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 Trailing StopIntroduction
Trailing stop are important indicators in technical analysis, today i propose a new trailing stop A2RTS based on my last published indicator A2RMA (1), this last indicator directly used an error measurement thus providing a way to create enveloppes, which provide a direct way to create trailing stops based on highest/lowest rules.
The Indicator
If you need a more detailed explanation of this indicator i encourage you to check the A2RMA indicator post i made, parameters does not differ from the supertrend, thus having a length parameter and a factor parameter who is here described as gamma , gamma control how far away are the bands from each others thus spotting longer terms trends when gamma is higher.
On BTCUSD
Something worth mentioning is that the indicator sometimes behave like my MTA trailing stop indicator (2) who is closer to the price when a trend persist thus providing early exit points, however A2RTS behave a bit better.
Price can sometimes break the trailing stop, this can be interpreted as a support/resistance or just as an exit point, the support resistance methodology on trailing stop is not the most recommended.
Sometimes it is recommended to have an higher length rather than an high gamma like in this case for INTEL CORP, below gamma = 3 and length = 20
The microprocessor market like to use higher length's instead of higher gamma's , A2RMA is a non-linear filter, this would explain such behaviour.
Conclusion
Trailing stops might not suffer as much from whipsaw trades than MA crossovers but they still remain inefficient when market is not trending, results of the proposed indicator on major forex pairs are more than disappointing, but i hope this will serve as basis for other trailing stops that might act a little bit better. I conclude this post by thanking everyone who support my work and i encourage you to modify this indicator and share it with the community.
Thanks for reading !
Cited Articles
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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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Combo Backtest 123 Reversal & Bandpass FilterThis is combo strategies for get
a cumulative signal. Result signal will return 1 if two strategies
is long, -1 if all strategies is short and 0 if signals of strategies is not equal.
First strategy
This System was created from the Book "How I Tripled My Money In The
Futures Market" by Ulf Jensen, Page 183. This is reverse type of strategies.
The strategy buys at market, if close price is higher than the previous close
during 2 days and the meaning of 9-days Stochastic Slow Oscillator is lower than 50.
The strategy sells at market, if close price is lower than the previous close price
during 2 days and the meaning of 9-days Stochastic Fast Oscillator is higher than 50.
Second strategy
The related article is copyrighted material from
Stocks & Commodities Mar 2010
You can use in the xPrice any series: Open, High, Low, Close, HL2, HLC3, OHLC4 and ect...
WARNING:
- For purpose educate only
- This script to change bars colors. Strategy
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Combo Strategy 123 Reversal & Bandpass Filter This is combo strategies for get
a cumulative signal. Result signal will return 1 if two strategies
is long, -1 if all strategies is short and 0 if signals of strategies is not equal.
First strategy
This System was created from the Book "How I Tripled My Money In The
Futures Market" by Ulf Jensen, Page 183. This is reverse type of strategies.
The strategy buys at market, if close price is higher than the previous close
during 2 days and the meaning of 9-days Stochastic Slow Oscillator is lower than 50.
The strategy sells at market, if close price is lower than the previous close price
during 2 days and the meaning of 9-days Stochastic Fast Oscillator is higher than 50.
Second strategy
The related article is copyrighted material from
Stocks & Commodities Mar 2010
You can use in the xPrice any series: Open, High, Low, Close, HL2, HLC3, OHLC4 and ect...
WARNING:
- For purpose educate only
- This script to change bars colors. Indicator
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Well Rounded Moving AverageIntroduction
There are tons of filters, way to many, and some of them are redundant in the sense they produce the same results as others. The task to find an optimal filter is still a big challenge among technical analysis and engineering, a good filter is the Kalman filter who is one of the more precise filters out there. The optimal filter theorem state that : The optimal estimator has the form of a linear observer , this in short mean that an optimal filter must use measurements of the inputs and outputs, and this is what does the Kalman filter. I have tried myself to Kalman filters with more or less success as well as understanding optimality by studying Linear–quadratic–Gaussian control, i failed to get a complete understanding of those subjects but today i present a moving average filter (WRMA) constructed with all the knowledge i have in control theory and who aim to provide a very well response to market price, this mean low lag for fast decision timing and low overshoots for better precision.
Construction
An good filter must use information about its output, this is what exponential smoothing is about, simple exponential smoothing (EMA) is close to a simple moving average and can be defined as :
output = output(1) + α(input - output(1))
where α (alpha) is a smoothing constant, typically equal to 2/(Period+1) for the EMA.
This approach can be further developed by introducing more smoothing constants and output control (See double/triple exponential smoothing - alpha-beta filter) .
The moving average i propose will use only one smoothing constant, and is described as follow :
a = nz(a ) + alpha*nz(A )
b = nz(b ) + alpha*nz(B )
y = ema(a + b,p1)
A = src - y
B = src - ema(y,p2)
The filter is divided into two components a and b (more terms can add more control/effects if chosen well) , a adjust itself to the output error and is responsive while b is independent of the output and is mainly smoother, adding those components together create an output y , A is the output error and B is the error of an exponential moving average.
Comparison
There are a lot of low-lag filters out there, but the overshoots they induce in order to reduce lag is not a great effect. The first comparison is with a least square moving average, a moving average who fit a line in a price window of period length .
Lsma in blue and WRMA in red with both length = 100 . The lsma is a bit smoother but induce terrible overshoots
ZLMA in blue and WRMA in red with both length = 100 . The lag difference between each moving average is really low while VWRMA is way more precise.
Hull MA in blue and WRMA in red with both length = 100 . The Hull MA have similar overshoots than the LSMA.
Reduced overshoots moving average (ROMA) in blue and WRMA in red with both length = 100 . ROMA is an indicator i have made to reduce the overshoots of a LSMA, but at the end WRMA still reduce way more the overshoots while being smoother and having similar lag.
I have added a smoother version, just activate the extra smooth option in the indicator settings window. Here the result with length = 200 :
This result is a little bit similar to a 2 order Butterworth filter. Our filter have more overshoots which in this case could be useful to reduce the error with edges since other low pass filters tend to smooth their amplitude thus reducing edge estimation precision.
Conclusions
I have presented a well rounded filter in term of smoothness/stability and reactivity. Try to add more terms to have different results, you could maybe end up with interesting results, if its the case share them with the community :)
As for control theory i have seen neural networks integrated to Kalman flters which leaded to great accuracy, AI is everywhere and promise to be a game a changer in real time data smoothing. So i asked myself if it was possible for a neural networks to develop pinescript indicators, if yes then i could be replaced by AI ? Brrr how frightening.
Thanks for reading :)
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Zero Phase Filtering [Repaint] - ExperimentalImportant !
The indicator is for experimental purpose only, it must not be used as a decisional tool but only as a visual one (like Zig-Zag, Fractal etc). The information this indicator display is uncertain and subject to drastic changes over time. If you have further question feel free to pm me.
Introduction
Most of the filters you will find are causal, this mean that they depend on present and past input values, this explain the lag they produce. Non causal filters however will use future input values. A well know way to get a zero-phase filter is by using the forward backward method, but this is not possible in pinescript as i recall. So we have to use some kind of function that will display future values, this is possible using the security function in version 2 or the one in version 3 using barmerge.lookahead_on .
The Use Of A Repainting Indicator
Its always better to filter data in order to have a clearer view of what is happening, this can be useful when doing some forecasting or doing less formal kind of analysis. However since it repaint you cant use it as a signal provider or use signals of other indicators using this filter as source.
For example if you want to forecast a smooth indicator, the forecast of this indicator under normal circumstances could still have lag associated with it, so you would have to react before your forecast, this wont happen if you apply this filter as your indicator source.
The Filter
We smooth with a simple moving average the price provided by the security function twice, length control the smoothing level. Since security depend on the time frame you are in you must select your time frame in the indicator parameter selection window.
Filtering using 45 minutes time frame close price in a 5 minutes chart, we fix this by selecting our time frame.
Consider the fact that the input of the indicator is just periodic price, so sometimes the lag can sometimes be less or more than 0 and the estimation not centered.
The indicator can work on time frames up to 1h, after that the filter have some lag, i tried fixing this and i ended up having data errors.
Applying our filter as source for the rsi oscillator.
Conclusion
It is possible to have a kind of zero-phase filters, but it would be better if pinescript could support backward indexing thus making us able to do forward backward filtering.
Since noise can affect our analysis, applying smoothing without having to use offset in plot can be considered useful.
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Simple LinesIntroduction
Making lines is great in technical analysis since it can highlights principal movements and make the analysis of the price easier when using certain methodologies (Elliott Waves, patterns).
However most of the indicators making lines (Zig-Zag, simple linear regression) are non causal (repaint), this is the challenge i tried to overcome, making an indicator capable of making lines in a smart way (able to follow price without loosing a linear approach) and with the least lag possible, i inspired myself from the behaviour of the renko when using a small brick size. This indicator does not repaint .
The code is short and i hope, understandable for all of you, making lines is not a difficult task and its important to know that when a problem appear complex it does not mean that the code used to solve this problem must be complex. Lets see the indicator in details.
The indicator
The indicator have 4 parameters, the length parameter who control the length of lines, the emphasis parameter who control the stability and also the ability to make lines closer to the price (thus minimizing the sum of squares) , the mult parameter which is similar to emphasis and a point option that we will discuss later.
When emphasis and mult are both equal to 1 the indicator will sometimes draw a perfect line, however this line will try to follow the price and thus can create a noisy result.
This is where emphasis and mult will correct this behaviour. The emphasis parameter give a more periodic look as well as some control to the lines but can also destroy them.
This should not happen with mult , this parameter also give more predictability to the lines. Overall it correct the drawbacks of the parameters combinations mentioned earlier.
Its also possible to mix both the emphasis and mult parameter, but take into account that when both are equals the result consist of less reactive lengthy lines with low accuracy. Its better to only use one of them and let the other stay to 1.
Point Option
The indicator can sometimes have a weird look, appearing almost flat or just dont appearing at all. When such thing happen use the point option.
XPDUSD without point option.
with point option :
Time Frame Problem and Its Fix
When using higher time-frames the result of the indicator can appear different, in general the higher the time frame the lengthier are the lines. In order to fix this you can use decimals in the length parameter
length and mult both equal to 5.5, emphasis cant use decimals.
Conclusion
I have highlighted a simple way to make use of the small renko box size method in order to return reactive lines without making the indicator repaint. However Its ability to be close to the price as well as being always super reactive is not a guarantee.
For any suggestion/help feel free to pm me, i would be happy to help you :)
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General Filter Estimator-An Experiment on Estimating EverythingIntroduction
The last indicators i posted where about estimating the least squares moving average, the task of estimating a filter is a funny one because its always a challenge and it require to be really creative. After the last publication of the 1LC-LSMA , who estimate the lsma with 1 line of code and only 3 functions i felt like i could maybe make something more flexible and less complex with the ability to approximate any filter output. Its possible, but the methods to do so are not something that pinescript can do, we have to use another base for our estimation using coefficients, so i inspired myself from the alpha-beta filter and i started writing the code.
Calculation and The Estimation Coefficients
Simplicity is the key word, its also my signature style, if i want something good it should be simple enough, so my code look like that :
p = length/beta
a = close - nz(b ,close)
b = nz(b ,close) + a/p*gamma
3 line, 2 function, its a good start, we could put everything in one line of code but its easier to see it this way. length control the smoothing amount of the filter, for any filter f(Period) Period should be equal to length and f(Period) = p , it would be inconvenient to have to use a different length period than the one used in the filter we want to estimate (imagine our estimation with length = 50 estimating an ema with period = 100) , this is where the first coefficients beta will be useful, it will allow us to leave length as it is. In general beta will be greater than 1, the greater it will be the less lag the filter will have, this coefficient will be useful to estimate low lagging filters, gamma however is the coefficient who will estimate lagging filters, in general it will range around .
We can get loose easily with those coefficients estimation but i will leave a coefficients table in the code for estimating popular filters, and some comparison below.
Estimating a Simple Moving Average
Of course, the boxcar filter, the running mean, the simple moving average, its an easy filter to use and calculate.
For an SMA use the following coefficients :
beta = 2
gamma = 0.5
Our filter is in red and the moving average in white with both length at 50 (This goes for every comparison we will do)
Its a bit imprecise but its a simple moving average, not the most interesting thing to estimate.
Estimating an Exponential Moving Average
The ema is a great filter because its length times more computing efficient than a simple moving average. For the EMA use the following coefficients :
beta = 3
gamma = 0.4
N.B : The EMA is rougher than the SMA, so it filter less, this is why its faster and closer to the price
Estimating The Hull Moving Average
Its a good filter for technical analysis with tons of use, lets try to estimate it ! For the HMA use the following coefficients :
beta = 4
gamma = 0.85
Looks ok, of course if you find better coefficients i will test them and actualize the coefficient table, i will also put a thank message.
Estimating a LSMA
Of course i was gonna estimate it, but this time this estimation does not have anything a lsma have, no moving average, no standard deviation, no correlation coefficient, lets do it.
For the LSMA use the following coefficients :
beta = 3.5
gamma = 0.9
Its far from being the best estimation, but its more efficient than any other i previously made.
Estimating the Quadratic Least Square Moving Average
I doubted about this one but it can be approximated as well. For the QLSMA use the following coefficients :
beta = 5.25
gamma = 1
Another ok estimate, the estimate filter a bit more than needed but its ok.
Jurik Moving Average
Its far from being a filter that i like and its a bit old. For the comparison i will use the JMA provided by @everget described in this article : c.mql5.com
For the JMA use the following coefficients :
for phase = 0
beta = pow*2 (pow is a parameter in the Jma)
gamma = 0.5
Here length = 50, phase = 0, pow = 5 so beta = 10
Looks pretty good considering the fact that the Jma use an adaptive architecture.
Discussion
I let you the task to judge if the estimation is good or not, my motivation was to estimate such filters using the less amount of calculations as possible, in itself i think that the code is quite elegant like all the codes of IIR filters (IIR Filters = Infinite Impulse Response : Filters using recursion) .
It could be possible to have a better estimate of the coefficients using optimization methods like the gradient descent. This is not feasible in pinescript but i could think about it using python or R.
Coefficients should be dependant of length but this would lead to a massive work, the variation of the estimation using fixed coefficients when using different length periods is just ok if we can allow some errors of precision.
I dont think it should be possible to estimate adaptive filter relying a lot on their adaptive parameter/smoothing constant except by making our coefficients adaptive (gamma could be)
So at the end ? What make a filter truly unique ? From my point of sight the architecture of a filter and the problem he is trying to solve is what make him unique rather than its output result. If you become a signal, hide yourself into noise, then look at the filters trying to find you, what a challenging game, this is why we need filters.
Conclusion
I wanted to give a simple filter estimator relying on two coefficients in order to estimate both lagging and low-lagging filters. I will try to give more precise estimate and update the indicator with new coefficients.
Thanks for reading !
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1LC-LSMA (1 line code lsma with 3 functions)Even Shorter Estimation
I know that i'am insistent with the lsma but i really like it and i'm happy to deconstruct it like a mad pinescript user. But if you have an idea about some kind of indicator then dont hesitate to contact me, i would be happy to help you if its feasible.
My motivation for such indicator was to use back the correlation function (that i had putted aside in the ligh-lsma code) and provide a shorter code than the estimation using the line rescaling method (see : Approximating A Least Square Moving Average In Pine) .
The Method
Fairly simple, lets name y our estimation, we calculate it as follow:
y = x̄ + r*o*1.7
where x̄ is the price moving average, r the correlation between the price and a line (or n) and o the standard deviation. If plotted against a classic lsma the difference would be meaningless at first glance so lets plot the absolute value between the difference of the lsma and our estimation of both period 100.
The difference is under 0.0000 on eurusd, its really low.
In general the longer the period of the estimation, the lower the difference between a normal lsma, but when using shorter period they can differ a little bit.
Why 1.7 ?
We need to multiply the standard deviation by a constant in order to match the overshoot and the rise-time of the original lsma. The constant 1.7 is one that work well but actually this constant should be dependant of the length period of the filter to make the estimation more accurate.
More About Step-Response
Most of the time when a filter have less lag, it mean that he induce overshoot in order to decrease the rise-time . Rise-time is the time the output take to match the target input, its related to the lag. Overshoot mean that the output exceed the target input, you can clearly see those concept in the image above.
Conclusion
I've showed that its possible to be even more concise about the code it take to estimate an lsma. I've also briefly explained the concept of rise-time and overshoot, concepts really important to signal processing and particularly in filter design. I'm sure that it can be even more simplified and i have some ideas for such estimate.
Thanks for reading !
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