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TF Segmented Linear RegressionFit a line at successive intervals, where the interval period is determined by a user-selected time frame, this allows the user to have an estimate of the intrinsic trend within various intervals.
Settings
Timeframe : Determine the period of the interval, if the timeframe is weekly then a new line will be fit at the start each weeks, by default "Daily"
Mult : Multiplication factor for the RMSE, determine the distance between the upper and lower extremities
Src : Input data for the indicator
Plot Extremities : Logical value, if true then the extremities of the channel are plotted, if false only the midline is plotted, true by default.
Usage
The timeframe setting should be higher than the current chart timeframe, note however that too large values of timeframe might return an error. Since the maximum number of lines that can be plotted is 54, using the extremities will only return 18 channels.
The indicator can be compared to the "regression trend" drawing tool
Main tf = 5 min with the indicator using a daily timeframe, the filled area is produced by the regression trend drawing tool using the same interval as the indicator, and coincide with it.
Main tf = 15 min with the indicator using a weekly timeframe, wider channel indicate that the values tend to be farther away from the fitted line.
A line with a significant slope indicates a strong trend, in that case, the width of the channel is determined by the amplitude of the retracements in the trend, with a narrower channel indicating a cleaner trend.
When the fitted line has a low slope value and the channel is wide, it means that there were two or more variations of opposite directions with large amplitudes within the interval, this also indicates that a linear model is not appropriate.
A slope approximately equal to 0 with a low channel width indicates a trendless market with cyclical variations of low amplitude in it.
Refrences
Determining the starting and ending points of the fitted line was done using a linear combination between the wma and sma
The wma and sma functions both use a series as period by making use of the Wma and Sum functions in the following script
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Computing The Linear Regression Using The WMA And SMAPlot a linear regression channel through the last length closing prices, with the possibility to use another source as input. The line is fit by using linear combinations between the WMA and SMA thus providing both an interesting and efficient method. The results are the same as the one provided by the built-in linear regression, only the computation differ.
Settings
length : Number of inputs to be used.
src : Source input of the indicator.
mult : Multiplication factor for the RMSE, determine the distance between the upper and lower level.
Usage
In technical analysis a linear regression can provide an estimate of the underlying trend in the price, this result can be extrapolated to have an estimate of the future evolution of the trend, while the upper and lower level can be used as support and resistance levels.
The slope of the fitted line indicates both the direction and strength of the trend, with a positive slope indicating an up-trending market while a negative slope indicates a down-trending market, a steeper line indicates a stronger trend.
We can see that the trend of the S&P500 in this chart is approximately linear, the upper and lower levels were previously tested and might return accurate support and resistance points in the future.
By using a linear regression we are making the following assumptions:
The trend is linear or approximately linear.
The cycle component has an approximately constant amplitude (this allows the upper and lower level to be more effective)
The underlying trend will have the same evolution in the future
In the case where the growth of a trend is non-linear, we can use a logarithmic scale to have a linear representation of the trend.
Details
In a simple linear regression, we want to the slope and intercept parameters that minimize the sum of squared residuals between the data points and the fitted line
intercept + x*slope
Both the intercept and slope have a simple solution, you can find both in the calculations of the lsma, in fact, the last point of the lsma with period length is equal to the last point of a linear regression fitted through the same length data points. We have seen many times that the lsma is an FIR filter with a series of coefficients representing a linearly decaying function with the last coefficients having a negative value, as such we can calculate the lsma more easily by using a linear combination between a WMA and SMA: 3WMA - 2SMA , this linear combination gives us the last point of our linear regression, denoted point B .
Now we need the first point of our linear regression, by using the calculations of the lsma we get this point by using:
intercept + (x-length+1)*slope
If we get the impulse response of such lsma we get
In blue the impulse response of a standard lsma, in red the impulse response of the lsma using the previous calculation, we can see that both are the same with the exception that the red one appears as being time inverted, the first coefficients are negative values and as such we also have a linear operation involving the WMA and SMA but with inverted terms and different coefficients, therefore the first point of our linear regression, denoted point A , is given by 4SMA - 3WMA , we then only need to join these two points thanks to "line.new".
The levels are simply equal to the fitted line plus/minus the root mean squared error between the fitted line and the data points, right now we only have two points, we need to find all the points of the fitted line, as such we first need to find the slope, which can be calculated by diving the vertical distance between B and A (the rise) with the horizontal distance between B and A (the run), that is
(A - B)/(length-1)
Once done we can find each point of our line by using
B + slope*i
where i is the position of the point starting from B, i=0 give B since B + slope*0 = B , then we continue for every i , we then only need to sum the squared distance between each closing prices at position i and the point found at that same position, we divide by length-1 and take the square root of the result in order to have the RMSE.
In Summary
The following post as shown that it was possible to compute a linear regression by using a linear combination between the WMA and SMA, since both had extremely efficient computations (see link at the end of the post) we could have a calculation for the linear regression where the number of operations is independent of length .
This post took me eons to make because it's related to the lsma, and I am rarely short on words when it comes to anything related to the lsma. Thx to LucF for the feedback and everything.
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Price-Line Channel - A Friendly Support And Resistance IndicatorIntroduction
Lines are the most widely used figures in technical analysis, this is due to the linear trends that some securities posses (daily log SP500 for example), support and resistances are also responsible for the uses of lines, basically linear support and resistances are made with the assumption that the line connecting two local maximas or minimas will help the user detect a new local maxima or minima when the price will cross the line.
Technical indicators attempting to output lines have always been a concern in technical analysis, the mostly know certainly being the linear regression, however any linear models would fit in this category. In general those indicators always reevaluate their outputs values (repainting), others non repainting indicators returning lines are sometimes to impractical to set-up. This is what has encouraged me to make a simpler indicator based on the framework used in the recursive bands indicator that i published.
The proposed indicator aim to be extremely flexible and easy to use while returning linear support and resistances, an option that allow readjustment is also introduced, thus allowing for a "smarter" indicator.
The Indicator
The indicator return two extremities, the upper one aim to detect resistance points while the lower one aim to detect support points. The length setting control the steepness of the line, with higher values of length involving a lower slope, this make the indicator less reactive and interact with the price less often.
The name "price-line" comes from the fact that the channel is dependent on its own interaction with the price, therefore a breakout methodology can also be used, where price is up-trending when crossing with the upper extremity and down trending when crossing with the lower one.
Readjusted Option
The line steepness can be readjusted based on the market volatility, it make more sense for the line to be more steep when the market is more volatile, thus making it converge faster toward the price, this of course is done at the cost of some linearity. This is achieved by checking the "readjustment" option. The effects can be shown on BTCUSD, below the indicator without the readjusted option :
when the "readjustment" option is checked we have the following results :
The volatile down movement on BTCUSd make the upper extremity converge faster toward the price, this option can be great for volatile markets.
Conclusion
The recursive bands indicator prove to be an excellent framework that allow for the creation of lots of indicators, the proposed indicator is extremely efficient and provide an easy solution for returning linear support and resistances without much drawbacks, the readjusted option allow the indicator to adapt to the market volatility at the cost of linearity.
The performance of the indicator is relative to the motion of the price, however the indicator show signs of returning accurate support and resistances points. I hope the indicator find its use in the community.
Thanks for reading !
Note
Respect the house rules, always request permission before publishing open source code. This is an original work, requesting permission is the least you can do.
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Forecasting - Drift MethodIntroduction
Nothing fancy in terms of code, take this post as an educational post where i provide information rather than an useful tool.
Time-Series Forecasting And The Drift Method
In time-series analysis one can use many many forecasting methods, some share similarities but they can all by classified in groups and sub-groups, the drift method is a forecasting method that unlike averages/naive methods does not have a constant (flat) forecast, instead the drift method can increase or decrease over time, this is why its a great method when it comes to forecasting linear trends.
Basically a drift forecast is like a linear extrapolation, first you take the first and last point of your data and draw a line between those points, extend this line into the future and you have a forecast, thats pretty much it.
One of the advantage of this method is first its simplicity, everyone could do it by hand without any mathematical calculations, then its ability to be non-conservative, conservative methods involve methods that fit the data very well such as linear/non-linear regression that best fit a curve to the data using the method of least-squares, those methods take into consideration all the data points, however the drift method only care about the first and last point.
Understanding Bias And Variance
In order to follow with the ability of methods to be non-conservative i want to introduce the concept of bias and variance, which are essentials in time-series analysis and machine learning.
First lets talk about training a model, when forecasting a time-series we can divide our data set in two, the first part being the training set and the second one the testing set. In the training set we fit a model to the training data, for example :
We use 200 data points, we split this set in two sets, the first one is for training which is in blue, and the other one for testing which is in green.
Basically the Bias is related to how well a forecasting model fit the training set, while the variance is related to how well the model fit the testing set. In our case we can see that the drift line does not fit the training set very well, it is then said to have high bias. If we check the testing set :
We can see that it does not fit the testing set very well, so the model is said to have high variance. It can be better to talk of bias and variance when using regression, but i think you get it. This is an important concept in machine learning, you'll often see the term "overfitting" which relate to a model fitting the training set really well, those models have a low to no bias, however when it comes to testing they don't fit well at all, they have high variance.
Conclusion On The Drift Method
The drift method is good at forecasting linear trends, and thats all...you see, when forecasting financial data you need models that are able to capture the complexity of the price structure as well as being robust to noise and outliers, the drift method isn't able to capture such complexity, its not a super smart method, same goes for linear regression. This is why more peoples are switching to more advanced models such a neural networks that can sometimes capture such complexity and return decent results.
So this method might not be the best but if you like lines then here you go.
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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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Efficient Auto LineMore Efficiency
Based on the Auto-Line code, the Efficient Auto Line aim to provide a more controlled adaptivity of the indicator. The first indicator of this sort worked this way : when the absolute difference between the price and the indicator is higher than the previous indicator +/- A pips of amplitude, the indicator will display the closing price, else its anterior value. The second indicator (Auto-Line) was adaptive and used the standard deviation instead of a constant A . This indicator will run both methodology providing both a trend strength indicator (Efficiency Ratio) parameter and two constant parameter.
Parameters
The length parameter will control the period of the efficiency ratio, a high period return lower values of the efficiency ratio. Since its an indicator in a range of (0,1) we use it to make our indicator more adaptive in trending market, this is when we need our two constant parameters, the fast/slow parameter can be any amount of pips where fast < slow , when the price is trending (efficiency ratio close to 1) the indicator will use the fast parameter, if its ranging (efficiency ratio away from 1) the indicator will use the slow parameter, then it will work like the first methodology previously explained. So the fast parameter should be equal to a small movement of pips (0.0001 or 1 pip) and the slow parameter should be equal to a number of pips you wont expect to see in a ranging market. At this point it is good to test for both parameter and see which values work better (a more automatic process is in development) .
Hope you like it ! Indicator
