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Smoothed Delta's Ratio OscillatorIntroduction
Scaled and smoothed oscillators can provide easy to read/use information regarding price, therefore i will introduce a new oscillator who create smooth results and use a fast and practical scaling method. In order to allow for even more smoothness the option to smooth the input with a lsma has been added.
Scaling Using Changes
In this indicator scaling in a range of (1,-1) is achieved through the following calculations :
a = sma(abs(change(src,length)),length)
b = change(sma(src,length),length)
c = b/a
where src is our input. The two elements a and b are quite similar, a smooth the absolute change of the input over length period while b calculate the change of the smoothed input over length period, this make a > b and able us to perform scaling in a range of (1,-1).
The Indicator Parameters
Length control the differencing/smoothing period of the indicator, greater values create smoother and less volatile results, this mean that the oscillator will tend to be equal to 1 or -1 in a longer period of time if length is high. The smooth option allow for even smoother results by enabling the input to be smoothed by a lsma of length period.
Conclusions
I presented a smooth oscillator using a new rescaling technique. Parameters can be separated to provide different results, i believe the code is simple enough for everyone to modify it in order to provide interesting creations.
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Japanese Correlation CoefficientIntroduction
This indicator was asked and named by a trading meetup participant in Sevilla. The original question was "How to estimate the correlation between the price and a line as easy as possible", a question who got little attention. I previously proposed a correlation estimate using a modification of the standard score (see at the end of the post) for the estimation of a Savitzky-Golay moving average (LSMA) of order 1, however something faster could maybe be done and this is why i accepted the challenge.
Japanese Correlation
Correlation is defined as the linear relationship between two variables x and y , if x and y follow the same direction then the correlation increase else decrease. The correlation coefficient is always equal or below 1 and equal or above -1, it also have to be taken into account that this coefficient is quite smooth. Smoothing is not a problem, scaling however require more attention, high price > closing price > low price, therefore scaling can be done. First we smooth the closing/high/low price with a simple moving average of period p/2 , then we take the difference of the smoothed close with the smoothed close p/2 bars back, this result is then divided by the difference between the highest smoothed high's with the lowest smoothed low's over period p/2 .
Since we use information provided by candlesticks (close/high/low) i have been asked to publish this estimator with the name Japanese correlation coefficient , this name don't imply the use of data from Japanese markets, "Japanese" is used because of the candlestick method coming from Japan.
Comparison
I compare this estimation with the correlation coefficient provided in pinescript by the correlation function.
The estimation in orange with the original correlation coefficient using n as independent variable in blue with both length = 50.
comparison with length = 200.
Conclusion
I have shown that it is possible to roughly estimate the correlation coefficient between price and a linear function by using different price information. Correlation can be further estimated by using homogeneous bridge OHLC volatility estimators thus making able the use of different independent variables. I really hope you like this indicator and thanks to the meetup participant asking the question, i had a lot of fun making the indicator.
An alternative method
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Linear Quadratic Convergence Divergence OscillatorIntroduction
I inspired myself from the MACD to present a different oscillator aiming to show more reactive/predictive information. The MACD originally show the relationship between two moving averages by subtracting one of fast period and another one of slow period. In my indicator i will use a similar concept, i will subtract a quadratic least squares moving average with a linear least squares moving average of same period, since the quadratic least squares moving average is faster than the linear one and both methods have low-lag this will result in a reactive oscillator.
LQCD In Details
A quadratic least squares moving average try to fit a quadratic function (parabola) to the price by using the method of least squares, the linear least squares moving average try to fit a line. Non-linear fit tend to minimize the sum of squares in non-linear data, this is why a quadratic method is more reactive. The difference of both filters give us an oscillator, then we apply a simple moving average to this oscillator to provide the signal line, subtracting the oscillator and its signal line give us the histogram, those two last steps are the same used in the MACD.
Length control the period of the quadratic/linear moving average. While the MACD use a signal line for plotting the histogram i also added the option to plot the momentum of the quadratic moving average instead, the result is smoother and reduce irregularities, in order to do so just check the differential option in the parameter box.
The period of the signal line and the momentum are both controlled by the signal parameter.
A predictive approach can be made by subtracting the histogram with the signal line, this process make the histogram way more predictive, in order to do so just check the predictive histogram option in the parameter box.
Predictive histogram with simple histogram option. The differential mode can also be used with the predictive parameter, this result in a smoother but less reactive prediction.
Information Interpretation
The amount of information the MACD can give us is high. We can use the histogram as signal generator, or the if the oscillator is over/under 0, combine the oscillator/signal line with histogram, combinations can provide various systems. Some traders use the histogram as signal generator and use the cross between the histogram and the signal line as a stop signal, this method can avoid some whipsaw trades. The study of divergences with the price is also another method.
Conclusion
This oscillator aim to show the same amount of information as the MACD with a similar calculation method but using different kind of filters as well as eliminating the need to use two separates periods for the moving averages calculation, its still possible to use different periods for the quadratic/linear moving average but the results can be less accurate. This indicator can be used like the MACD.
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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 ! Indicator
Absolute Strength MTF IndicatorIntroduction
The non-signal version of the absolute strength indicator from fxcodebase.com requested by ernie76 . This indicator originally from mt4 aim to estimate the bullish/bearish force of the market by using various methods.
The Indicator
Two lines are plotted, a bull line (blue) representing the bullish/buying force and a bear one (red) representing the bearish/selling force, when the bull line is greater than the bear line the market is considered to be strongly bullish, else strongly bearish.
The indicator use various method, Rsi, stochastic, adx. The Rsi method is the one by default.
The stochastic method is less reactive but smoother
The Adx method is way different, while the other two methods make the bull and bear lines somewhat uncorrelated, the adx method focus more on the overall market strength than individual buyer/seller strength.
The smoothing method use 3 different filters, SMA, EMA and LSMA, LSMA is more reactive than the two previous one while EMA is just more computer efficient.
It is possible to use price data of different time frames for the calculation of the indicator.
Stochastic method with 4 hour price close as source.
Conclusion
A classic indicator who can be derived into a lot of ways using a more adaptive architecture or recursion. Hope you find it a use :)
A big thanks to ernie76 for the request and the support/testing of the indicator
Feel free to pm me for any request. Indicator
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Surface Roughness EstimatorIntroduction
Roughness of a signal is often non desired since smooth signals are easier to analyse, its logical to say that anything interacting with rough price is subject to decrease in accuracy/efficiency and can induce non desired effects such as whipsaws. Being able to measure it can give useful information and potentially avoid errors in an analysis.
It is said that roughness appear when a signal have high-frequencies (short wavelengths) components with considerable amplitudes, so its not wrong to say that "estimating roughness" can be derived into "estimating complexity".
Measuring Roughness
There are a lot of way to estimate roughness in a signal, the most well know method being the estimation of fractal dimensions. Here i will use a first order autocorrelation function.
Auto-correlation is defined by the linear relationship between a signal and a delayed version of itself, for exemple if the price goes on the same direction than the price i bars back then the auto-correlation will increase, else decrease. So what this have to do with roughness ? Well when the auto-correlation decrease it means that the dominant frequency is high, and therefore that the signal is rough.
Interpretation Of The Indicator
When the indicator is high it means that price is rough, when its low it indicate that price is smooth. Originally its the inverse way but i found that it was more convenient to do it this way. We can interpret low values of the indicator as a trending market but its not totally true, for example high values dont always indicate that the market is ranging.
Here the comparison with the indicator applied to price (orange) and a moving average (purple)
The average measurement applied to a moving average is way lower than the one using the price, this is because a moving average is smoother than price.
Its also interesting to see that some trend strength estimator like efficiency ratio can treat huge volatility signals as trend as shown below.
Here the efficiency ratio treat this volatile movement as a trending market, our indicator instead indicate that this movement is rough, such indication can avoid situation where price is followed by another huge volatile movement in the opposite direction.
Its important to make the distinction between volatility and trend strength, the trend is defined by low frequencies components of a signal, therefore measuring trend strength can be resumed as measuring the amplitude of such frequencies, but roughness estimation can do a great job as well.
Conclusion
I have showed how to estimate roughness in price and compared how our indicator behaved in comparison with a classic trend strength measurement tool. Filters or any other indicator can be way more efficient if they know how to filter according to a situation, more commonly smoothing more when price is rough and smoothing less when price is smooth. Its good to have a wider view of how market is behaving and not sticking with the binary view of "Trending" and "Ranging" .
I hope you find a use to this script :)
Best Regards
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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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Efficient PriceTrading The Movements That Matters
Inspired by the Price Volume Trend indicator the Efficient Price aim to create a better version of the price containing only the information a trend trader must need.
Calculation
This indicator use the Efficiency Ratio as a smoothing constant, it is calculated as follow :
ER = abs(change(close,length))/sum(abs(change(close)),length)
The goal of the Efficiency Ratio is to show if the market is trending or ranging.If ER is high then the market is considered to be trending, if ER is low then the market is considered to be ranging.
Then the Efficient Price is calculated :
EP = cum(change(close)*ER)
When the price is trending, the indicator will show movements of the price with unchanged volatility, but if the price is not trending then the indicator will flatten those movements.Think of this indicator as both a filter and a compressor and the Efficient Price as some kind of threshold.
The Efficient Price As Input For Indicators/Strategies
If the indicator show the movement of the trending price, it can be interesting to use it as input in order to reduce the number of false signals in a strategy.
We will test 2 MACD strategy provided by pulsewire, one using the closing price (In Red) and one with the efficient price (In White) as input
with both the following parameters :
fastLength = 50
slowlength = 200
MACDLength = 20
length = 50
Where length is the parameter of the Efficient Price.A spread of 2 pips is used.
Without Efficient Price : 26.88% of profitability, 69 pips of profit.
With Efficient Price : 38.46% of profitability, 336 pips of profit.
The difference of profitability is of 11.58%, the strategy with the Efficient Price made few trades and its equity have a lower variance than the equity of the MACD strategy using closing price.
Smoothed Version
It is possible to smooth the indicator output by using the following code :
EP = cum(change(close,length)*ER)
Hope you enjoy
For any questions/demands feel free to pm me, i would be happy to help you Indicator
Recursive StochasticThe Self Referencing Stochastic Oscillator
The stochastic oscillator bring values in range of (0,100). This process is called Feature scaling or Unity-Based Normalization
When a function use recursion you can highlights cycles or create smoother results depending on various factors, this is the goal of a recursive stochastic.
For example : k = s(alpha*st+(1-alpha)*nz(k )) where st is the target source.
Using inputs with different scale level can modify the result of the indicator depending on which instrument it is applied, therefore the input must be normalized, here the price is first passed through a stochastic, then this result is used for the recursion.
In order to control the level of the recursion, weights are distributed using the alpha parameter. This parameter is in a range of (0,1), if alpha = 1, then the indicator act as a normal stochastic oscillator, if alpha = 0, then the indicator return na since the initial value for k = 0. The smaller the alpha parameter, the lower the correlation between the price and the indicator, but the indicator will look more periodic.
Comparison
Recursive Stochastic oscillator with alpha = 0.1 and bellow a classic oscillator (alpha = 1)
The use of recursion can both smooth the result and make it more reactive as well.
Filter As Source
It is possible to stabilize the indicator and make it less affected by outliers using a filter as input.
Lower alpha can be used in order to recover some reactivity, this will also lead to more periodic results (which are not inevitably correlated with price)
Hope you enjoy
For any questions/demands feel free to pm me, i would be happy to help you Indicator
Karobein OscillatorDeveloped by Emily Karobein, the Karobein oscillator is an oscillator that aim to rescale smoothed values with more reactivity in a range of (0,1)
Calculation
The scaling method is similar to the one used in a kalman filter for the kalman gain.
We first average the up/downs x, those calculations are similar to the ones used for calculating the average gain/loss in the relative strength index.
a = ema(src < src ? x : 0,length)
b = ema(src > src ? x : 0,length)
where src is a exponential moving average of length period and x is src/src in the standard calculations, but anything else can be used as long as x > 0 .
Then we rescale the results.
c = x/(x + b)
d = 2*(x/(x + c*a)) - 1
How To Use
It is better to use centerline-cross/breakouts/signal line.
In general when we use something smooth as input in oscillators, breakouts are better than reversals, you can see this with the stochastic and rsi.
So a simple approach could be buying when crossing over 0.8 and selling when crossing under 0.2.
Here is the balance of a strategy using those conditions, length = 50 .
20 trades have been mades since the 29 oct we made 341 pips with eur/usd, of course this backtest was made during good trends period,
this result is not representative of how the strategy work with other conditions/markets.
For any questions/suggestions feel free to contact me
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