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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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LWMA: Linear Weighted Moving AverageCouldn't find searching for Linearly Weighted Moving Average (LWMA) in pulsewire. Found one with the LWMA title, but it uses plain WMA calculation without the linearity which more heavily weights recent price data, which I need, so I try to made one.
LWMAs are also quicker to react to price changes than SMA and EMA. If you want a moving average with less lag than an SMA, try a LWMA.
It kind of also have a more clarity in defining the price trend and reversals. Trade signals usually based on crossovers, they can also indicate areas of potential support or resistance. But beware though, multiple false signals may also occur before a significant trend develops. Use a filter, some decent volatility oscillator might do the job.
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The formula for this Linearly Weighted Moving Average is:
LWMA = (( P n∗ W 1)+( P n−1∗ W 2)+( P n−2∗ W 3)...) / ∑W
P = Price for the period
n = The most recent period, n-1 is the prior period, and n-2 is two periods prior
W = The assigned weight to each period, with the highest weight going first and then descending linearly based on the number of periods being used.
I hope I'm doing right translating it to Pine Script 4. Let me know if I miss something.
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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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Linear Regression Trend ChannelThis is my first public release of indicator code and my PSv4.0 version of "Linear Regression Channel", as it is more commonly known. It replicates TV's built-in "Linear Regression" without the distraction of heavy red/blue fill bleeding into other indicators. We can't fill() line.new() at this time in Pine Script anyways. I entitled it Linear Regression Trend Channel, simply because it seems more accurate as a proper description. I nicely packaged this to the size of an ordinary napkin within 20 lines of compact code, simplifying the math to the most efficient script I could devise that fits in your pocket. This is commonly what my dense intricate code looks like behind the veil, and if you are wondering why there is no notes, that's because the notation is in the variable naming. I excluded Pearson correlation because it doesn't seem very useful to me, and it would comprise of additional lines of code I would rather avoid in this public release. Pearson correlation is included in my invite-only advanced version of "Enhanced Linear Regression Trend Channel", where I have taken Linear Regression Channeling to another level of fully featured novel attainability using this original source code.
Features List Includes:
"Period" adjustment
"Deviation(s)" adjustment
"Extend Method" option to extend or not extend the upper, medial, and lower channeling
Showcased in the chart below is my free to use "Enhanced Schaff Trend Cycle Indicator", having a common appeal to TV users frequently. If you do have any questions or comments regarding this indicator, I will consider your inquiries, thoughts, and ideas presented below in the comments section, when time provides it. As always, "Like" it if you simply just like it with a proper thumbs up, and also return to my scripts list occasionally for additional postings. Have a profitable future everyone! Indicator
Time Series ForecastIntroduction
Forecasting is a blurry science that deal with lot of uncertainty. Most of the time forecasting is made with the assumption that past values can be used to forecast a time series, the accuracy of the forecast depend on the type of time series, the pre-processing applied to it, the forecast model and the parameters of the model.
In pulsewire we don't have much forecasting models appart from the linear regression which is definitely not adapted to forecast financial markets, instead we mainly use it as support/resistance indicator. So i wanted to try making a forecasting tool based on the lsma that might provide something at least interesting, i hope you find an use to it.
The Method
Remember that the regression model and the lsma are closely related, both share the same equation ax + b but the lsma will use running parameters while a and b are constants in a linear regression, the last point of the lsma of period p is the last point of the linear regression that fit a line to the price at time p to 1, try to add a linear regression with count = 100 and an lsma of length = 100 and you will see, this is why the lsma is also called "end point moving average".
The forecast of the linear regression is the linear extrapolation of the fitted line, however the proposed indicator forecast is the linear extrapolation between the value of the lsma at time length and the last value of the lsma when short term extrapolation is false, when short term extrapolation is checked the forecast is the linear extrapolation between the lsma value prior to the last point and the last lsma value.
long term extrapolation, length = 1000
short term extrapolation, length = 1000
How To Use
Intervals are create from the running mean absolute error between the price and the lsma. Those intervals can be interpreted as possible support and resistance levels when using long term extrapolation, make sure that the intervals have been priorly tested, this mean the intervals are more significants.
The short term extrapolation is made with the assumption that the price will follow the last two lsma points direction, the forecast tend to become inaccurate during a trend change or when noise affect heavily the lsma.
You can test both method accuracy with the replay mode.
Comparison With The Linear Regression
Both methods share similitudes, but they have different results, lets compare them.
In blue the indicator and in red a linear regression of both period 200, the linear regression is always extremely conservative since she fit a line using the least squares method, at the contrary the indicator is less conservative which can be an advantage as well as a problem.
Conclusion
Linear models are good when what we want to forecast is approximately linear, thats not the case with market price and this is why other methods are used. But the use of the lsma to provide a forecast is still an interesting method that might require further studies.
Thanks for reading !
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