Indicator
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Smoothed Heikin Ashi Trend on Chart - TraderHalai BACKTESTSmoothed Heikin Ashi Trend on chart - Backtest
This is a backtest of the Smoothed Heikin Ashi Trend indicator, which computes the reverse candle close price required to flip a Heikin Ashi trend from red to green and vice versa. The original indicator can be found in the scripts section of my profile.
This particular back test uses this indicator with a Trend following paradigm with a percentage-based stop loss.
Note, that backtesting performance is not always indicative of future performance, but it does provide some basis for further development and walk-forward / live testing.
Testing was performed on Bitcoin , as this is a primary target market for me to use this kind of strategy.
Sample Backtesting results as of 10th June 2022:
Backtesting parameters:
Position size: 10% of equity
Long stop: 1% below entry
Short stop: 1% above entry
Repainting: Off
Smoothing: SMA
Period: 10
8 Hour:
Number of Trades: 1046
Gross Return: 249.27 %
CAGR Return: 14.04 %
Max Drawdown: 7.9 %
Win percentage: 28.01 %
Profit Factor (Expectancy): 2.019
Average Loss: 0.33 %
Average Win: 1.69 %
Average Time for Loss: 1 day
Average Time for Win: 5.33 days
1 Day:
Number of Trades: 429
Gross Return: 458.4 %
CAGR Return: 15.76 %
Max Drawdown: 6.37 %
Profit Factor (Expectancy): 2.804
Average Loss: 0.8 %
Average Win: 7.2 %
Average Time for Loss: 3 days
Average Time for Win: 16 days
5 Day:
Number of Trades: 69
Gross Return: 1614.9 %
CAGR Return: 26.7 %
Max Drawdown: 5.7 %
Profit Factor (Expectancy): 10.451
Average Loss: 3.64 %
Average Win: 81.17 %
Average Time for Loss: 15 days
Average Time for Win: 85 days
Analysis:
The strategy is typical amongst trend following strategies with a less regular win rate, but where profits are more significant than losses. Most of the losses are in sideways, low volatility markets. This strategy performs better on higher timeframes, where it shows a positive expectancy of the strategy.
The average win was positively impacted by Bitcoin’s earlier smaller market cap, as the percentage wins earlier were higher.
Overall the strategy shows potential for further development and may be suitable for walk-forward testing and out of sample analysis to be considered for a demo trading account.
Note in an actual trading setup, you may wish to use this with volatility filters, combined with support resistance zones for a better setup.
As always, this post/indicator/strategy is not financial advice, and please do your due diligence before trading this live.
Original indicator links:
On chart version -
Oscillator version -
Update - 27/06/2022
Unfortunately, It appears that the original script had been taken down due to auto-moderation because of concerns with no slippage / commission. I have since adjusted the backtest, and re-uploaded to include the following to address these concerns, and show that I am genuinely trying to give back to the community and not mislead anyone:
1) Include commission of 0.1% - to match Binance's maker fees prior to moving to a fee-less model.
2) Include slippage of 10 ticks (This is a realistic slippage figure from searching online for most crypto exchanges)
3) Adjust account balance to 10,000 - since most of us are not millionaires.
The rest of the backtesting parameters are comparable to previous results:
Backtesting parameters:
Initial capital: 10000 dollars
Position size: 10% of equity
Long stop: 2% below entry
Short stop: 2% above entry
Repainting: Off
Smoothing: SMA
Period: 10
Slippage: 10 ticks
Commission: 0.1%
This script still remains to shows viability / profitablity on higher term timeframes (with slightly higher drawdown), and I have included the backtest report below to document my findings:
8 Hour:
Number of Trades: 1082
Gross Return: 233.02%
CAGR Return: 14.04 %
Max Drawdown: 7.9 %
Win percentage: 25.6%
Profit Factor (Expectancy): 1.627
Average Loss: 0.46 %
Average Win: 2.18 %
Average Time for Loss: 1.33 day
Average Time for Win: 7.33 days
Once again, please do your own research and due dillegence before trading this live. This post is for education and information purposes only, and should not be taken as financial advice.
Strategy
Library
Heikin Ashi Volatility Percentile - TraderHalaiThe Heikin Ashi Volatility Percentile (HAVP) Oscillator was inspired by the legendary Bollinger Band Width Percentile indicator(known as BBWP), written by Caretaker, and made famous by Eric Krown, a famous influencer.
This script borrows aspects of the BBWP indicator which enables the HAVP oscillator to visually match the look and feel of BBWP and allows similar configuration functions (such as colouring function, smoothing MAs and alerts)
The fundamentals of this script are however different to BBWP. Instead of Bollinger band width, this script uses a reverse function of Heikin Ashi close (implemented in my Smoothed Heikin Ashi Trend
indicator, linked below).
The reverse Heikin Ashi close is smoothed using Ehler's SuperSmoother function, providing smooth oscillation and earlier signals of volatility tops and bottoms.
From an automated backtest that I have conducted on the BTCUSD index pair, I have observed comparable performance to BBWP across multiple timeframes when combining with stochastic direction to give a bias on overall direction. Using parameters I have tested, it performs better on mid-term timeframes such as 3h,4h and 6h. BBWP outperforms on 1h and 1d, with lower timeframes being comparable.
From the results, using HAVP over BBWP tends to result in reduced holding time and more frequent trades, which may or may not be desirable, although the behaviour can be adjusted using the parameters provided.
For instance, the smoother oscillation provided by HAVP provides a great predictability factor and earlier confirmation signals, which is something that Ehler emphasised in his trading style, and something which I agree with personally. I would encourage you to try out both HAVP and BBWP and see which fits your trading style.
Releasing this as open source allows for the betterment of the community and further development, criticism and discussion.
Thanks and enjoy! :) Indicator
Indicator
High-Low IndexHello All,
High-Low Index is a breadth indicator based on Record High Percent (RHP). RHP is based on new 52-week highs and new 52-week lows. RHP => 100 * (new highs) / (new highs + new lows). High-Low Index is a 10-day Simple Moving Average of the RHP, which makes it a smoothed version of RHP. You can find many articles about High-Low Index on the net.
High-Low Index above 50 indicates that there are more new highs than new lows, and considered as Bullish.
High-Low Index below 50 indicates that there are more new lows than new highs, and considered as Bearish.
High-Low Index = 0 indicates there is no new highs (0% new highs).
High-Low Index = 100 indicates that there is at least 1 new high and no new lows.
and High-Low Index = 50 indicates that new highs and new lows is equal.
by default 40 cryptos are used in the script and shows High-Low Index for these cryptos. but you can change them as you wish. for example you can set all of them as stocks and see High-Low Index for these stocks.
You can set " Time frame " and the " Length " using the options. For example; if you set " Time frame " = 1 Week and the " Length " = 52 then it finds High-Low Index for 52weeks .
or another example; if you set " Time frame " = 1 Day and the " Length " = 22 the High-Low Indexn it finds High-Low Index for 22days.
You can enable/disable Record High Percent or Simple Moving Average of High-Low Index. Some traders use High-Low Index with its SMA, for example; High-Low Index generates a buy signal when it crosses above its moving average, and a sell signal when it crosses below its moving average.
Optionally you can see the securities in a table on the left bottom, you can change table size by usşng the options.
In the Table, for each security/cell;
=> if background is green then it has New High
=> if background is red then it has New Low
=> if background is gray then no New High, no New Low
=> if background is back then Data is not available for the security
As you can see in the screenshot below, the securities were changed and stocks are used instead of cryptos, so it calculates & shows High-Low Index for these stocks.
you can also find explanation in this screenshot:
Enjoy!
Indicator
AnalysisInterpolationLoessLibrary "AnalysisInterpolationLoess"
LOESS, local weighted Smoothing function.
loess(sample_x, sample_y, point_span) LOESS, local weighted Smoothing function.
Parameters:
sample_x : int array, x values.
sample_y : float array, y values.
point_span : int, local point interval span.
aloess(sample_x, sample_y, point_span) aLOESS, adaptive local weighted Smoothing function.
Parameters:
sample_x : int array, x values.
sample_y : float array, y values.
point_span : int, local point interval span.
Library
Strategy
Indicator
Heikin Ashi Candle OverlayHello Friend,
This is a very simple script for fun to demonstrate the new ability to change the colors of attributes pertaining to the plotbar() and plotcandle() functions using series inputs.
For Heiken Ashi lovers, this script does several things. It gives you both bars and hollow candles with Heikin Ashi values - something TV does not currently support.
It also gives you the ability to see your favorite HA candles while on the main series plot. When viewing indicators in the "Heikin Ashi" candle setting on PulseWire, the input values are "smoothed' with HA values. This skews the way your indicators behave as the OLHC are calculated averages. Only the regular candle settings will give your indicators "real close" etc.
By 'Muting' the main series bars by toggling the 👁 symbol next to your ticker id, it makes the normal candles invisible. You then overlay this script, which allows you to see the HA Candle of your choice, while not affecting the way your indicators behave.
You now have the best of 2 worlds. Smoothed behavior of price action to help visualize trends, and accurate indicator values derived from actual OLHC data.
Plus, something about hollow HA candles is just kind of clean and soothing isn't it?
Cheers,
Bjorgum
Hollow Setting:
Bars
Or just plain old regular, but on the main chart
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Trigonometric On Balance Volume (OBV) OscillatorLove volume analysis but it's hard for you to implement a simple strategy by it?
Use OBV.
Is OBV still not quite as it should be for you to get it in your trading system?
Use OBV Oscillator.
Does OBV Oscillator give you too many false signals and when you smooth it, it lags by a ton?
Then this indicator is the answer to your problem.
Introducing the Trigonometric OBV Oscillator.
The Trigonometric OBV Oscillator or "Trig OBV" for short, uses an old, but uniquely extremely reliable mathematical formula to smooth the OBV, while eliminating more than 95% of its false signals (noises) and keeping with the real direction of the trend without introducing any lags.
It is very responsive, predictive even to some degree, very reliable, and keeps you out of false trades (like false breakouts, sudden changes in the price, etc).
To go long: wait until the white line crosses up the purple line and continues in that direction.
To go short: wait until the white line crosses down the blue line and continues in that direction.
To exit, do the opposite.
Better to be used with a baseline filter such as Kaufman's moving average.
Use it and let me know what you think about it. Indicator
Trend Regularity Adaptive Moving Average [LuxAlgo]The following moving average adapt to the average number of highest high/lowest low made over a specific period, thus adapting to trend strength. Interesting results can be obtained when using the moving average in a MA crossover system or as a trailing support/resistance.
Settings
Length : Period of the indicator, with higher values returning smoother results.
Src : Source input of the indicator.
Usage
The trend regularity adaptive moving average (TRAMA) can be used like most moving averages, with the advantage of being smoother during ranging markets.
Notice how the moving closer to the price the longer a trend last, such effect can be practical to have early entry points when using the moving average in a MA crossover system, such effect is due to the increasing number of average highest high/lowest low made during longer trends. Note that in the case of a significant uptrend followed by a downtrend, the moving average might penalize the start of the downtrend (and vice versa).
The moving average can also act as an interesting trailing support/resistance.
Details
The moving average is calculated using exponential averaging, using as smoothing factor the squared simple moving average of the number of highest high/lowest low previously made, highest high/lowest low are calculated using rolling maximums/minimums.
Using higher values of length will return fewer highest high/lowest low which explains why the moving average is smoother for higher length values. Squaring allows the moving average to penalize lower values, thus appearing more stationary during ranging markets, it also allows to have some consistency regarding the length setting.
🧙 this moving average would not be possible without the existence of corn syrup 🦎 Indicator
A Useful MA Weighting Function For Controlling Lag & SmoothnessSo far the most widely used moving average with an adjustable weighting function is the Arnaud Legoux moving average (ALMA), who uses a Gaussian function as weighting function. Adjustable weighting functions are useful since they allow us to control characteristics of the moving average such as lag and smoothness.
The following moving average has a simple adjustable weighting function that allows the user to have control over the lag and smoothness of the moving average, we will see that it can also be used to get both an SMA and WMA.
A high-resolution gradient is also used to color the moving average, makes it fun to watch, the plot transition between 200 colors, would be tedious to make but everything was made possible using a custom R script, I only needed to copy and paste the R console output in the Pine editor.
Settings
length : Period of the moving average
-Lag : Setting decreasing the lag of the moving average
+Lag : Setting increasing the lag of the moving average
Estimating Existing Moving Averages
The weighting function of this moving average is derived from the calculation of the beta distribution, advantages of such distribution is that unlike a lot of PDF, the beta distribution is defined within a specific range of values (0,1). Parameters alpha and beta controls the shape of the distribution, with alpha introducing negative skewness and beta introducing positive skewness, while higher values of alpha and beta increase kurtosis.
Here -Lag is directly associated to beta while +Lag is associated with alpha . When alpha = beta = 1 the distribution is uniform, and as such can be used to compute a simple moving average.
Moving average with -Lag = +Lag = 1 , its impulse response is shown below.
It is also possible to get a WMA by increasing -Lag , thus having -Lag = 2 and +Lag = 1 .
Using values of -Lag and +Lag equal to each other allows us to get a symmetrical impulse response, increasing these two values controls the heaviness of the tails of the impulse response.
Here -Lag = +Lag = 3 , note that when the impulse response of a moving average is symmetrical its lag is equal to (length-1)/2 .
As for the gradient, the color is determined by the value of an RSI using the moving average as input.
I don't promise anything but I will try to respond to your comments Indicator
Indicator
Shapeshifting Moving Average - Switching From Low-Lag To SmoothThe term "shapeshifting" is more appropriate when used with something with a shape that isn't supposed to change, this is not the case of a moving average whose shape can be altered by the length setting or even by an external factor in the case of adaptive moving averages, but i'll stick with it since it describe the purpose of the proposed moving average pretty well.
In the case of moving averages based on convolution, their properties are fully described by the moving average kernel ( set of weights ), smooth moving averages tend to have a symmetrical bell shaped kernel, while low lag moving averages have negative weights. One of the few moving averages that would let the user alter the shape of its kernel is the Arnaud Legoux moving average, which convolve the input signal with a parametric gaussian function in which the center and width can be changed by the user, however this moving average is not a low-lagging one, as the weights don't include negative values.
Other moving averages where the user can change the kernel from user settings where already presented, i posted a lot of them, but they only focused on letting the user decrease or increase the lag of the moving average, and didn't included specific parameters controlling its smoothness. This is why the shapeshifting moving average is proposed, this parametric moving average will let the user switch from a smooth moving average to a low-lagging one while controlling the amount of lag of the moving average.
Settings/Kernel Interaction
Note that it could be possible to design a specific kernel function in order to provide a more efficient approach to today goal, but the original indicator was a simple low-lag moving average based on a modification of the second derivative of the arc tangent function and because i judged the indicator a bit boring i decided to include this parametric particularity.
As said the moving average "kernel", who refer to the set of weights used by the moving average, is based on a modification of the second derivative of the arc tangent function, the arc tangent function has a "S" shaped curve, "S" shaped functions are called sigmoid functions, the first derivative of a sigmoid function is bell shaped, which is extremely nice in order to design smooth moving averages, the second derivative of a sigmoid function produce a "sinusoid" like shape ( i don't have english words to describe such shape, let me know if you have an idea ) and is great to design bandpass filters.
We modify this 2nd derivative in order to have a decreasing function with negative values near the end, and we end up with:
The function is parametric, and the user can change it ( thus changing the properties of the moving average ) by using the settings, for example an higher power value would reduce the lag of the moving average while increasing overshoots. When power < 3 the moving average can act as a slow moving average in a moving average crossover system, as weights would not include negative values.
Here power = 0 and length = 50. The shapeshifting moving average can approximate a simple moving average with very low power values, as this would make the kernel approximate a rectangular function, however this is only a curiosity and not something you should do.
As A Smooth Moving Average
“So smooth, and so tranquil. It doesn't get any quieter than this”
A smooth moving average kernel should be : symmetrical, not to width and not to sharp, bell shaped curve are often appropriates, the proposed moving average kernel can be symmetrical and can return extremely smooth results. I will use the Blackman filter as comparison.
The smooth version of the moving average can be used when the "smooth" setting is selected. Here power can only be an even number, if power is odd, power will be equal to the nearest lowest even number. When power = 0, the kernel is simply a parabola:
More smoothness can be achieved by using power = 2
In red the shapeshifting moving average, in green a Blackman filter of both length = 100. Higher values of power will create lower negative values near the border of the kernel shape, this often allow to retain information about the peaks and valleys in the input signal. Power = 6 approximate the Blackman filter pretty well.
Conclusion
A moving average using a modification of the 2nd derivative of the arc tangent function as kernel has been presented, the kernel is parametric and allow the user to switch from a low-lag moving average where the lag can be increased/decreased to a really smooth moving average.
As you can see once you get familiar with a function shape, you can know what would be the characteristics of a moving average using it as kernel, this is where you start getting intimate with moving averages.
On a side note, have you noticed that the views counter in posted ideas/indicators has been removed ? This is truly a marvelous idea don't you think ?
Thanks for reading !
Indicator
Right Sided Ricker Moving Average And The Gaussian DerivativesIn general gaussian related indicators are built by using the gaussian function in one way or another, for example a gaussian filter is built by using a truncated gaussian function as filter kernel (kernel refer to the set weights) and has many great properties, note that i say truncated because the gaussian function is not supposed to be finite. In general the gaussian function is represented by a symmetrical bell shaped curve, however the gaussian function is parametric, and the user might adjust the position of the peak as well as the width of the curve, an indicator using this parametric approach is the Arnaud Legoux moving average (ALMA) who posses a length parameter controlling the filter length, a peak parameter controlling the position of the peak of the gaussian function as well as a width parameter, those parameters can increase/decrease the lag and smoothness of the moving average output.
However what about the derivatives of the gaussian function ? We don't talk much about them and thats a pity because they are extremely interesting and have many great properties as well, therefore in this post i'll present a low lag moving average based on the modification of the 2nd order derivative of the gaussian function, i believe this post will be extremely informative and i hope you will enjoy reading it, if you are not a math person you can skip the introduction on gaussian derivatives and their properties used as filter kernel.
Gaussian Derivatives And The Ricker Wavelet
The notion of derivative is continuous, so we will stick with the term discrete derivative instead, which just refer to the rate of change in the function, we have a change function in pinescript, and we will be using it to show an approximation of the gaussian function derivatives.
Earlier i used the term 2nd order derivative, here the derivative order refer to the order of differentiation, that is the number of time we apply the change function. For example the 0 (zeroth) order derivative mean no differentiation, the 1st order derivative mean we use differentiation 1 time, that is change(f) , 2nd order mean we use differentiation 2 times, that is change(change(f)) , derivates based on multiple differentiation are called "higher derivative". It will be easier to show a graphic :
Here we can see a normal gaussian function in blue, its scaled 1st order derivative in orange, and its scaled 2nd derivative in green, note that i use scaled because i used multiplication in order for you to see each curve, else it would have been less easy to observe them. The number of time a gaussian function derivative cross 0 is based on the order of differentiation, that is 2nd order = the function crossing 0 two times.
Now we can explain what is the Ricker wavelet, the Ricker wavelet is just the normalized 2nd order derivative of a gaussian function with inverted sign, and unlike the gaussian function the only thing you can change is the width parameter. The formula of the Ricker wavelet is show'n here en.wikipedia.org , where sigma is the width parameter.
The Ricker wavelet has this look :
Because she is shaped like a sombrero the Ricker wavelet is also called "mexican hat wavelet", now what would happen if we used a Ricker wavelet as filter kernel ? The response is that we would end-up with a bandpass filter, in fact the derivatives of the gaussian function would all give the kernel of a bandpass filter, with higher order derivatives making the frequency response of the filter approximate a symmetrical gaussian function, if i recall a filter using the first order derivative of a gaussian function would give a frequency response that is left skewed, this skewness is removed when using higher order derivatives.
The Indicator
I didn't wanted to make a bandpass filter, as lately i'am more interested in low-lag filters, so how can we use the Ricker wavelet to make a low-lag low-pass filter ? The response is by taking the right side of the Ricker wavelet, and since values of the wavelets are negatives near the border we know that the filter passband is non-monotonic, that is we know that the filter will have low-lag as frequencies in the passband will be amplified.
So taking the right side of the Ricker wavelet only mean that t has to be greater than 0 and linearly increasing, thats easy, however the width parameter can be tricky to use, this was already the case with ALMA, so how can we work with it ? First it can be seen that values of width needs to be adjusted based on the filter length.
In red width = 14, in green width = 5. We can see that an higher values of width would give really low weights, when the number of negative weights is too important the filter can have a negative group delay thus becoming predictive, this simply mean that the overshoots/undershoots will be crazy wild and that a great fit will be impossible.
Here two moving averages using the previous described kernels, they don't fit the price well at all ! In order to fix this we can simply define width as a function of the filter length, therefore the parameter "Percentage Width" was introduced, and simply set the width of the Ricker wavelet as p percent of the filter length. Lower values of percent width reduce the lag of the moving average, but lets see precisely how this parameter influence the filter output :
Here the filter length is equal to 100, and the percent width is equal to 60, the fit is quite great, lower values of percent width will increase overshoots, in fact the filter become predictive once the percent width is equal or lower to 50.
Here the percent width is equal to 50. Higher values of percent width reduce the overshoots, and a value of 100 return a filter with no overshoots that is suited to act as a lagging moving average.
Above percent width is set to 100. In order to make use of the predictive side of the filter, it would be great to introduce a forecast option, however this require to find the best forecast horizon period based on length and width, this is no easy task.
Finally lets estimate a least squares moving average with the proposed moving average, you know me...a percent width set to 63 will return a relatively good estimate of the LSMA.
LSMA in green and the proposed moving in red with percent width = 63 and both length = 100.
Conclusion
A new low-lag moving average using a right sided Ricker wavelet as filter kernel has been introduced, we have also seen some properties of gaussian derivatives. You can see that lately i published more moving averages where the user can adjust certain properties of the filter kernel such as curve width for example, if you like those moving averages you can check the Parametric Corrective Linear Moving Averages indicator published last month :
I don't exclude working with pure forms of gaussian derivatives in the future, as i didn't published much oscillators lately.
Thx for reading !
Indicator
Grover Llorens Cycle Oscillator [alexgrover & Lucía Llorens]Cycles represent relatively smooth fluctuations with mean 0 and of varying period and amplitude, their estimation using technical indicators has always been a major task. In the additive model of price, the cycle is a component :
Price = Trend + Cycle + Noise
Based on this model we can deduce that :
Cycle = Price - Trend - Noise
The indicators specialized on the estimation of cycles are oscillators, some like bandpass filters aim to return a correct estimate of the cycles, while others might only show a deformation of them, this can be done in order to maximize the visualization of the cycles.
Today an oscillator who aim to maximize the visualization of the cycles is presented, the oscillator is based on the difference between the price and the previously proposed Grover Llorens activator indicator. A relative strength index is then applied to this difference in order to minimize the change of amplitude in the cycles.
The Indicator
The indicator include the length and mult settings used by the Grover Llorens activator. Length control the rate of convergence of the activator, lower values of length will output cycles of a faster period.
here length = 50
Mult is responsible for maximizing the visualization of the cycles, low values of mult will return a less cyclical output.
Here mult = 1
Finally you can smooth the indicator output if you want (smooth by default), you can uncheck the option if you want a noisy output.
The smoothing amount is also linked with the period of the rsi.
Here the smoothing amount = 100.
Conclusion
An oscillator based on the recently posted Grover Llorens activator has been proposed. The oscillator aim to maximize the visualization of cycles.
Maximizing the visualization of cycles don't comes with no cost, the indicator output can be uncorrelated with the actual cycles or can return cycles that are not present in the price. Other problems arises from the indicator settings, because cycles are of a time-varying periods it isn't optimal to use fixed length oscillators for their estimation.
Thanks for reading !
If my work has ever been of use to you you can donate, addresses on my signature :)
Indicator
Grand Trend Forecasting - A Simple And Original Approach Today we'll link time series forecasting with signal processing in order to provide an original and funny trend forecasting method, the post share lot of information, if you just want to see how to use the indicator then go to the section "Using The Indicator".
Time series forecasting is an area dealing with the prediction of future values of a series by using a specific model, the model is the main tool that is used for forecasting, and is often an expression based on a set of predictor terms and parameters, for example the linear regression (model) is a 1st order polynomial (expression) using 2 parameters and a predictor variable ax + b . Today we won't be using the linear regression nor the LSMA.
In time series analysis we can describe the time series with a model, in the case of the closing price a simple model could be as follows :
Price = Trend + Cycles + Noise
The variables of the model are the components, such model is additive since we add the component with each others, we should be familiar with each components of the model, the trend represent a simple long term variation of high amplitude, the cycles are periodic fluctuations centered around 0 of varying period and amplitude, the noise component represent shorter term irregular variations with mean 0.
As a trader we are mostly interested by the cycles and the trend, altho the cycles are relatively more technical to trade and can constitute parasitic fluctuations (think about retracements in a trend affecting your trend indicator, causing potential false signals).
If you are curious, in signal processing combining components has a specific name, "synthesis" , here we are dealing with additive synthesis, other type of synthesis are more specific to audio processing and are relatively more complex, but could be used in technical analysis.
So what to do with our components ? If we want to trade the trend, we should estimate right ? Estimating the trend component involve removing the cycle and noise component from the price, if you have read stuff about filters you should know where i'am going, yep, we should use filters, in the case of keeping the trend we can use a simple moving average of relatively high period, and here we go.
However the lag problem, which is recurrent, come back again, we end up with information easier to interpret (here the trend, which is a simple fluctuation such as a line or other smooth curve) at the cost of decision timing, that is unfortunate but as i said the information, here the moving average output, is relatively simple, and could be easily forecasted right ? If you plot a moving average of high period it would be easier for you to forecast its future values. And thats what we aim to do today, provide an estimate of the trend that should be easy to forecast, and should fit to the price relatively well in order to produce forecast that could determine the position of future closing prices observations.
Estimating And Forecasting The Trend
The parameter of the indicator dealing with the estimation of the trend is length , with higher values of length attenuating the cycle and noise component in the price, note however that high values of length can return a really long term trend unlike a simple moving average, so a small value of length, 14 for example can still produce relatively correct estimate of trend.
here length = 14.
The rough estimate of the trend is t in the code, and is an IIR filter, that is, it is based on recursion. Now i'll pass on the filter design explanation but in short, weights are constants, with higher weights allocated to the previous length values of the filter, you can see on the code that the first part of t is similar to an exponential moving average with :
t(n) = 0.9t(n-length) + 0.1*Price
However while the EMA only use the precedent value for the recursion, here we use the precedent length value, this would just output a noisy and really slow output, therefore in order to create a better fit we add : 0.9*(t(n-length) - t(n-2length)) , and this create the rough trend estimate that you can see in blue. On the parameters, 0.9 is used since it gives the best estimate in my opinion, higher values would create more periodic output and lower values would just create a rougher output.
The blue line still contain a residual of the cycle/noise component, this is why it is smoothed with a simple moving average of period length. If you are curious, a filter estimating the trend but still containing noisy fluctuations is called "Notch" filter, such filter would depending on the cutoff remove/attenuate mid term cyclic fluctuations while preserving the trend and the noise, its the opposite of a bandpass filter.
In order to forecast values, we simply sum our trend estimate with the trend estimate change with period equal to the forecasting horizon period, this is a really really simple forecasting method, but it can produce decent results, it can also allows the forecast to start from the last point of the trend estimate.
Using The Indicator
We explained the length parameter in the precedent section, src is the input series which the trend is estimated, forecast determine the forecasting horizon, recommend values for forecast should be equal to length, length/2 or length*2, altho i strongly recommend length.
here length and forecast are both equal to 14 .
The corrective parameter affect the trend estimate, it reduce the overshoot and can led to a curve that might fit better to the price.
The indicator with the non corrective version above, and the corrective one below.
The source parameter determine the source of the forecast, when "Noisy" is selected the source is the blue line, and produce a noisy forecast, when "Smooth" is selected the source is the moving average of t , this create a smoother forecast.
The width interval control...the width of the intervals, they can be seen above and under the forecast plot, they are constructed by adding/subtracting the forecast with the forecast moving average absolute error with respect to the price. Prediction intervals are often associated with a probability (determining the probability of future values being between the interval) here we can't determine such probability with accuracy, this require (i think) an analysis of the forecasting distribution as well as assumptions on the distribution of the forecasting error.
Finally it is possible to see historical forecasts, that is, forecasts previously generated by checking the "Show Historical Forecasts" option.
Examples
Good forecasts mostly occur when the price is close to the trend estimate, this include the following highlighted periods on AMD 15TF with default settings :
We can see the same thing at the end of EURUSD :
However we can't always obtain suitable fits, here it is isn't sufficient on BTCUSD :
We can see wide intervals, we could change length or use the corrective option to get better results, another option is to use a log scale.
We will end the examples with the log SPX, who posses a linear trend, so for example a linear model such as a linear regression would be really adapted, lets see how the indicator perform :
Not a great fit, we could try to use an higher length value and use "Smooth" :
Most recent fits are quite decent.
Conclusions
A forecasting indicator has been presented in this post. The indicator use an original approach toward estimating the trend component in the closing price. Of course i should have given statistics related to the forecasting error, however such analysis is worth doing with better methods and in more advanced environment allowing for optimization.
But we have learned some stuff related to signal processing as well as time series analysis, seeing a time series as the sum of various components is really helpful when it comes to make sense of chaotic and noisy series and is a basic topic in time series analysis.
You can see that in this new year i work harder on the visual of my indicators without trying to fall in the label addict trap, something that i wasn't really doing before, let me know what do you think of it.
Thanks for reading !
Indicator
