Least Squares Moving Average (LSMA)

Parametric Corrective Linear Moving Averages Impulse responses can fully describe their associated systems, for example a linearly weighted moving average (WMA) has a linearly decaying impulse response, therefore we can deduce that lag is reduced since recent values are the ones with the most weights, the Blackman moving average (or Blackman filter) has a bell shaped impulse response, that is mid term values are the ones with the most weights, we can deduce that such moving average is pretty smooth, the least squares moving average has neg

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oleh alexgrover

LSMA - A Fast And Simple Alternative Calculation Introduction At the start of 2019 i published my first post "Approximating A Least Square Moving Average In Pine", who aimed to provide alternatives calculation of the least squares moving average (LSMA), a moving average who aim to estimate the underlying trend in the price without excessive lag. The LSMA has the form of a linear regression ax + b where x is a linear sequence 1.2.3..N and with time varying a and b , the exact formula of the LSMA is as follows : a = stdev(close,len

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oleh alexgrover

Volume weighted LSMA Quick script made by reusing some functions written for other projects. This is a variation on the least squares moving average, but with custom weights on the linear regression. This gives higher weights to recent values and values with high volume. Behaves very similarly to my volume weighted Hull moving average, especially with the hull smoothing option turned on.

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Least Squares Bollinger Bands Similar to Bollinger Bands but adjusted for momentum. Instead of having the centerline be a simply moving average and the bands showing the rolling variance, this does a linear regression, and shows the LSMA at the center, while the band width is the average deviation from the regression line instead of from the SMA. This means that unlike for normal Bollinger bands, momentum does not make the bands wider, and that the bands tend to be much better centered around the price action with band walk

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RSX-D [ID: AC-P]The "AC-P" version of Jaggedsoft's RSX Divergence and Everget's RSX script is my personal customized version of RSX with the following additions and modifications: LSMA-D line that averages in three LSMA components to form a composite, the LSMA-D line. Offset for the LSMA-D line is set to -2 to offset latency from averaging togther the LSMA components to form a composite - recommended to adjust to your timeframe and asset/pair accordingly. Divergence component from JustUncle, RicardoSantos

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oleh UnknownUnicorn2796841

Quadratic Least Squares Moving Average - Smoothing + Forecast Introduction Technical analysis make often uses of classical statistical procedures, one of them being regression analysis, and since fitting polynomial functions that minimize the sum of squares can be achieved with the use of the mean, variance, covariance...etc, technical analyst only needed to replace the mean in all those calculations with a moving average, we then end up with a low lag filter called least squares moving average (lsma) . The least squares moving average could be classif

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oleh alexgrover

Fast/Slow Degree Oscillator Introduction The estimation of a least squares moving average of any degree isn't an interesting goal, this is due to the fact that lsma of high degrees would highly overshoot as well as overfit the closing price, which wouldn't really appear smooth. However i proposed an estimate of an lsma of any degree using convolution and a new sine wave series, all the calculation are described in the paper : "Pierrefeu, Alex (2019): A New Low-Pass FIR Filter For Signal Processing." Today i want to make

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T-Step LSMA Introduction The trend step indicator family has produced much interest in the community, those indicators showed in certain cases robustness and reactivity. Their ease of use/interpretation is also a major advantage. Although those indicators have a relatively good fit with the input price, they can still be improved by introducing least-squares fitting on their calculations. This is why i propose a new indicator (T-Step LSMA) which aim to gather all the components of the trend-step indicator

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Regression Channel [DW]This is an experimental study which calculates a linear regression channel over a specified period or interval using custom moving average types for its calculations. Linear regression is a linear approach to modeling the relationship between a dependent variable and one or more independent variables. In linear regression, the relationships are modeled using linear predictor functions whose unknown model parameters are estimated from the data. The regression channel in this study is modeled u

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oleh DonovanWall

Kaufman Adaptive Least Squares Moving Average Introduction It is possible to use a wide variety of filters for the estimation of a least squares moving average, one of the them being the Kaufman adaptive moving average (KAMA) which adapt to the market trend strength, by using KAMA in an lsma we therefore allow for an adaptive low lag filter which might provide a smarter way to remove noise while preserving reactivity. The Indicator The lsma aim to minimize the sum of the squared residuals, paired with KAMA we obtain a great adaptive s

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Time Series Forecast Introduction 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 tradingview we don't have much forecasting models appart from the linear regression which is definitely not adapted to forecast financial markets, inst

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oleh alexgrover

Bilateral Stochastic Oscillator Strategy Introduction Strategy based on the bilateral stochastic oscillator, this oscillator aim to detect trends and possible reversal points of the current trend. The oscillator is composed of 1 bull line in blue and 1 bear line in red as well as a signal line in orange, the strategy have many options such as two different strategy framework and a martingale mode. If you require more information about the indicator go check it into my uploaded indicators. Strategy Frameworks There are two framewo

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oleh alexgrover

IIR Least-Squares Estimate Introduction Another lsma estimate, i don't think you are surprised, the lsma is my favorite low-lag filter and i derived it so many times that our relationship became quite intimate. So i already talked about the classical method, the line-rescaling method and many others, but we did not made to many IIR estimate, the only one was made using a general filter estimator and was pretty inaccurate, this is why i wanted to retry the challenge. Before talking about the formula lets breakdown again

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Fisher Least Squares Moving Average Introduction I already estimated the least-squares moving average numerous times, one of the most elegant ways was by rescaling a linear function to the price by using the z-score, today i will propose a new smoother (FLSMA) based on the line rescaling approach and the inverse fisher transform of a scaled moving average error with the goal to provide an alternative least-squares smoother, the indicator won't use the correlation coefficient and will try to adresses problems such as overshoots a

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oleh alexgrover

Many Moving Averages This script allows you to add two moving averages to a chart, where the type of moving average can be chosen from a collection of 15 different moving average algorithms. Each moving average can also have different lengths and crossovers/unders can be displayed and alerted on. The supported moving average types are: Simple Moving Average ( SMA ) Exponential Moving Average ( EMA ) Double Exponential Moving Average ( DEMA ) Triple Exponential Moving Average ( TEMA ) Weighted Moving Av

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R2-Adaptive Regression Introduction I already mentioned various problems associated with the lsma, one of them being overshoots, so here i propose to use an lsma using a developed and adaptive form of 1st order polynomial to provide several improvements to the lsma. This indicator will adapt to various coefficient of determinations while also using various recursions. More In Depth A 1st order polynomial is in the form : y = ax + b , our indicator however will use : y = a*x + a1*x1 + (1 - (a + a1))*y , where

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oleh alexgrover

Inverse Fisher Fast Z-score Introduction The fast z-score is a modification of the classic z-score that allow for smoother and faster results by using two least squares moving averages, however oscillators of this kind can be hard to read and modifying its shape to allow a better interpretation can be an interesting thing to do. The Indicator I already talked about the fisher transform, this statistical transform is originally applied to the correlation coefficient, the normal transform allow to get a result similar

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oleh alexgrover

Trigonometric Oscillator Its a pretty old script and i have absolutely no idea how i did it, the code kinda look like the phase wrapping/unwrapping formula. This indicator is an oscillator, sometimes its reactivity is impressive so i think its a good idea to post it, feel free to experiment with it.

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Well Rounded Moving Average Introduction There are tons of filters, way to many, and some of them are redundant in the sense they produce the same results as others. The task to find an optimal filter is still a big challenge among technical analysis and engineering, a good filter is the Kalman filter who is one of the more precise filters out there. The optimal filter theorem state that : The optimal estimator has the form of a linear observer , this in short mean that an optimal filter must use measurements of the in

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Smoothed Delta's Ratio Oscillator Introduction 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

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Linear Quadratic Convergence Divergence Oscillator Introduction 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

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oleh alexgrover

Least Squares Moving Average With Overshoot Reduction Introduction The ability to reduce lag while keeping a good level of stability has been a major challenge for smoothing filters in technical analysis. Stability involve many parameters, one of them being overshoots. Overshoots are a common effect induced by low-lagging filters, they are defined as the ability of a signal output to exceed a target input. This effect can lead to major drawbacks such as whipsaw and reduction of precision. I propose a modification of the least squares moving avera

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oleh alexgrover

Fast Z-Score Introduction 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 differenc

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Linear Regression Curve - Average Idea is that the average of price has something to do with sudden changes in trend. Finding trend shifts in mundane.

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