side step shapes while a lower k will preserve the smoothness of the output.
Conclusion
The fisher transform sure is useful to kinda filter visual information, it also allow to draw levels since the rescaling is in a specific range, i encourage you to use it.
Notes
During those almost 2 weeks i was even lazier and sadder than ever before, so i think its no use to leave, i also have papers to publish and i need tv for that.
Thanks for reading ! Indicator
Autonomous Recursive Moving AverageIntroduction
People often ask me what is my best indicators, i can't really respond to this question with a straight answer but i would say you to check this indicator. The Autonomous Recursive Moving Average (ARMA) is an adaptive moving average that try to minimize the sum of squares thanks to a ternary operator, this choice can seem surprising since most of the adaptive moving averages adapt to a smoothing variable thanks to exponential averaging, but there are lot of downsides to this method, i really wanted to have a flat filter during flat markets and this is what i achieved.
The Indicator
length control the amount of smoothing during trending periods, gamma is the trend sensitivity threshold, higher values of gamma will make an overall flat filter, adjust gamma to skip ranging markets.
gamma = 2, we can adjust to 3 while preserving smoothing reactivity with trading periods.
gamma = 3
low length and higher gamma create more boxy result, the filter add overshoots directly in the output, its unfortunate.
The Zero-Lag option can reduce the lag as well as getting additional flat results without changing gamma.
Conclusion
The indicator need work, but i can't leave without publishing it, the overshoots are a big problems, changing sma for another stable filter can help. I hope you find an use to it, i really like this indicator.
Thanks for reading Indicator
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