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Extrapolation

Variable Sine Wave Fit [LuxAlgo]The Variable Sine Wave Fit indicator uses Ordinary Least Squares (OLS) to fit a dynamic, damped, or expanding sine wave with an underlying linear trend to recent price action. This tool aims to identify cyclical patterns and project their potential continuation into the future, providing a mathematical framework for understanding market regimes and turning points. This indicator is subject to repainting and is displayed retrospectively. 🔶 USAGE The indicator fits a complex trigonometric model to the price data within a user-defined window. The resulting fit is displayed as a solid line over historical bars and transitions into a dashed extrapolation for the forecasted period. To use the indicator effectively, traders should observe the relationship between the price and the RMSE bands. If the price remains within these bands, the current cyclical model is considered to be tracking the price action effectively. If the price breaks significantly outside, the cycle may be shifting or breaking down. 🔹 Extrema Markers Small dot markers are placed at the local maxima and minima of the dashed forecast line. These serve as visual guides for the timing of potential future turning points based on the current mathematical fit. 🔹 Market Regime Dashboard The dashboard provides a real-time summary of the fitted model's characteristics: State: Classified based on the amplitude behavior (Damped, Expanding, or Constant) and the linear component (Trending or Ranging). Best Period: The cycle length (in bars) that currently provides the best fit to the data. RMSE: The Root Mean Square Error, representing the average deviation of price from the fit. 🔶 DETAILS The script solves for the best parameters of the following equation: y = e^(λ * t) * (a * sin(ω * t) + b * cos(ω * t)) + m * t + c Where: e^(λ * t): The damping/expansion factor. If λ > 0, the cycle is expanding; if λ < 0, it is damping. a, b: Coefficients determining the phase and initial amplitude of the sine wave. m * t + c: A linear regression component that accounts for the underlying price trend. The "Best Period" is determined through a grid search that minimizes the Sum of Squared Errors (SSE), ensuring the frequency (ω) matches the most dominant local cycle within the search range. 🔶 SETTINGS 🔹 Settings Window Size (N): The number of historical bars used to calculate the fit. Auto Period: When enabled, the script searches for the best period within the specified min/max range. Fixed Period (P): The period used if Auto Period is disabled. Min/Max Search Period: Defines the boundaries for the automatic cycle search. Forecast Length: The number of bars to project the fit into the future. RMSE Band Multiplier: Determines the width of the bands surrounding the fit based on the fit error. 🔹 Visuals Bullish/Bearish Color: Colors used for the fit line and extrema markers based on the final slope. Band Color: The color of the RMSE-based envelope. 🔹 Dashboard Dashboard: Toggles the visibility of the data table. Position: Moves the dashboard to different corners of the chart. Size: Adjusts the text and table scale.
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LuxAlgoの投稿
LOWESS Channel & Extrapolation [LuxAlgo]The LOWESS Channel & Extrapolation indicator calculates a Locally Weighted Scatterplot Smoothing (LOWESS) curve to define a non-linear trend and projects it into future bars using local regression slopes. It provides a dynamic channel based on the standard deviation of residuals, helping traders identify overextended price levels and potential mean-reversion points. The LOWESS Channel & Extrapolation indicator is subject to repainting and displayed retrospectively. 🔶 USAGE This tool is primarily designed for trend analysis and identifying exhaustion points. Because the LOWESS algorithm recalculates based on the most recent data window, the entire historical curve can adjust, making it a powerful tool for backtesting and analyzing past market structures rather than for real-time signal generation without confirmation. 🔹 Trend Identification The central fit line represents the smoothed local trend. When the curve is sloping upward, the local market sentiment is considered bullish; conversely, a downward slope indicates bearish sentiment. 🔹 Overbought/Oversold Conditions The dashed outer channels represent a volatility-adjusted boundary. When price moves outside these boundaries, it is statistically overextended relative to the local trend, often preceding a move back toward the mid-line. 🔹 Extrapolation The indicator extends the most recent local regression slope into the future. This provides a "path of least resistance" projection based on the current momentum of the smoothed curve. 🔶 DETAILS The LOWESS (Locally Weighted Scatterplot Smoothing) algorithm works by performing a separate weighted linear regression for every data point in the window. It uses a "tricube" weighting function, which ensures that data points closer to the focal point have a higher influence on the fit than points further away. This results in a curve that is much more flexible than a simple moving average and can adapt to complex price cycles without the lag associated with traditional filters. The channel width is determined by calculating the Standard Deviation of the residuals (the difference between the actual price and the LOWESS fit). This ensures the channel expands during high volatility and contracts during consolidation. 🔶 SETTINGS Length : Determines the number of historical observations used to fit the LOWESS curve. Larger values result in a smoother, more macro trend. Span : The fraction of data points used for each local regression. A higher span (closer to 1.0) creates a smoother line, while a lower span allows the curve to follow price more tightly. Channel Multiplier : Multiplier applied to the standard deviation of residuals to define the distance of the upper and lower bands from the mid-line. Extrapolation Bars : The number of bars to project the current trend into the future. Fit Color : Sets the color and transparency of the central LOWESS line. Channel Color : Sets the color of the dashed outer bands and the background fill. Line Width : Adjusts the thickness of the central fit line.
Pine Script® インジケーター
LuxAlgoの投稿
Whittaker Envelope [LuxAlgo]The Whittaker Envelope indicator is a visualization tool that uses Asymmetric Least Squares (ALS) to create a smooth, non-linear envelope that adapts to price extremes and troughs. This indicator is for visualization purposes only and should not be used for direct trading signals without confirmation. It is important to note that this script is displayed retrospectively . Because it calculates the best fit over a fixed historical window (the last N bars) using an iterative optimization process, the entire shape of the envelope can change as new data arrives. This means the indicator repaints and should be used to analyze overall market structure and volatility rather than for real-time execution. 🔶 USAGE The Whittaker Envelope provides a unique way to visualize the "breathing" of the market. By applying different asymmetry parameters, the indicator generates a lower boundary that seeks out price troughs and an upper boundary that seeks out price peaks. 🔹 Trend and Volatility Analysis The area between the upper and lower bounds represents the smoothed price range. A widening envelope suggests increasing volatility, while a narrowing one indicates consolidation. The dashed midline acts as a smoothed average of these two extremes, providing a baseline for the current trend. 🔹 Extrapolation The tool includes a linear extrapolation feature that projects the current trajectory of the envelope into the future. This can help users visualize the potential direction of the trend if the current momentum persists. 🔶 DETAILS The script implements the Whittaker-Eilers smoothing algorithm, which balances two conflicting goals: fitting the data points closely and keeping the resulting curve smooth. By using Asymmetric Least Squares (ALS), we assign different weights to prices depending on whether they are above or below the curve. For the upper band, we use a high asymmetry value ( p ) so the curve is "pushed" toward the peaks. For the lower band, a very low p value is used to "pull" the curve toward the troughs. 🔶 SETTINGS Length : The number of recent bars included in the calculation window. Lambda (λ) : The smoothing factor. Higher values result in a stiffer, straighter envelope, while lower values allow the bands to follow price more closely. Lower Asymmetry (p) : Controls how the lower band reacts to prices. Typically set to a very low value (e.g., 0.001) to ensure it follows the bottom of the price action. Upper Asymmetry (p) : Controls how the upper band reacts to prices. Typically set to a very high value (e.g., 0.999) to ensure it follows the top of the price action. Iterations : The number of times the ALS algorithm runs to refine the fit. More iterations provide a more accurate envelope but require more computational power. Extrapolation : The number of bars to project the current slope of the bands into the future. Source : The price data used for the calculation (default is Close).
Pine Script® インジケーター
LuxAlgoの投稿
Singular Spectrum Decomposition [LuxAlgo]The Singular Spectrum Decomposition indicator is a powerful analytical tool that decomposes price action into distinct, interpretable components—Trend, Periodic cycles, and Noise—using the Singular Spectrum Analysis (SSA) methodology. It provides traders with a clear view of underlying market structures and offers a jump-free, extrapolated trend forecast based on Linear Recurrence Relations (LRR). Warning: This decomposition is displayed retrospectively ; historical values observed are subject to repainting . 🔶 USAGE The indicator operates by analyzing a specific window of recent price data to extract its most significant internal dynamics. It splits the "messy" raw price into four visual layers: Trend (Overlay): The primary low-frequency component, plotted directly on the price chart. This represents the core directional bias of the asset. Long Term Periodic (P1): The most dominant cyclical component, typically representing major swings or seasonalities. Short Term Periodic (P2): The second most dominant cycle, capturing faster oscillations and intermediate pullbacks. Noise: The high-frequency residual data that lacks a consistent pattern, useful for identifying market volatility or "washout" periods. 🔹 Cycle Exhaustion (P1/P2 Extremes) Traders can monitor the separate indicator pane to identify when cyclical components (P1 and P2) reach historical extremes. When the Long Term Periodic (P1) line begins to curve back toward the zero line after a prolonged extension, it often signals "cycle exhaustion," suggesting that the current swing is losing momentum and a reversal or consolidation may be imminent. 🔹 Trend-Forecast Confluence & Mean Reversion The dashed Trend extrapolation acts as a projected path for the market's core bias. If the current market price is significantly far from the solid Trend line while the forecast indicates a flattening or reversal, traders can look for mean-reversion opportunities. A price returning to a rising Trend forecast confirms the trend's strength, while a price crossing through a flat Trend forecast suggests a structural shift. 🔹 Timing Entries with Dashboard Metrics The "Average Period" displayed on the dashboard provides a mathematical blueprint for entry timing. For example, if the Short Term (P2) Average Period is 20 bars, a trader might look for long entries approximately 10 bars after a peak (the expected trough). By aligning these peak-to-trough measurements with the Trend's direction, users can improve the precision of their entries within a trending market. 🔹 Filtering Fakeouts with the Noise Component The Noise component helps distinguish between high-conviction moves and market "static." A sharp price breakout accompanied by a relatively flat Noise component suggests a sustainable, structurally supported move. Conversely, if a breakout occurs while the Noise component is spiking aggressively, it may indicate a "washout" or a liquidity-driven fakeout that lacks a fundamental trend shift. 🔶 DETAILS The script implements a full SSA pipeline: Embedding (creating a trajectory matrix), Singular Value Decomposition (via eigendecomposition of the covariance matrix), and Diagonal Averaging (reconstructed the time series). 🔹 Jump-Free Extrapolation A common issue with LRR-based forecasts is a vertical "jump" at the connection point between historical data and the forecast. This tool solves this by calculating the relative deltas of the LRR projection and anchoring them to the final value of the smoothed SSA reconstruction. This ensures a seamless visual transition while maintaining the mathematical integrity of the projected trajectory. 🔹 Dashboard Metrics The indicator includes a real-time dashboard that calculates the "Average Period" of the periodic components using zero-crossing detection. This allows traders to quantify the frequency of cycles (e.g., a 40-bar cycle vs. a 15-bar cycle) without manual measurement. 🔶 SETTINGS Window Length (L): The embedding window. Larger values capture longer cycles and provide a smoother trend, but may increase lag in the decomposition. Buffer Length (N): The number of recent bars used for the static decomposition. Forecast Length: The number of bars to extrapolate the Trend component into the future. Show Trend on Price: Toggles the visibility of the reconstructed trend line on the main chart. Show Periodic/Noise: Toggles the visibility of the individual sub-components in the indicator pane. Show Extrapolation: Enables or disables the dashed forecast line for the trend. Dashboard Settings: Controls the visibility, position, and size of the metrics table.
Pine Script® インジケーター
LuxAlgoの投稿
Bitcoin Expectile Model [LuxAlgo]The Bitcoin Expectile Model is a novel approach to forecasting Bitcoin, inspired by the popular Bitcoin Quantile Model by PlanC. By fitting multiple Expectile regressions to the price, we highlight zones of corrections or accumulations throughout the Bitcoin price evolution. While we strongly recommend using this model with the Bitcoin All Time History Index INDEX:BTCUSD on the 3 days or weekly timeframe using a logarithmic scale, this model can be applied to any asset using the daily timeframe or superior. Please note that here on TradingView, this model was solely designed to be used on the Bitcoin 1W chart, however, it can be experimented on other assets or timeframes if of interest. 🔶 USAGE The Bitcoin Expectile Model can be applied similarly to models used for Bitcoin, highlighting lower areas of possible accumulation (support) and higher areas that allow for the anticipation of potential corrections (resistance). By default, this model fits 7 individual Expectiles Log-Log Regressions to the price, each with their respective expectile ( tau ) values (here multiplied by 100 for the user's convenience). Higher tau values will return a fit closer to the higher highs made by the price of the asset, while lower ones will return fits closer to the lower prices observed over time. Each zone is color-coded and has a specific interpretation. The green zone is a buy zone for long-term investing, purple is an anomaly zone for market bottoms that over-extend, while red is considered the distribution zone. The fits can be extrapolated, helping to chart a course for the possible evolution of Bitcoin prices. Users can select the end of the forecast as a date using the "Forecast End" setting. While the model is made for Bitcoin using a log scale, other assets showing a tendency to have a trend evolving in a single direction can be used. See the chart above on QQQ weekly using a linear scale as an example. The Start Date can also allow fitting the model more locally, rather than over a large range of prices. This can be useful to identify potential shorter-term support/resistance areas. 🔶 DETAILS 🔹 On Quantile and Expectile Regressions Quantile and Expectile regressions are similar; both return extremities that can be used to locate and predict prices where tops/bottoms could be more likely to occur. The main difference lies in what we are trying to minimize, which, for Quantile regression, is commonly known as Quantile loss (or pinball loss), and for Expectile regression, simply Expectile loss. You may refer to external material to go more in-depth about these loss functions; however, while they are similar and involve weighting specific prices more than others relative to our parameter tau, Quantile regression involves minimizing a weighted mean absolute error, while Expectile regression minimizes a weighted squared error. The squared error here allows us to compute Expectile regression more easily compared to Quantile regression, using Iteratively reweighted least squares. For Quantile regression, a more elaborate method is needed. In terms of comparison, Quantile regression is more robust, and easier to interpret, with quantiles being related to specific probabilities involving the underlying cumulative distribution function of the dataset; on the other expectiles are harder to interpret. 🔹 Trimming & Alterations It is common to observe certain models ignoring very early Bitcoin price ranges. By default, we start our fit at the date 2010-07-16 to align with existing models. By default, the model uses the number of time units (days, weeks...etc) elapsed since the beginning of history + 1 (to avoid NaN with log) as independent variable, however the Bitcoin All Time History Index INDEX:BTCUSD do not include the genesis block, as such users can correct for this by enabling the "Correct for Genesis block" setting, which will add the amount of missed bars from the Genesis block to the start oh the chart history. 🔶 SETTINGS Start Date: Starting interval of the dataset used for the fit. Correct for genesis block: When enabled, offset the X axis by the number of bars between the Bitcoin genesis block time and the chart starting time. 🔹 Expectiles Toggle: Enable fit for the specified expectile. Disabling one fit will make the script faster to compute. Expectile: Expectile (tau) value multiplied by 100 used for the fit. Higher values will produce fits that are located near price tops. 🔹 Forecast Forecast End: Time at which the forecast stops. 🔹 Model Fit Iterations Number: Number of iterations performed during the reweighted least squares process, with lower values leading to less accurate fits, while higher values will take more time to compute.
Pine Script® インジケーター
LuxAlgoの投稿
8
Birdies [LuxAlgo]The Birdies indicator uses a unique technique to provide support/resistance curves based on a circle connecting the last swing high/low. A specific, customizable part of this circle acts as a curve of interest, which can trigger visual breakout signals. 🔶 USAGE The script projects a bird-like pattern when a valid Swing point is found. Multiple customization options are included. 🔹 Trend & Support/Resistance Tool The color fill patterns and the wing boundaries can give insights into the current trend direction as well as serve as potential support/resistance areas. In the example above, "Birdies" coincide with pullback and support/resistance zones. 🔹 Swing Length & Buffer Besides the "Swing Length", with higher values returning longer-term Swing Levels, the script's behavior can be fine-tuned with filters ("Settings" - "Validation"). 🔹 Validation To minimize clutter, three filters are included: Minimum X-Distance: The minimum amount of bars between subsequent Swings Minimum Y-Distance: The minimum amount of bars between subsequent Swings Buffer (Multiple of ATR) The "Minimum X/Y-Distance" creates a zone where a new Swing is considered invalid. Only when the Swing is out of the zone, can it be considered valid. In other words, in the example above, a Swing High can only be valid when enough bars/time have passed, and the difference between the last Swing and the previous is more than the ATR multiplied by the "Minimum Y-Distance" factor. The "Buffer" creates a line above/below the "Birdy", derived from the measured ATR at the conception of the "Birdy" multiplied with a factor ("Buffer"). When the closing price crosses the "Birdy", it must also surpass this buffer line to produce a valid signal, lowering the risk of clutter as a result. 🔶 DETAILS Birdies are derived from a circle that connects two Swing points. The left-wing curve originates from the most recent "Swing point" to the last value on the circle before crossing its midline. The mirror image of the left wing creates the right wing. Enabling "Origine" will draw a line from the last Swing to the first. 🔹 Style The publication includes a style setting with four options. The first, "Birdy," shows a bird-like shape derived from a circle connecting the last Swing High and Swing Low. The second option holds everything from the first option but connects both wingtips, providing potential horizontal levels of interest. When setting "Birdy" to "None", the visual breakout signals will not defer from previous settings, but the focus is shifted towards the fill color, which can help detect potential trend shift. A fourth setting, "Left Wing", will only show the left part of the "Birdy" pattern, removing the right part from the equation. This will change the visual breakout signals, providing alternative signals. 🔶 SETTINGS Swing Length: The period used for swing detection, with higher values returning longer-term Swing Levels. 🔹 Validation Minimum X-Distance: The minimum amount of bars between subsequent Swings Minimum Y-Distance: The minimum amount of bars between subsequent Swings Buffer (Multiple of ATR) 🔹 Style Bullish Patterns: Enable / color Bearish Patterns: Enable / color Buffer Zone: Show / Color Color Fill: Show color fill between two Birdies (if available) Origine: Show the line between both Swing Points 🔹 Calculation Calculated Bars: Allows the usage of fewer bars for performance/speed improvement
Pine Script® インジケーター
LuxAlgoの投稿
Extrapolated Previous Trend [LuxAlgo]The Extrapolated Previous Trend indicator extrapolates the estimated linear trend of the prices within a previous interval to the current interval. Intervals can be user-defined. 🔶 USAGE Returned lines can be used to provide a forecast of trends, assuming trends are persistent in sign and slope. Using them as support/resistance can also be an effecting usage in case the trend in a new interval does not follow the characteristic of the trend in the previous interval. The indicator includes a dashboard showing the degree of persistence between segmented trends for uptrends and downtrends. A higher value is indicative of more persistent trend signs. A lower value could hint at an anti-persistent behavior, with uptrends over an interval often being followed by a down-trend and vice versa. We can invert candle colors to determine future trend direction in this case. 🔶 DETAILS This indicator can be thought of as a segmented linear model ( a(n)t + b(n) ), where n is the specific interval index. Unlike a regular segmented linear regression model, this indicator is not subject to lookahead bias, coefficients of the model are obtained on previous intervals. The quality of the fit of the model is dependent on the variability of its coefficients a(n) and b(n) . Coefficients being less subject to change over time are more indicative of trend persistence. 🔶 SETTINGS Timeframe: Determine the frequency at which new trends are estimated.
Pine Script® インジケーター
LuxAlgoの投稿
9
Advanced Donchian Channels Advanced Donchian Channels displays future donchian channel values based on the current information on the chart. It displays a normal donchian channel at the specified user length with the future values extending from the current bar. Depending on the direction of price movement, these values do not repaint. It is known when it does and does not repaint, and the actions are normal. See below for more information. In a down trend, when the price is making new lows, the future "channel low" value will update every time the low is broken. The mean will also update, since the mean is the average of the channel high and channel low. In a downtrend, the "channel high" value is concrete . It will not update until the high is broken. Reverse these examples for uptrends. Q; How does it know the future values? A: Consider This: If we are below the current highest high, going down (aka: not setting new highs), the donchian channel "high" value will create a flat top, the flat top will start to decrease after we go further than our specified length. This is because the highest high within our specified length is no longer what it was previously. This action of time decay is a consistent movement of donchian channels . Because of this I am able to calculate these values before the current bar actually reaches them. The indicator calculates the current length donchian channel at the current bar and then for every future bar up to your length specified it subtracts 1 from your length, calculates and displays the values accordingly. The farthest future value is 1 length and the current bar is your specified length. VALUES WILL ONLY BE UPDATED WHEN THE CHANNEL HIGH OR LOW IS BROKEN. If price stays within the channel, all the future channel values will become solidified when the time reaches them. This is not a gimmick, This data is accurate and can be used to help see future price trends This chart should assist in visualizing what data you are seeing in this indicator. Enjoy!
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SamRecioの投稿
5
Fourier Spectrometer of Price w/ Extrapolation Forecast [Loxx]Fourier Spectrometer of Price w/ Extrapolation Forecast is a forecasting indicator that forecasts the sinusoidal frequency of input price. This method uses Linear Regression with a Fast Fourier Transform function for the forecast and is different from previous forecasting methods I've posted. Dotted lines are the forecast frequencies. You can change the UI colors and line widths. This comes with 8 frequencies out of the box. Instead of drawing sinusoidal manually on your charts, you can use this instead. This will render better results than eyeballing the Sine Wave that folks use for trading. this is the real math that automates that process. Each signal line can be shown as a linear superposition of periodic (sinusoidal) components with different periods (frequencies) and amplitudes. Roughly, the indicator shows those components. It strongly depends on the probing window and changes (recalculates) after each tick; e.g., you can see the set of frequencies showing whether the signal is fast or slow-changing, etc. Sometimes only a small number of leading / strongest components (e.g., 3) can extrapolate the signal quite well. Related Indicators Fourier Extrapolator of 'Caterpillar' SSA of Price Real-Fast Fourier Transform of Price w/ Linear Regression Fourier Extrapolator of Price w/ Projection Forecast Itakura-Saito Autoregressive Extrapolation of Price Helme-Nikias Weighted Burg AR-SE Extra. of Price ***The period parameter doesn't correspond to how many bars back the drawing begins. Lines re rendered according to skipping mechanism due to TradingView limitations.
Pine Script® インジケーター
loxxの投稿
5
Ehlers Linear Extrapolation Predictor [Loxx]Ehlers Linear Extrapolation Predictor is a new indicator by John Ehlers. The translation of this indicator into PineScript™ is a collaborative effort between @cheatcountry and I. The following is an excerpt from "PREDICTION" , by John Ehlers Niels Bohr said “Prediction is very difficult, especially if it’s about the future.”. Actually, prediction is pretty easy in the context of technical analysis. All you have to do is to assume the market will behave in the immediate future just as it has behaved in the immediate past. In this article we will explore several different techniques that put the philosophy into practice. LINEAR EXTRAPOLATION Linear extrapolation takes the philosophical approach quite literally. Linear extrapolation simply takes the difference of the last two bars and adds that difference to the value of the last bar to form the prediction for the next bar. The prediction is extended further into the future by taking the last predicted value as real data and repeating the process of adding the most recent difference to it. The process can be repeated over and over to extend the prediction even further. Linear extrapolation is an FIR filter, meaning it depends only on the data input rather than on a previously computed value. Since the output of an FIR filter depends only on delayed input data, the resulting lag is somewhat like the delay of water coming out the end of a hose after it supplied at the input. Linear extrapolation has a negative group delay at the longer cycle periods of the spectrum, which means water comes out the end of the hose before it is applied at the input. Of course the analogy breaks down, but it is fun to think of it that way. As shown in Figure 1, the actual group delay varies across the spectrum. For frequency components less than .167 (i.e. a period of 6 bars) the group delay is negative, meaning the filter is predictive. However, the filter has a positive group delay for cycle components whose periods are shorter than 6 bars. Figure 1 Here’s the practical ramification of the group delay: Suppose we are projecting the prediction 5 bars into the future. This is fine as long as the market is continued to trend up in the same direction. But, when we get a reversal, the prediction continues upward for 5 bars after the reversal. That is, the prediction fails just when you need it the most. An interesting phenomenon is that, regardless of how far the extrapolation extends into the future, the prediction will always cross the signal at the same spot along the time axis. The result is that the prediction will have an overshoot. The amplitude of the overshoot is a function of how far the extrapolation has been carried into the future. But the overshoot gives us an opportunity to make a useful prediction at the cyclic turning point of band limited signals (i.e. oscillators having a zero mean). If we reduce the overshoot by reducing the gain of the prediction, we then also move the crossing of the prediction and the original signal into the future. Since the group delay varies across the spectrum, the effect will be less effective for the shorter cycles in the data. Nonetheless, the technique is effective for both discretionary trading and automated trading in the majority of cases. EXPLORING THE CODE Before we predict, we need to create a band limited indicator from which to make the prediction. I have selected a “roofing filter” consisting of a High Pass Filter followed by a Low Pass Filter. The tunable parameter of the High Pass Filter is HPPeriod. Think of it as a “stone wall filter” where cycle period components longer than HPPeriod are completely rejected and cycle period components shorter than HPPeriod are passed without attenuation. If HPPeriod is set to be a large number (e.g. 250) the indicator will tend to look more like a trending indicator. If HPPeriod is set to be a smaller number (e.g. 20) the indicator will look more like a cycling indicator. The Low Pass Filter is a Hann Windowed FIR filter whose tunable parameter is LPPeriod. Think of it as a “stone wall filter” where cycle period components shorter than LPPeriod are completely rejected and cycle period components longer than LPPeriod are passed without attenuation. The purpose of the Low Pass filter is to smooth the signal. Thus, the combination of these two filters forms a “roofing filter”, named Filt, that passes spectrum components between LPPeriod and HPPeriod. Since working into the future is not allowed in EasyLanguage variables, we need to convert the Filt variable to the data array XX . The data array is first filled with real data out to “Length”. I selected Length = 10 simply to have a convenient starting point for the prediction. The next block of code is the prediction into the future. It is easiest to understand if we consider the case where count = 0. Then, in English, the next value of the data array is equal to the current value of the data array plus the difference between the current value and the previous value. That makes the prediction one bar into the future. The process is repeated for each value of count until predictions up to 10 bars in the future are contained in the data array. Next, the selected prediction is converted from the data array to the variable “Prediction”. Filt is plotted in Red and Prediction is plotted in yellow. The Predict Extrapolation indicator is shown above for the Emini S&P Futures contract using the default input parameters. Filt is plotted in red and Predict is plotted in yellow. The crossings of the Predict and Filt lines provide reliable buy and sell timing signals. There is some overshoot for the shorter cycle periods, for example in February and March 2021, but the only effect is a late timing signal. Further reducing the gain and/or reducing the BarsFwd inputs would provide better timing signals during this period. ADDITIONS Loxx's Expanded source types: Library for expanded source types: Explanation for expanded source types: Three different signal types: 1) Prediction/Filter crosses; 2) Prediction middle crosses; and, 3) Filter middle crosses. Bar coloring to color trend. Signals, both Long and Short. Alerts, both Long and Short.
Pine Script® インジケーター
loxxの投稿
6
Polynomial Regression Bands w/ Extrapolation of Price [Loxx]Polynomial Regression Bands w/ Extrapolation of Price is a moving average built on Polynomial Regression. This indicator paints both a non-repainting moving average and also a projection forecast based on the Polynomial Regression. I've included 33 source types and 38 moving average types to smooth the price input before it's run through the Polynomial Regression algorithm. This indicator only paints X many bars back so as to increase on screen calculation speed. Make sure to read the tooltips to answer any questions you have. What is Polynomial Regression? In statistics, polynomial regression is a form of regression analysis in which the relationship between the independent variable x and the dependent variable y is modeled as an nth degree polynomial in x. Polynomial regression fits a nonlinear relationship between the value of x and the corresponding conditional mean of y, denoted E(y |x). Although polynomial regression fits a nonlinear model to the data, as a statistical estimation problem it is linear, in the sense that the regression function E(y | x) is linear in the unknown parameters that are estimated from the data. For this reason, polynomial regression is considered to be a special case of multiple linear regression . Related indicators Polynomial-Regression-Fitted Oscillator Polynomial-Regression-Fitted RSI PA-Adaptive Polynomial Regression Fitted Moving Average Poly Cycle Fourier Extrapolator of Price w/ Projection Forecast
Pine Script® インジケーター
loxxの投稿
9
Nearest Neighbor Extrapolation of Price [Loxx]I wasn't going to post this because I don't like how this calculates by puling in the Open price, but I'm posting it anyway. This does work in it's current form but there is a. better way to do this. I'll revisit this in the future. Anyway... The k-Nearest Neighbor algorithm (k-NN) searches for k past patterns (neighbors) that are most similar to the current pattern and computes the future prices based on weighted voting of those neighbors. This indicator finds only one nearest neighbor. So, in essence, it is a 1-NN algorithm. It uses the Pearson correlation coefficient between the current pattern and all past patterns as the measure of distance between them. Also, this version of the nearest neighbor indicator gives larger weights to most recent prices while searching for the closest pattern in the past. It uses a weighted correlation coefficient, whose weight decays linearly from newer to older prices within a price pattern. This indicator also includes an error window that shows whether the calculation is valid. If it's green and says "Passed", then the calculation is valid, otherwise it'll show a red background and and error message. Inputs Npast - number of past bars in a pattern; Nfut -number of future bars in a pattern (must be < Npast). lastbar - How many bars back to start forecast? Useful to show past prediction accuracy barsbark - This prevents Pine from trying to calculate on all past bars Related indicators Hodrick-Prescott Extrapolation of Price Itakura-Saito Autoregressive Extrapolation of Price Helme-Nikias Weighted Burg AR-SE Extra. of Price Weighted Burg AR Spectral Estimate Extrapolation of Price Levinson-Durbin Autocorrelation Extrapolation of Price Fourier Extrapolator of Price w/ Projection Forecast
Pine Script® インジケーター
loxxの投稿
5
Hodrick-Prescott Extrapolation of Price [Loxx]Hodrick-Prescott Extrapolation of Price is a Hodrick-Prescott filter used to extrapolate price. The distinctive feature of the Hodrick-Prescott filter is that it does not delay. It is calculated by minimizing the objective function. F = Sum((y(i) - x(i))^2,i=0..n-1) + lambda*Sum((y(i+1)+y(i-1)-2*y(i))^2,i=1..n-2) where x() - prices, y() - filter values. If the Hodrick-Prescott filter sees the future, then what future values does it suggest? To answer this question, we should find the digital low-frequency filter with the frequency parameter similar to the Hodrick-Prescott filter's one but with the values calculated directly using the past values of the "twin filter" itself, i.e. y(i) = Sum(a(k)*x(i-k),k=0..nx-1) - FIR filter or y(i) = Sum(a(k)*x(i-k),k=0..nx-1) + Sum(b(k)*y(i-k),k=1..ny) - IIR filter It is better to select the "twin filter" having the frequency-independent delay Тdel (constant group delay). IIR filters are not suitable. For FIR filters, the condition for a frequency-independent delay is as follows: a(i) = +/-a(nx-1-i), i = 0..nx-1 The simplest FIR filter with constant delay is Simple Moving Average (SMA): y(i) = Sum(x(i-k),k=0..nx-1)/nx In case nx is an odd number, Тdel = (nx-1)/2. If we shift the values of SMA filter to the past by the amount of bars equal to Тdel, SMA values coincide with the Hodrick-Prescott filter ones. The exact math cannot be achieved due to the significant differences in the frequency parameters of the two filters. To achieve the closest match between the filter values, I recommend their channel widths to be similar (for example, -6dB). The Hodrick-Prescott filter's channel width of -6dB is calculated as follows: wc = 2*arcsin(0.5/lambda^0.25). The channel width of -6dB for the SMA filter is calculated by numerical computing via the following equation: |H(w)| = sin(nx*wc/2)/sin(wc/2)/nx = 0.5 Prediction algorithms: The indicator features the two prediction methods: Metod 1: 1. Set SMA length to 3 and shift it to the past by 1 bar. With such a length, the shifted SMA does not exist only for the last bar (Bar = 0), since it needs the value of the next future price Close(-1). 2. Calculate SMA filer's channel width. Equal it to the Hodrick-Prescott filter's one. Find lambda. 3. Calculate Hodrick-Prescott filter value at the last bar HP(0) and assume that SMA(0) with unknown Close(-1) gives the same value. 4. Find Close(-1) = 3*HP(0) - Close(0) - Close(1) 5. Increase the length of SMA to 5. Repeat all calculations and find Close(-2) = 5*HP(0) - Close(-1) - Close(0) - Close(1) - Close(2). Continue till the specified amount of future FutBars prices is calculated. Method 2: 1. Set SMA length equal to 2*FutBars+1 and shift SMA to the past by FutBars 2. Calculate SMA filer's channel width. Equal it to the Hodrick-Prescott filter's one. Find lambda. 3. Calculate Hodrick-Prescott filter values at the last FutBars and assume that SMA behaves similarly when new prices appear. 4. Find Close(-1) = (2*FutBars+1)*HP(FutBars-1) - Sum(Close(i),i=0..2*FutBars-1), Close(-2) = (2*FutBars+1)*HP(FutBars-2) - Sum(Close(i),i=-1..2*FutBars-2), etc. The indicator features the following inputs: Method - prediction method Last Bar - number of the last bar to check predictions on the existing prices (LastBar >= 0) Past Bars - amount of previous bars the Hodrick-Prescott filter is calculated for (the more, the better, or at least PastBars>2*FutBars) Future Bars - amount of predicted future values The second method is more accurate but often has large spikes of the first predicted price. For our purposes here, this price has been filtered from being displayed in the chart. This is why method two starts its prediction 2 bars later than method 1. The described prediction method can be improved by searching for the FIR filter with the frequency parameter closer to the Hodrick-Prescott filter. For example, you may try Hanning, Blackman, Kaiser, and other filters with constant delay instead of SMA. Related indicators Itakura-Saito Autoregressive Extrapolation of Price Helme-Nikias Weighted Burg AR-SE Extra. of Price Weighted Burg AR Spectral Estimate Extrapolation of Price Levinson-Durbin Autocorrelation Extrapolation of Price Fourier Extrapolator of Price w/ Projection Forecast
Pine Script® インジケーター
loxxの投稿
Modified Covariance Autoregressive Estimator of Price [Loxx]What is the Modified Covariance AR Estimator? The Modified Covariance AR Estimator uses the modified covariance method to fit an autoregressive (AR) model to the input data. This method minimizes the forward and backward prediction errors in the least squares sense. The input is a frame of consecutive time samples, which is assumed to be the output of an AR system driven by white noise. The block computes the normalized estimate of the AR system parameters, A(z), independently for each successive input. Characteristics of Modified Covariance AR Estimator Minimizes the forward prediction error in the least squares sense Minimizes the forward and backward prediction errors in the least squares sense High resolution for short data records Able to extract frequencies from data consisting of p or more pure sinusoids Does not suffer spectral line-splitting May produce unstable models Peak locations slightly dependent on initial phase Minor frequency bias for estimates of sinusoids in noise Order must be less than or equal to 2/3 the input frame size Purpose This indicator calculates a prediction of price. This will NOT work on all tickers. To see whether this works on a ticker for the settings you have chosen, you must check the label message on the lower right of the chart. The label will show either a pass or fail. If it passes, then it's green, if it fails, it's red. The reason for this is because the Modified Covariance method produce unstable models H(z)= G / A(z) = G / (1+. a(2)z −1 +…+a(p+1)z) You specify the order, "ip", of the all-pole model in the Estimation order parameter. To guarantee a valid output, you must set the Estimation order parameter to be less than or equal to two thirds the input vector length. The output port labeled "a" outputs the normalized estimate of the AR model coefficients in descending powers of z. The implementation of the Modified Covariance AR Estimator in this indicator is the fast algorithm for the solution of the modified covariance least squares normal equations. Inputs x - Array of complex data samples X(1) through X(N) ip - Order of linear prediction model (integer) Notable local variables v - Real linear prediction variance at order IP Outputs a - Array of complex linear prediction coefficients stop - value at time of exit, with error message false - for normal exit (no numerical ill-conditioning) true - if v is not a positive value true - if delta and gamma do not lie in the range 0 to 1 true - if v is not a positive value true - if delta and gamma do not lie in the range 0 to 1 errormessage - an error message based on "stop" parameter; this message will be displayed in the lower righthand corner of the chart. If you see a green "passed" then the analysis is valid, otherwise the test failed. Indicator inputs LastBar = bars backward from current bar to test estimate reliability PastBars = how many bars are we going to analyze LPOrder = Order of Linear Prediction, and for Modified Covariance AR method, this must be less than or equal to 2/3 the input frame size, so this number has a max value of 0.67 FutBars = how many bars you'd like to show in the future. This algorithm will either accept or reject your value input here and then project forward Further reading Spectrum Analysis-A Modern Perspective 1380 PROCEEDINGS OF THE IEEE, VOL. 69, NO. 11, NOVEMBER 1981 Related indicators Levinson-Durbin Autocorrelation Extrapolation of Price Weighted Burg AR Spectral Estimate Extrapolation of Price Helme-Nikias Weighted Burg AR-SE Extra. of Price Itakura-Saito Autoregressive Extrapolation of Price Modified Covariance Autoregressive Estimator of Price
Pine Script® インジケーター
loxxの投稿
9
Itakura-Saito Autoregressive Extrapolation of Price [Loxx]Itakura-Saito Autoregressive Extrapolation of Price is an indicator that uses an autoregressive analysis to predict future prices. This is a linear technique that was originally derived or speech analysis algorithms. What is Itakura-Saito Autoregressive Analysis? The technique of linear prediction has been available for speech analysis since the late 1960s (Itakura & Saito, 1973a, 1970; Atal & Hanauer, 1971), although the basic principles were established long before this by Wiener (1947). Linear predictive coding, which is also known as autoregressive analysis, is a time-series algorithm that has applications in many fields other than speech analysis (see, e.g., Chatfield, 1989). Itakura and Saito developed a formulation for linear prediction analysis using a lattice form for the inverse filter. The Itakura–Saito distance (or Itakura–Saito divergence) is a measure of the difference between an original spectrum and an approximation of that spectrum. Although it is not a perceptual measure it is intended to reflect perceptual (dis)similarity. It was proposed by Fumitada Itakura and Shuzo Saito in the 1960s while they were with NTT. The distance is defined as: The Itakura–Saito distance is a Bregman divergence, but is not a true metric since it is not symmetric and it does not fulfil triangle inequality. read more: Selected Methods for Improving Synthesis Speech Quality Using Linear Predictive Coding: System Description, Coefficient Smoothing and Streak Data inputs Source Settings: -Loxx's Expanded Source Types. You typically use "open" since open has already closed on the current active bar LastBar - bar where to start the prediction PastBars - how many bars back to model LPOrder - order of linear prediction model; 0 to 1 FutBars - how many bars you want to forward predict Things to know Normally, a simple moving average is calculated on source data. I've expanded this to 38 different averaging methods using Loxx's Moving Avreages. This indicator repaints Related Indicators (linear extrapolation of price) Levinson-Durbin Autocorrelation Extrapolation of Price Weighted Burg AR Spectral Estimate Extrapolation of Price Helme-Nikias Weighted Burg AR-SE Extra. of Price
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loxxの投稿
6
Fourier Extrapolator of Variety RSI w/ Bollinger Bands [Loxx]Fourier Extrapolator of Variety RSI w/ Bollinger Bands is an RSI indicator that shows the original RSI, the Fourier Extrapolation of RSI in the past, and then the projection of the Fourier Extrapolated RSI for the future. This indicator has 8 different types of RSI including a new type of RSI called T3 RSI. The purpose of this indicator is to demonstrate the Fourier Extrapolation method used to model past data and to predict future price movements. This indicator will repaint. If you wish to use this for trading, then make sure to take a screenshot of the indicator when you enter the trade to save your analysis. This is the first of a series of forecasting indicators that can be used in trading. Due to how this indicator draws on the screen, you must choose values of npast and nfut that are equal to or less than 200. this is due to restrictions by TradingView and Pine Script in only allowing 500 lines on the screen at a time. Enjoy! What is Fourier Extrapolation? This indicator uses a multi-harmonic (or multi-tone) trigonometric model of a price series xi, i=1..n, is given by: xi = m + Sum( a*Cos(w*i) + b*Sin(w*i), h=1..H ) Where: xi - past price at i-th bar, total n past prices; m - bias; a and b - scaling coefficients of harmonics; w - frequency of a harmonic ; h - harmonic number; H - total number of fitted harmonics. Fitting this model means finding m, a, b, and w that make the modeled values to be close to real values. Finding the harmonic frequencies w is the most difficult part of fitting a trigonometric model. In the case of a Fourier series, these frequencies are set at 2*pi*h/n. But, the Fourier series extrapolation means simply repeating the n past prices into the future. This indicator uses the Quinn-Fernandes algorithm to find the harmonic frequencies. It fits harmonics of the trigonometric series one by one until the specified total number of harmonics H is reached. After fitting a new harmonic , the coded algorithm computes the residue between the updated model and the real values and fits a new harmonic to the residue. see here: A Fast Efficient Technique for the Estimation of Frequency , B. G. Quinn and J. M. Fernandes, Biometrika, Vol. 78, No. 3 (Sep., 1991), pp . 489-497 (9 pages) Published By: Oxford University Press The indicator has the following input parameters: src - input source npast - number of past bars, to which trigonometric series is fitted; Nfut - number of predicted future bars; nharm - total number of harmonics in model; frqtol - tolerance of frequency calculations. Included: Loxx's Expanded Source Types Loxx's Variety RSI Other indicators using this same method Fourier Extrapolator of Price w/ Projection Forecast Fourier Extrapolator of Price
Pine Script® インジケーター
loxxの投稿
Quadratic RegressionFit a quadratic polynomial (parabola) to the last length data points by minimizing the sum of squares between the data and the fitted results. The script can extrapolate the results in the future and can also display the R-squared of the model. Note that this script is subject to some limitations (more in the "Notes" section). Settings Length : Number of data points to use as input. Offset : Determine the number of past fitted values to be displayed, if 0 only the extrapolated values are displayed, if 55 only the past fitted values are displayed. Src : Input data of the indicator Show R2 : Determine if the value of the R-squared must be displayed, by default true. Usage When the underlying trend in the price is not linear, we might use more advanced models to estimate it, this is where using a higher-degree regression model might be required, as such a quadratic model (second-degree) is appropriate when the underlying trend is parabolic. Here we can see that the quadratic regression (in blue) offer a better fit than a linear one. Another advantage of the quadratic regression is that a linear one will always have the same direction, that's not the case with the quadratic regression and as such, it is possible to forecast reversals. Above a linear regression (in red) and two quadratic regression (in blue) with both length = 54. Note that for the sake of clarity, the above image uses a quadratic regression to show all the past fitted values and another one to show all the forecasted values. The R-Squared is also extremely useful when it comes to measuring the accuracy of the model, with values closer to 1 indicating that the model is appropriate, and thus suggesting that the underlying trend in the price is parabolic. The R-squared can also measure the strength of the trend. Notes The script uses the function line.new , as such only a maximum of 54 observations are displayed, getting more observations can be done by using an additional quadratic regression like we did in the previous section. Another thing is that line.new use xloc.bar_time , as such it is possible to observe some errors with the displayed results of the indicator, such as: This will happen when applying the indicator to symbols with session breaks, I apologize for this inconvenience and I'll try to find solutions. Note however that the indicator will work perfectly on cryptos. Summary That's an indicator I really wanted to make, even if it is important to note that such models are rarely useful in stock markets, however it is more than possible to create a quadratic regression (with severe limitations) with pinescript. Today I turn 21, while I should be celebrating I still wanted to share something with the community, it's also some kind of present to myself that tells me that I am a bit better at using pinescript than last year, and I am glad I could progress (instead of regress, regression , got it?). Thx a lot for reading!
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alexgroverの投稿
81
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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alexgroverの投稿
18
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 tradingview 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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alexgroverの投稿
24
Linear ChannelsIntroduction I already made an indicator (simple line) that tried to make lines on price such that the results would not repaint and give a good fit to the price, today i publish a channels indicator based on the simple line indicator. The indicator aim to show possible support and resistance levels when the central line posses a low sum of squares with the price, a linear extrapolation was also provided in order to show possible future price positions respective to the channels. The Indicator The emphasis parameter of the simple line indicator has been removed, instead we keep length and mult as numerical input parameters. In general length control how persistent the lines are, larger values will create longer lines on average, mult help make the line fit to the price better but might as well affect how spread the channels are as well as the lines average length. When mult > length the lines will fit better the price while when length >= mult the fit might not be the best. The point parameter allow you to fix the indicator when using it on high market price values or when the indicator exhibit a weird behaviour. point = false on btcusd point = true If the lines still does not fit well enough try to lower length. I know this might result inconvenient in so many ways but i'am working on simplifying things. Therefore some larger price values might use lower length and use mult instead. For market not using the point parameters a settings of : length > 1 and mult = length*2 might provide a good to go setup. The channel spreading parameter allow to make spread the channels by a certain factor. Issues I'am still not good with line extensions, if it bother you deactivate the extrapolation parameter. Sorry for the inconvenience. Conclusion It is possible to make non repainting linear indicators, and i'am working on some of them. While some might argue that price is not linear thus not requiring the use of linear indicators it can still be interesting to use those if they, unlike the linear regression, don't repaints and provide a way to change their directions according to the price trend. Thanks for reading !
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alexgroverの投稿
22
Stationary Extrapolated Levels OscillatorIntroduction The oscillator version of the stationary extrapolated levels indicator. The methodology behind the extrapolated levels where to minimize the risk of making a decision based only on a forecast, therefore the indicator plotted levels in order to determine possible reversal points, signals where generated when the detrended series crossed over/under those levels. The Indicator First we detrend the price, this is because forecasting the trend is often harder than a series without trend (stationarity > non-stationarity) , then we forecast the detrended price with a linear extrapolation over a period of length and apply a max/min filter twice to the forecast, the max/min filters are just the highest and lowest function in pine. So the max/min filter have lag length/2 , by applying it two times we have a lag of length which is the period of the forecast. Because we use highest and lowest we can apply min-max normalization in the form of : x' = (x - min(x, min'))/(max(x,max') - min(x, min')) where x is the detrended price, max' the highest of the forecast of x and min' the lowest of the forecast of x . This result in a scaled oscillator in a range of (1,0), When the indicator is equal to 1 or 0 there are high chances of reversals, more in depth this mean that the detrended price have crossed the highest/lowest of the forecast, when the indicator is equal to 0 or 1 for a long time this mean that the forecast was quite inaccurate, you can minimize risk by focusing on the cross between the detrended price and the 0.8/0.2 levels. Conclusion I've shown an oscillator version of my previous "Stationary extrapolated levels" indicator, the method involving taking the highest and lowest of the forecast is a great way to minimize the risk involved by time-series forecasting driven decisions. So i hope you find an use to it. Thanks for reading !
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alexgroverの投稿
13
Pseudo Polynomial ChannelIntroduction Back when i started using pine i made a script called periodic channel who aimed to rescale an average correlated sine wave to the price...don't worked very well. So i tried to fix problems induced by the indicator without much success, i had to redo it from scratch while abandoning the idea of rescaling correlated smooth functions to the price, at that time i also received requests regarding polynomial channel, some plateformes included this indicator, this led me to the idea to estimate it in order to both respond to the periodic channel problems and the requests i received, i have tried many many things and recently i tweaked a linear extrapolation to have an approximation. Linear Extrapolation To Pseudo Polynomial Regression I could be wrong but a polynomial regression must use constant parameters in order to provide a really smooth output, at least constant for a set of time. The moving averages forms (Savitzky-Golay moving average) who smooth polynomials across a window to the data don't have such smoothness, so how to estimate a polynomial regression while having a parameter providing control over the smoothness, a response to this is by using a recursive linear extrapolation. I posted a linear extrapolation indicator long ago, i used the same formula while adding a function to morph the output and the input in the form of : morph * output + (1-morph) * input How can this provide an estimate of a polynomial regression ? Well i'm not even sure myself but if you use the output as input (morph = 1) for the linear extrapolation function you should get a rough estimate of a line, this is what i thought at first and it proved to be right Based on this observation i thought that it would be possible to get polynomial results by lowering morph, and as expected it worked well but showed a periodic pattern, this is why i smooth k in line 10. 0.9 for morph work well, higher values create sometimes smoother results but damage heavily the estimation. Parameters Morph have been introduced earlier, it control the amount of output and input the linear extrapolation should process, lower values create rougher but more stables results, if you see that the estimation is going nuts lower morph or change length, also lower length if you increase morph . High overshoot, morph to 0.8 can help have a better estimation at the cost of less smoothness. Length control the indicator smoothing, this parameter differ heavily from other filters, therefore low values can create mid/long term smoothing, it can also depend on which market instrument you are applying it, so there are no fixed optimal length. Mult control how spread the bands are, to do so mult multiply the cumulative mean error, you can change this error measurement by anything you want like standard deviation/atr/range but take into account that you may create a separate parameter to control the error instead of length . Mult can be a float and like length can have different optimal values depending on the market the indicator is applied to. Flatten do exactly what is name imply, it flatten the overall output to have a better estimation, can be a float. The result is less smooth. Flatten = 2 More Exemples BTCUSD length = 25 and mult = 4 XPDUSD length = 25 and mult = 1 ALPHABET length = 6 and morph = 0.99 Conclusion I tried to estimate a polynomial channel by using recursion in the linear extrapolation function. This build is way more stable than the periodic channel but its still a bit inaccurate in my opinion. I hope this code can still help someone build something really nice, if so share your results :) I apologize for those expecting a legit polynomial channel build but i really don't know how to do that, as i said parameters for the regression must be constants, i hope it still fine :) Thanks for reading !
Pine Script® インジケーター
alexgroverの投稿
24
Spiky Iguana Multi RSI Bands (Reverse RSI for the Price) by RRBSpiky Iguana Multi RSI Bands by RagingRocketBull 2018 Version 1.0 This indicator shows multiple RSI Bands with prices corresponding to specified overbought/oversold RSI levels. It is used to extrapolate the exact price levels currently matching a given set of RSI levels based on prior price/RSI levels action. You can think of it as a reverse RSI where RSI levels are moving dynamically around the price instead of price bouncing between straight lines. Features: - 6+6 = 12 customizable Overbought(R)/Oversold(S) RSI Levels + 6 Mean(M) lines - Multicolor levels/fill ranges - Show/Hide specific S/R/M levels and fill ranges 1. uses plot*, fill and is based on RSIBANDS_LB Good Luck! Feel free to explore and learn from the code
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RagingRocketBullの投稿
9