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TASC 2026.02 Portfolio Diversification█ OVERVIEW This indicator is a simplified framework for analyzing hypothetical portfolios, based on the concepts in the February 2026 edition of the TASC Traders' Tips , "Foundational Portfolio Design, Not Stock-Picking”. It requests datasets for spread symbols that represent weighted combinations of user-selected or predefined instruments, compares the returns in the data to those of a selected benchmark, and calculates risk-related metrics. █ CONCEPTS One of the core concepts of portfolio design is diversification. A diversified portfolio distributes market exposure across multiple, ideally uncorrelated, instruments to reduce potential risks. Investors often diversify their portfolios by allocating capital to instruments from different classes, sectors, or regions rather than investing in only a single instrument or multiple related instruments. As described in the article, the motivation behind creating diversified portfolios is simple: "No single position should have the capacity to sink the entire portfolio." This indicator estimates a portfolio's performance by requesting combined price data for spread symbols from user inputs or predefined options, and then analyzing the data's annual arithmetic returns alongside those of a specified benchmark instrument. It displays the returns of the spread and the benchmark in a table at the bottom left. The indicator also displays the following metrics described in the article in a table at the bottom right of the pane for additional performance information: Max drawdown: The maximum drop in the portfolio's value from a local peak. Standard deviation: The dispersion of portfolio values relative to their mean. Sharpe ratio: The ratio of excess returns in an investment compared to a hypothetical risk-free rate of return. Pain index: A measure of risk based on the depth, duration, and frequency of losses. The metric in this script considers only the bars where drawdown is nonzero. Ulcer index: A measure of downside risk based on the root mean square of drawdowns. The metric in this script considers only the bars where drawdown is nonzero. Correlation: The Pearson correlation coefficient between the returns of the hypothetical portfolio and those of a selected benchmark. The first five metrics are direct risk measures. The correlation metric helps assess whether the hypothetical portfolio closely follows the broader market. High correlation with a broad benchmark might indicate an elevated sensitivity to systematic risk. █ USAGE Users can select a combination of up to 10 symbols with specific weights to construct a hypothetical portfolio to analyze. Alternatively, users can select a predefined combination of symbols and weights based on the article's examples of optimized portfolios for different levels of risk tolerance. The script plots the calculated returns from the selected combination and the benchmark instrument for visual comparison. It also generates tables to compare returns and display risk metrics. Note: This indicator is intended to provide a simplified demonstration of portfolio concepts, and some metric calculations differ slightly from those in the article. The script does not produce any signals, and the calculated metrics are estimates intended for EOD timeframes such as 1D. If the hypothetical portfolio consists of instruments with different sessions, we recommend using 1W or a higher timeframe. █ INPUTS Benchmark: The symbol of the instrument to compare against the hypothetical portfolio. Portfolio Type: Choose between named options for predefined portfolio configurations based on risk profiles outlined in the article. To create a custom portfolio from up to 10 symbols, select "Custom" and adjust the 10 sets of inputs below. Risk-free rate: The hypothetical annual risk-free rate for the Sharpe ratio. Periods per year: If not zero, the script uses the value as the number of bars per year for annualization, which affects Sharpe ratio and standard deviation metrics. Display Toggles: The display for the returns and metrics tables can be toggled on or off.
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TASC 2026.01 The Reversion Index█ OVERVIEW This script implements the Reversion Index as presented by John F. Ehlers in the January 2026 edition of the TASC Traders' Tips , "Identifying Peaks And Valleys In Ranging Markets”. This indicator was created to provide timely buy and sell signals for mean reversion strategies. █ CONCEPTS Ehlers came up with the idea for the Reversion Index following the development of the "Continuation Index" (featured in the September 2025 edition). While the Continuation Index provides indications for trend onset, continuation, and exhaustion; the Reversion Index serves as its counterpart for mean-reversion trading. The raw Reversion Index value is calculated as the net change in price normalized to the sum of the absolute value of change in price over the same period; for clarity, it is then smoothed using Ehlers' SuperSmoother. The Smooth Reversion Index value is led by a "Trigger" line, which is created by smoothing the raw data to half the smoothing period of the smoothed index. Note: Ehlers suggests the smoothing lengths be left at 8 and 4 (Reversion Index & Trigger). For this reason these lengths are hard-coded in the script but can be easily modified in the code. █ USAGE In order to identify peaks and valleys effectively, the "Length" should ideally be set to half of that of the expected cycle of the data. If the expected cycle of your trading data is 20 bars, a 10 bar length should be set. Note: The Reversion Index is intended to identify peaks and valleys within a cycle, not over a large sample period. Ehlers suggests that this would create an estimation of trend, which is not the goal here. Once the length is set, peaks and valleys are interpreted as the cross of the "Trigger" and "Smooth" lines.
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TASC 2025.11 The Points and Line Chart█ OVERVIEW This script implements the Points and Line Chart described by Mohamed Ashraf Mahfouz and Mohamed Meregy in the November 2025 edition of the TASC Traders' Tips , "Efficient Display of Irregular Time Series”. This novel chart type interprets regular time series chart data to create an irregular time series chart. █ CONCEPTS When formatting data for display on a price chart, there are two main categorizations of chart types: regular time series (RTS) and irregular time series (ITS). RTS charts, such as a typical candlestick chart, collect data over a specified amount of time and display it at one point. A one-minute candle, for example, represents the entirety of price movements within the minute that it represents. ITS charts display data only after certain conditions are met. Since they do not plot at a consistent time period, they are called “irregular”. Typically, ITS charts, such as Point and Figure (P&F) and Renko charts, focus on price change, plotting only when a certain threshold of change occurs. The Points and Line (P&L) chart operates similarly to a P&F chart, using price change to determine when to plot points. However, instead of plotting the price in points, the P&L chart (by default) plots the closing price from RTS data. In other words, the P&L chart plots its points at the actual RTS close, as opposed to (price) intervals based on point size. This approach creates an ITS while still maintaining a reference to the RTS data, allowing us to gain a better understanding of time while consolidating the chart into an ITS format. █ USAGE Because the P&L chart forms bars based on price action instead of time, it displays displays significantly more history than a typical RTS chart. With this view, we are able to more easily spot support and resistance levels, which we could use when looking to place trades. In the chart below, we can see over 13 years of data consolidated into one single view. To view specific chart details, hover over each point of the chart to see a list of information. In addition to providing a compact view of price movement over larger periods, this new chart type helps make classic chart patterns easier to interpret. When considering breakouts, the closing price provides a clearer representation of the actual breakout, as opposed to point size plots which are limited. Because P&L is a new charting type, this script still requires a standard RTS chart for proper calculations. However, the main price chart is not intended for interpretation alongside the P&L chart; users can hide the main price series to keep the chart clean. █ DISPLAYS This indicator creates two displays: the "Price Display" and the "Data Display". With the "Price display" setting, users can choose between showing a line or OHLC candles for the P&L drawing. The line display shows the close price of the P&L chart. In the candle display, the close price remains the same, while the open, high, and low values depend on the price action between points. With the "Data display" setting, users can enable the display of a histogram that shows either the total volume or days/bars between the points in the P&L chart. For example, a reading of 12 days would indicate that the time since the last point was 12 days. Note: The "Days" setting actually shows the number of chart bars elapsed between P&L points. The displayed value represents days only if the chart uses the "1D" timeframe. The "Overlay P&L on chart" input controls whether the P&L line or candles appear on the main chart pane or in a separate pane. Users can deactivate either display by selecting "None" from the corresponding input. Technical Note: Due to drawing limitations, this indicator has the following display limits: The line display can show data to 10,000 P&L points. The candle display and tooltips show data for up to 500 points. The histograms show data for up to 3,333 points. █ INPUTS Reversal Amount: The number of points/steps required to determine a reversal. Scale size Method: The method used to filter price movements. By default, the P&L chart uses the same scaling method as the P&F chart. Optionally, this scaling method can be changed to use ATR or Percent. P&L Method: The prices to plot and use for filtering: “Close” plots the closing price and uses it to determine movements. “High/Low” uses the high price on upside moves and low price on downside moves. "Point Size" uses the closing price for filtration, but locks the price to plot at point size intervals.
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TASC 2025.09 The Continuation Index █ OVERVIEW This script implements the "Continuation Index" as described by John F. Ehlers in the September 2025 edition of TASC's Trader's Tips . The Continuation Index uses Laguerre filters (featured in the July 2025 edition) to provide an early indication of trend direction, continuation, and exhaustion. █ CONCEPTS The idea for the Continuation Index was formed from an observation about Laguerre filters. In his article, Ehlers notes that when price is in trend, it tends to stay to one side of the filter. When considering smoothing, the UltimateSmoother was an obvious choice to reduce lag. With that in mind, The Continuation Index normalizes the difference between UltimateSmoother and the Laguerre filter to produce a two-state oscillator. To minimize lag, the UltimateSmoother length in this indicator is fixed to half the length of the Laguerre filter. █ USAGE The Continuation Index consists of two primary states. +1 suggests that the trader should position on the long side. -1 suggests that the user should position on the short side. Other readings can imply other opportunities, such as: High Value Fluctuation could be used as a "buy the dip" opportunity. Low Value Fluctuation could be used as a "sell the pop" opportunity. █ INPUTS By understanding the inputs and adjusting them as needed, each trader can benefit more from this indicator: Gamma : Controls the Laguerre filter's response. This can be set anywhere between 0 and 1. If set to 0, the filter’s value will be the same as the UltimateSmoother. Order : Controls the lag of the Laguerre filter, which is important when considering the timing of the system for spotting reversals. This can be set from 1 to 10, with lower values typically producing faster timing. Length : Affects the smoothing of the display. Ehlers recommends starting with this value set to the intended amount of time you plan to hold a position. Consider your chart timeframe when setting this input. For example, on a daily chart, if you intend to hold a position for one month, set a value of 20.
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TASC 2025.05 Trading The Channel█ OVERVIEW This script implements channel-based trading strategies based on the concepts explained by Perry J. Kaufman in the article "A Test Of Three Approaches: Trading The Channel" from the May 2025 edition of TASC's Traders' Tips . The script explores three distinct trading methods for equities and futures using information from a linear regression channel. Each rule set corresponds to different market behaviors, offering flexibility for trend-following, breakout, and mean-reversion trading styles. █ CONCEPTS Linear regression Linear regression is a model that estimates the relationship between a dependent variable and one or more independent variables by fitting a straight line to the observed data. In the context of financial time series, traders often use linear regression to estimate trends in price movements over time. The slope of the linear regression line indicates the strength and direction of the price trend. For example, a larger positive slope indicates a stronger upward trend, and a larger negative slope indicates the opposite. Traders can look for shifts in the direction of a linear regression slope to identify potential trend trading signals, and they can analyze the magnitude of the slope to support trading decisions. One caveat to linear regression is that most financial time series data does not follow a straight line, meaning a regression line cannot perfectly describe the relationships between values. Prices typically fluctuate around a regression line to some degree. As such, analysts often project ranges above and below regression lines, creating channels to model the expected extent of the data's variability. This strategy constructs a channel based on the method used in Kaufman's article. It measures the maximum distances from points on the linear regression line to historical price values, then adds those distances and the current slope to the regression points. Depending on the trading style, traders might look for prices to move outside an established channel for breakout signals, or they might look for price action to reach extremes within the channel for potential mean reversion opportunities. █ STRATEGY CALCULATIONS Primary trade rules This strategy implements three distinct sets of rules for trend, breakout, and mean-reversion trades based on the methods Kaufman describes in his article: Trade the trend (Rule 1) : Open new positions when the sign of the slope changes, indicating a potential trend reversal. Close short trades and enter a long trade when the slope changes from negative to positive, and do the opposite when the slope changes from positive to negative. Trade channel breakouts (Rule 2) : Open new positions when prices cross outside the linear regression channel for the current sample. Close short trades and enter a long trade when the price moves above the channel, and do the opposite when the price moves below the channel. Trade within the channel (Rule 3) : Open new positions based on price values within the channel's range. Close short trades and enter a long trade when the price is near the channel's low, within a specified percentage of the channel's range, and do the opposite when the price is near the channel's high. With this rule, users can also filter the trades based on the channel's slope. When the filter is active, long positions are allowed only when the slope is positive, and short positions are allowed only when it is negative. Position sizing Kaufman's strategy uses specific trade sizes for equities and futures markets: For an equities symbol, the number of shares traded is $10,000 divided by the current price. For a futures symbol, the number of contracts traded is based on a volatility-adjusted formula that divides $25,000 by the product of the 20-bar average true range and the instrument's point value. By default, this script automatically uses these sizes for its trade simulation on equities and futures symbols and does not simulate trading on other symbols. However, users can control position sizes from the "Settings/Properties" tab and enable trade simulation on other symbol types by selecting the "Manual" option in the script's "Position sizing" input. Stop-loss This strategy includes the option to place an accompanying stop-loss order for each trade, which users can enable from the "SL %" input in the "Settings/Inputs" tab. When enabled, the strategy places a stop-loss order at a specified percentage distance from the closing price where the entry order occurs, allowing users to compare how the strategy performs with added loss protection. █ USAGE This strategy adapts its display logic for the three trading approaches based on the rule selected in the "Trade rule" input: For all rules, the script plots the linear regression slope in a separate pane. The plot is color-coded to indicate whether the current slope is positive or negative. When the selected rule is "Trade the trend", the script plots triangles in the separate pane to indicate when the slope's direction changes from positive to negative or vice versa. Additionally, it plots a color-coded SMA on the main chart pane, allowing visual comparison of the slope to directional changes in a moving average. When the rule is "Trade channel breakouts" or "Trade within the channel", the script draws the current period's linear regression channel on the main chart pane, and it plots bands representing the history of the channel values from the specified start time onward. When the rule is "Trade within the channel", the script plots overbought and oversold zones between the bands based on a user-specified percentage of the channel range to indicate the value ranges where new trades are allowed. Users can customize the strategy's calculations with the following additional inputs in the "Settings/Inputs" tab: Start date : Sets the date and time when the strategy begins simulating trades. The script marks the specified point on the chart with a gray vertical line. The plots for rules 2 and 3 display the bands and trading zones from this point onward. Period : Specifies the number of bars in the linear regression channel calculation. The default is 40. Linreg source : Specifies the source series from which to calculate the linear regression values. The default is "close". Range source : Specifies whether the script uses the distances from the linear regression line to closing prices or high and low prices to determine the channel's upper and lower ranges for rules 2 and 3. The default is "close". Zone % : The percentage of the channel's overall range to use for trading zones with rule 3. The default is 20, meaning the width of the upper and lower zones is 20% of the range. SL% : If the checkbox is selected, the strategy adds a stop-loss to each trade at the specified percentage distance away from the closing price where the entry order occurs. The checkbox is deselected by default, and the default percentage value is 5. Position sizing : Determines whether the strategy uses Kaufman's predefined trade sizes ("Auto") or allows user-defined sizes from the "Settings/Properties" tab ("Manual"). The default is "Auto". Long trades only : If selected, the strategy does not allow short positions. It is deselected by default. Trend filter : If selected, the strategy filters positions for rule 3 based on the linear regression slope, allowing long positions only when the slope is positive and short positions only when the slope is negative. It is deselected by default. NOTE: Because of this strategy's trading rules, the simulated results for a specific symbol or channel configuration might have significantly fewer than 100 trades. For meaningful results, we recommend adjusting the start date and other parameters to achieve a reasonable number of closed trades for analysis. Additionally, this strategy does not specify commission and slippage amounts by default, because these values can vary across market types. Therefore, we recommend setting realistic values for these properties in the "Cost simulation" section of the "Settings/Properties" tab.
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TASC 2025.04 The Ultimate Oscillator█ OVERVIEW This script implements an alternative, refined version of the Ultimate Oscillator (UO) designed to reduce lag and enhance responsiveness in momentum indicators, as introduced by John F. Ehlers in his article "Less Lag In Momentum Indicators, The Ultimate Oscillator" from the April 2025 edition of TASC's Traders' Tips . █ CONCEPTS In his article, Ehlers states that indicators are essentially filters that remove unwanted noise (i.e., unnecessary information) from market data. Simply put, they process a series of data to place focus on specific information, providing a different perspective on price dynamics. Various filter types attenuate different periodic signals within the data. For instance, a lowpass filter allows only low-frequency signals, a highpass filter allows only high-frequency signals, and a bandpass filter allows signals within a specific frequency range . Ehlers explains that the key to removing indicator lag is to combine filters of different types in such a way that the result preserves necessary, useful signals while minimizing delay (lag). His proposed UltimateOscillator aims to maintain responsiveness to a specific frequency range by measuring the difference between two highpass filters' outputs. The oscillator uses the following formula: UO = (HP1 - HP2) / RMS Where: HP1 is the first highpass filter. HP2 is another highpass filter that allows only shorter wavelengths than the critical period of HP1. RMS is the root mean square of the highpass filter difference, used as a scaling factor to standardize the output. The resulting oscillator is similar to a bandpass filter , because it emphasizes wavelengths between the critical periods of the two highpass filters. Ehlers' UO responds quickly to value changes in a series, providing a responsive view of momentum with little to no lag. █ USAGE Ehlers' UltimateOscillator sets the critical periods of its highpass filters using two parameters: BandEdge and Bandwidth : The BandEdge sets the critical period of the second highpass filter, which determines the shortest wavelengths in the response. The Bandwidth is a multiple of the BandEdge used for the critical period of the first highpass filter, which determines the longest wavelengths in the response. Ehlers suggests that a Bandwidth value of 2 works well for most applications. However, traders can use any value above or equal to 1.4. Users can customize these parameters with the "Bandwidth" and "BandEdge" inputs in the "Settings/Inputs" tab. The script plots the UO calculated for the specified "Source" series in a separate pane, with a color based on the chart's foreground color. Positive UO values indicate upward momentum or trends, and negative UO values indicate the opposite. Additionally, this indicator provides the option to display a "cloud" from 10 additional UO series with different settings for an aggregate view of momentum. The "Cloud" input offers four display choices: "Bandwidth", "BandEdge", "Bandwidth + BandEdge", or "None". The "Bandwidth" option calculates oscillators with different Bandwidth values based on the main oscillator's setting. Likewise, the "BandEdge" option calculates oscillators with varying BandEdge values. The "Bandwidth + BandEdge" option calculates the extra oscillators with different values for both parameters. When a user selects any of these options, the script plots the maximum and minimum oscillator values and fills their space with a color gradient. The fill color corresponds to the net sum of each UO's sign , indicating whether most of the UOs reflect positive or negative momentum. Green hues mean most oscillators are above zero, signifying stronger upward momentum. Red hues mean most are below zero, indicating stronger downward momentum.
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TASC 2025.03 A New Solution, Removing Moving Average Lag█ OVERVIEW This script implements a novel technique for removing lag from a moving average, as introduced by John Ehlers in the "A New Solution, Removing Moving Average Lag" article featured in the March 2025 edition of TASC's Traders' Tips . █ CONCEPTS In his article, Ehlers explains that the average price in a time series represents a statistical estimate for a block of price values, where the estimate is positioned at the block's center on the time axis. In the case of a simple moving average (SMA), the calculation moves the analyzed block along the time axis and computes an average after each new sample. Because the average's position is at the center of each block, the SMA inherently lags behind price changes by half the data length. As a solution to removing moving average lag, Ehlers proposes a new projected moving average (PMA) . The PMA smooths price data while maintaining responsiveness by calculating a projection of the average using the data's linear regression slope. The slope of linear regression on a block of financial time series data can be expressed as the covariance between prices and sample points divided by the variance of the sample points. Ehlers derives the PMA by adding this slope across half the data length to the SMA, creating a first-order prediction that substantially reduces lag: PMA = SMA + Slope * Length / 2 In addition, the article includes methods for calculating predictions of the PMA and the slope based on second-order and fourth-order differences. The formulas for these predictions are as follows: PredictPMA = PMA + 0.5 * (Slope - Slope ) * Length PredictSlope = 1.5 * Slope - 0.5 * Slope Ehlers suggests that crossings between the predictions and the original values can help traders identify timely buy and sell signals. █ USAGE This indicator displays the SMA, PMA, and PMA prediction for a specified series in the main chart pane, and it shows the linear regression slope and prediction in a separate pane. Analyzing the difference between the PMA and SMA can help to identify trends. The differences between PMA or slope and its corresponding prediction can indicate turning points and potential trade opportunities. The SMA plot uses the chart's foreground color, and the PMA and slope plots are blue by default. The plots of the predictions have a green or red hue to signify direction. Additionally, the indicator fills the space between the SMA and PMA with a green or red color gradient based on their differences: Users can customize the source series, data length, and plot colors via the inputs in the "Settings/Inputs" tab. █ NOTES FOR Pine Script® CODERS The article's code implementation uses a loop to calculate all necessary sums for the slope and SMA calculations. Ported into Pine, the implementation is as follows: pma(float src, int length) => float PMA = 0., float SMA = 0., float Slope = 0. float Sx = 0.0 , float Sy = 0.0 float Sxx = 0.0 , float Syy = 0.0 , float Sxy = 0.0 for count = 1 to length float src1 = src Sx += count Sy += src Sxx += count * count Syy += src1 * src1 Sxy += count * src1 Slope := -(length * Sxy - Sx * Sy) / (length * Sxx - Sx * Sx) SMA := Sy / length PMA := SMA + Slope * length / 2 However, loops in Pine can be computationally expensive, and the above loop's runtime scales directly with the specified length. Fortunately, Pine's built-in functions often eliminate the need for loops. This indicator implements the following function, which simplifies the process by using the ta.linreg() and ta.sma() functions to calculate equivalent slope and SMA values efficiently: pma(float src, int length) => float Slope = ta.linreg(src, length, 0) - ta.linreg(src, length, 1) float SMA = ta.sma(src, length) float PMA = SMA + Slope * length * 0.5 To learn more about loop elimination in Pine, refer to this section of the User Manual's Profiling and optimization page.
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TASC 2025.02 Autocorrelation Indicator█ OVERVIEW This script implements the Autocorrelation Indicator introduced by John Ehlers in the "Drunkard's Walk: Theory And Measurement By Autocorrelation" article from the February 2025 edition of TASC's Traders' Tips . The indicator calculates the autocorrelation of a price series across several lags to construct a periodogram , which traders can use to identify market cycles, trends, and potential reversal patterns. █ CONCEPTS Drunkard's walk A drunkard's walk , formally known as a random walk , is a type of stochastic process that models the evolution of a system or variable through successive random steps. In his article, John Ehlers relates this model to market data. He discusses two first- and second-order partial differential equations, modified for discrete (non-continuous) data, that can represent solutions to the discrete random walk problem: the diffusion equation and the wave equation. According to Ehlers, market data takes on a mixture of two "modes" described by these equations. He theorizes that when "diffusion mode" is dominant, trading success is almost a matter of luck, and when "wave mode" is dominant, indicators may have improved performance. Pink spectrum John Ehlers explains that many recent academic studies affirm that market data has a pink spectrum , meaning the power spectral density of the data is proportional to the wavelengths it contains, like pink noise . A random walk with a pink spectrum suggests that the states of the random variable are correlated and not independent. In other words, the random variable exhibits long-range dependence with respect to previous states. Autocorrelation function (ACF) Autocorrelation measures the correlation of a time series with a delayed copy, or lag , of itself. The autocorrelation function (ACF) is a method that evaluates autocorrelation across a range of lags , which can help to identify patterns, trends, and cycles in stochastic market data. Analysts often use ACF to detect and characterize long-range dependence in a time series. The Autocorrelation Indicator evaluates the ACF of market prices over a fixed range of lags, expressing the results as a color-coded heatmap representing a dynamic periodogram. Ehlers suggests the information from the periodogram can help traders identify different market behaviors, including: Cycles : Distinguishable as repeated patterns in the periodogram. Reversals : Indicated by sharp vertical changes in the periodogram when the indicator uses a short data length . Trends : Indicated by increasing correlation across lags, starting with the shortest, over time. █ USAGE This script calculates the Autocorrelation Indicator on an input "Source" series, smoothed by Ehlers' UltimateSmoother filter, and plots several color-coded lines to represent the periodogram's information. Each line corresponds to an analyzed lag, with the shortest lag's line at the bottom of the pane. Green hues in the line indicate a positive correlation for the lag, red hues indicate a negative correlation (anticorrelation), and orange or yellow hues mean the correlation is near zero. Because Pine has a limit on the number of plots for a single indicator, this script divides the periodogram display into three distinct ranges that cover different lags. To see the full periodogram, add three instances of this script to the chart and set the "Lag range" input for each to a different value, as demonstrated in the chart above. With a modest autocorrelation length, such as 20 on a "1D" chart, traders can identify seasonal patterns in the price series, which can help to pinpoint cycles and moderate trends. For instance, on the daily ES1! chart above, the indicator shows repetitive, similar patterns through fall 2023 and winter 2023-2024. The green "triangular" shape rising from the zero lag baseline over different time ranges corresponds to seasonal trends in the data. To identify turning points in the price series, Ehlers recommends using a short autocorrelation length, such as 2. With this length, users can observe sharp, sudden shifts along the vertical axis, which suggest potential turning points from upward to downward or vice versa.
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TASC 2025.01 Linear Predictive Filters█ OVERVIEW This script implements a suite of tools for identifying and utilizing dominant cycles in time series data, as introduced by John Ehlers in the "Linear Predictive Filters And Instantaneous Frequency" article featured in the January 2025 edition of TASC's Traders' Tips . Dominant cycle information can help traders adapt their indicators and strategies to changing market conditions. █ CONCEPTS Conventional technical indicators and strategies often rely on static, unchanging parameters, which may fail to account for the dynamic nature of market data. In his article, John Ehlers applies digital signal processing principles to address this issue, introducing linear predictive filters to identify cyclic information for adapting indicators and strategies to evolving market conditions. This approach treats market data as a complex series in the time domain. Analyzing the series in the frequency domain reveals information about its cyclic components. To reduce the impact of frequencies outside a range of interest and focus on a specific range of cycles, Ehlers applies second-order highpass and lowpass filters to the price data, which attenuate or remove wavelengths outside the desired range. This band-limited analysis isolates specific parts of the frequency spectrum for various trading styles, e.g., longer wavelengths for position trading or shorter wavelengths for swing trading. After filtering the series to produce band-limited data, Ehlers applies a linear predictive filter to predict future values a few bars ahead. The filter, calculated based on the techniques proposed by Lloyd Griffiths, adaptively minimizes the error between the latest data point and prediction, successively adjusting its coefficients to align with the band-limited series. The filter's coefficients can then be applied to generate an adaptive estimate of the band-limited data's structure in the frequency domain and identify the dominant cycle. █ USAGE This script implements the following tools presented in the article: Griffiths Predictor This tool calculates a linear predictive filter to forecast future data points in band-limited price data. The crosses between the prediction and signal lines can provide potential trade signals. Griffiths Spectrum This tool calculates a partial frequency spectrum of the band-limited price data derived from the linear predictive filter's coefficients, displaying a color-coded representation of the frequency information in the pane. This mode's display represents the data as a periodogram . The bottom of each plotted bar corresponds to a specific analyzed period (inverse of frequency), and the bar's color represents the presence of that periodic cycle in the time series relative to the one with the highest presence (i.e., the dominant cycle). Warmer, brighter colors indicate a higher presence of the cycle in the series, whereas darker colors indicate a lower presence. Griffiths Dominant Cycle This tool compares the cyclic components within the partial spectrum and identifies the frequency with the highest power, i.e., the dominant cycle . Traders can use this dominant cycle information to tune other indicators and strategies, which may help promote better alignment with dynamic market conditions. Notes on parameters Bandpass boundaries: In the article, Ehlers recommends an upper bound of 125 bars or higher to capture longer-term cycles for position trading. He recommends an upper bound of 40 bars and a lower bound of 18 bars for swing trading. If traders use smaller lower bounds, Ehlers advises a minimum of eight bars to minimize the potential effects of aliasing. Data length: The Griffiths predictor can use a relatively small data length, as autocorrelation diminishes rapidly with lag. However, for optimal spectrum and dominant cycle calculations, the length must match or exceed the upper bound of the bandpass filter. Ehlers recommends avoiding excessively long lengths to maintain responsiveness to shorter-term cycles.
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TASC 2024.12 Dynamic ADX Histogram█ OVERVIEW This script introduces a new version of the ADX oscillator, designed by Neil Jon Harrington and featured in the "Revisualizing The ADX Oscillator" article from the  December 2024 edition of TASC's Traders' Tips . █ CONCEPTS The directional movement index (DMI+ and DMI−) and average directional index (ADX) indicators have long been popular with technical analysts. Developed by J. Welles Wilder in the 1970s, these indicators provide information about the direction and strength of price movements across bars. The DMI+ measures positive price movement, the DMI- measures negative price movement, and the ADX gauges the average strength of price trends. Although these indicators can provide helpful insights into price action and momentum, Neil Jon Harrington argues they are often misunderstood or misapplied. Harrington's indicator, the Dynamic ADX Histogram (DADX), applies directional information to the ADX based on DMI+ and DMI- values to create a single oscillator centered around 0. The indicator displays the oscillator as a histogram with dynamic colors based on ADX movements and user-defined strength thresholds. The author believes this modification of the ADX and DMI data offers a more intuitive visualization of the information provided by Wilder's calculations. An additional feature of the DADX is the option to use average (smooth) DMI+ and DMI- values in the oscillator's calculation, which reduces noise and choppiness at the cost of added lag. █ USAGE The "ADX Length" input determines the number of bars in the DMI and ADX calculation. The "DMI Smoothing Length" input controls the number of bars in the DMI smoothing calculation. Use a value of 1 for non-smoothed DMI data. The sign of the DADX indicates the direction of price movements based on the difference between the smoothed DMI+ and DMI- values. The absolute value of the oscillator corresponds to the ADX, representing the trend strength. The "Low Threshold" and "High Threshold" inputs define the ADX thresholds for categorizing trending, non-trending, and exhaustion states. The low threshold specifies the minimum absolute oscillator value required to indicate a trend, and the high threshold marks the absolute value where trend strength is excessive, possibly suggesting an upcoming consolidation or reversal. The indicator colors the histogram based on these thresholds and changes in the ADX, with brighter colors denoting a strengthening trend and darker colors signaling a weakening trend.
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TASC 2024.11 Ultimate Strength Index█ OVERVIEW This script implements the  Ultimate Strength Index (USI)  indicator, introduced by John Ehlers in his article titled "Ultimate Strength Index (USI)" from the  November 2024 edition of TASC's Traders' Tips . The USI is a modified version of Wilder's original Relative Strength Index (RSI) that incorporates Ehlers' UltimateSmoother lowpass filter to produce an output with significantly reduced lag. █ CONCEPTS Many technical indicators, including the RSI, lag due to their heavy reliance on historical data. John Ehlers reformulated the RSI to substantially reduce lag by applying his UltimateSmoother filter to upward movements ( strength up - SU ) and downward movements ( strength down - SD ) in the time series, replacing the standard process of smoothing changes with rolling moving averages (RMAs). Ehlers' recent works, covered in our recent script publications, have shown that the UltimateSmoother is an effective alternative to other classic averages, offering notably less lag in its response. Ehlers also modified the RSI formula to produce an index that ranges from -1 to +1 instead of 0 to 100. As a result, the USI indicates bullish conditions when its value moves above 0 and bearish conditions when it falls below 0. The USI retains many of the strengths of the traditional RSI while offering the advantage of reduced lag. It generally uses a larger lookback window than the conventional RSI to achieve similar behavior, making it suitable for trend trading with longer data lengths. When applied with shorter lengths, the USI's peaks and valleys tend to align closely with significant turning points in the time series, making it a potentially helpful tool for timing swing trades. █ CALCULATIONS The first step in the USI's calculation is determining each bar's strength up (SU) and strength down (SD) values. If the current bar's close exceeds the previous bar's, the calculation assigns the difference to SU. Otherwise, SU is zero. Likewise, if the current bar's close is below the previous bar's, it assigns the difference to SD. Otherwise, SD is zero. Next, instead of the RSI's typical smoothing process, the USI's calculation applies the UltimateSmoother to the short-term average SU and SD values, reducing high-frequency chop in the series with low lag. Finally, this formula determines the USI value: USI = ( Ult (SU) − Ult (SD)) / ( Ult (SU) + Ult (SD)), where Ult (SU) and Ult (SD) are the smoothed average strength up and strength down values.
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TASC 2024.10 Adaptive Oscillator Threshold█ OVERVIEW This script introduces a more dynamic approach to generating trading signals using the RSI indicator and a threshold that adapts to price trends and dispersion. This methodology comes from Francesco Bufi's article "Overbought/Oversold Oscillators: Useless Or Just Misused" from the October 2024 edition of TASC's Traders' Tips . █ CONCEPTS According to Francesco Bufi's observations, an oscillator-based buy signal should have a threshold that varies with the trend direction: higher during uptrends and lower during downtrends. Additionally, the level should decrease as the distance from the price to its mean increases to reduce signals in volatile conditions. Accordingly, Bufi proposes a formula for an adaptive buy level whose value is proportional to the trend (linear regression slope) and inversely proportional to the typical distance between price and its mean (standard deviation). Traders can apply this method to any oscillator to add adaptivity without modifying the oscillator's calculations, as it's simply an adaptive technique for interpreting the calculated values. This script demonstrates the application of Bufi's Adaptive Threshold (BAT) in a simple RSI-based strategy and allows users to compare its performance to the traditional fixed-threshold approach. Bufi's observations suggest that using the BAT instead of a static threshold can help improve the backtest performance of oscillator-based systems. █ DISCLAIMER This strategy script educates users on the trading systems outlined by the TASC article. By default, it uses 10% of equity as the order size and a slippage amount of 5 ticks. Traders should adjust these settings and the commission amount when using this script.
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TASC 2024.07 Gaps and Extreme Closes█ OVERVIEW This script, inspired by Perry Kaufman's article "Trading Opening Gaps and Extreme Closes in Stocks" from the  TASC's July 2024 edition of Traders' Tips , provides analytical insights into stock price behaviors following significant price moves. The information about the frequency, pullbacks, and closing patterns of these extreme price movements can aid in developing more effective trading strategies by understanding what to expect during volatile market conditions. █ CONCEPTS Perry Kaufman's article investigates the behavior of stock prices following substantial opening gaps and extreme closing moves to identify patterns and expectations that traders can utilize to make informed decisions. The motivation behind the article is to offer traders a more scientific approach to understanding price movements during volatile market conditions, particularly during earnings season or significant economic events. Kaufman's analysis reveals that stock prices have a history of exhibiting certain behaviors after substantial price gaps and extreme closes. This script follows Perry Kaufman's study and helps provide insight into how prices often behave after significant price changes. This analysis can help traders establish price movement expectations and potential strategies for trading such occurrences. █ CALCULATIONS Input Parameters: This script offers users the choice to analyze "Opening Gaps" or "Extreme Closes" for price movements of different predefined magnitudes in a specified direction ("Upward" or "Downward"). Outputs: Based on the specified inputs, the script performs the following calculations for the active ticker displayed on the chart: Frequency of Extreme Price Movements : Quantifies the occurrences of directional price movements within predefined percentage ranges. Average Pullbacks : Computes the average retracement (pullback) from analyzed price movements within each percentage range. Average Closes : Analyzes the typical closing behavior relative to the directional price movements within each range. The script organizes the results from these calculations within the table on a separate chart pane, providing users with helpful insights into how a stock historically behaved following significant price movements.
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TASC 2024.06 REIT ETF Trading System█ OVERVIEW This strategy script demonstrates the application of the Real Estate Investment Trust (REIT) ETF trading system presented in the article by Markos Katsanos titled "Is The Price REIT?" from TASC's June 2024 edition of Traders' Tips . █ CONCEPTS REIT stocks and ETFs offer a simplified, diversified approach to real estate investment. They exhibit sensitivity to interest rates, often moving inversely to interest rate and treasury yield changes. Markos Katsanos explores this relationship and the correlation of prices with the broader market to develop a trading strategy for REIT ETFs. The script employs Bollinger Bands and Donchian channel indicators to identify oversold conditions and trends in REIT ETFs. It incorporates the 10-year treasury yield index (TNX) as a proxy for interest rates and the S&P 500 ETF (SPY) as a benchmark for the overall market. The system filters trade entries based on their behavior and correlation with the REIT ETF price.  █ CALCULATIONS The strategy initiates long entries (buy signals) under two conditions: 1. Oversold condition The weekly ETF low price dips below the 15-week Bollinger Band bottom, the closing price is above the value by at least 0.2 * ATR ( Average True Range ), and the price exceeds the week's median. Either of the following: – The TNX index is down over 15% from its 25-week high, and its correlation with the ETF price is less than 0.3. – The yield is below 2%. 2. Uptrend The weekly ETF price crosses above the previous week's 30-week Donchian channel high. The SPY ETF is above its 20-week moving average. Either of the following: – Over ten weeks have passed since the TNX index was at its 30-week high. – The correlation between the TNX value and the ETF price exceeds 0.3. – The yield is below 2%. The strategy also includes three exit (sell) rules: 1. Trailing (Chandelier) stop The weekly close drops below the highest close over the last five weeks by over 1.5 * ATR. The TNX value rises over the latest 25 weeks, with a yield exceeding 4%, or its value surges over 15% above the 25-week low.  2. Stop-loss The ETF's price declines by at least 8% of the previous week's close and falls below the 30-week moving average.  The SPY price is down by at least 8%, or its correlation with the ETF's price is negative.  3. Overbought condition The ETF's value rises above the 100-week low by over 50%.  The ETF's price falls over 1.5 * ATR below the 3-week high. The ETF's 10-week Stochastic indicator exceeds 90 within the last three weeks.  █ DISCLAIMER This strategy script educates users on the system outlined by the TASC article. However, note that its default properties might not fully represent real-world trading conditions for an individual. By default, it uses 10% of equity as the order size and a slippage amount of 5 ticks. Traders should adjust these settings and the commission amount when using this script. Additionally, since this strategy utilizes compound conditions on weekly data to trigger orders, it will generate significantly fewer trades than other, higher-frequency strategies.
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TASC 2024.04 The Ultimate Smoother█ OVERVIEW This script presents an implementation of the digital smoothing filter introduced by John Ehlers in his article "The Ultimate Smoother" from the April 2024 edition of TASC's Traders' Tips . █ CONCEPTS The UltimateSmoother preserves low-frequency swings in the input time series while attenuating high-frequency variations and noise. The defining input parameter of the UltimateSmoother is the critical period , which represents the minimum wavelength (highest frequency) in the filter's pass band. In other words, the filter attenuates or removes the amplitudes of oscillations at shorter periods than the critical period. According to Ehlers, one primary advantage of the UltimateSmoother is that it maintains zero lag in its pass band and minimal lag in its transition band, distinguishing it from other conventional digital filters (e.g., moving averages ). One can apply this smoother to various input data series, including other indicators. █ CALCULATIONS Ehlers derived the UltimateSmoother using inspiration from the design principles he learned from his experience with analog filters , as described in the original publication. On a technical level, the UltimateSmoother's unique response involves subtracting a high-pass response from an all-pass response . At very low frequencies (lengthy periods), where the high-pass filter response has virtually no amplitude, the subtraction yields a frequency and phase response practically equivalent to the input data. At other frequencies, the subtraction achieves filtration through cancellation due to the close similarities in response between the high-pass filter and the input data.
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TASC 2024.03 Rate of Directional Change█ OVERVIEW This script implements the Rate of Directional Change (RODC) indicator introduced by Richard Poster in the "Taming The Effects Of Whipsaw" article featured in the March 2024 edition of TASC's Traders' Tips . █ CONCEPTS In his article, Richard Poster discusses an approach to potentially reduce false trend-following strategy entry signals due to whipsaws in forex data. The RODC indicator is central to this approach. The idea behind RODC is that one can characterize market whipsaw as alternating up and down ZigZag segments. By counting the number of up and down segments within a lookback window, the RODC indicator aims to identify if the window contains a significant whipsaw pattern: RODC = 100 * Segments / Window Size (bars) Larger RODC values suggest elevated whipsaw in the calculation window, while smaller values signify trending price activity. █ CALCULATIONS • For each price bar, the script iterates through the lookback window to identify up and down segments. • If the price change between subsequent bars within the window is in the direction opposite to the current segment and exceeds the specified threshold , the calculation interprets the condition as a reversal point and the start of a new segment. • The script uses the number of segments within the window to calculate RODC according to the above formula. • Finally, the script applies a simple moving average to smoothen the RODC data. Users can change the length of the lookback window , the threshold value, and the smoothing length in the "Inputs" tab of the script's settings.
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TASC 2024.02 Price-Time Filtering█ OVERVIEW This script implements a price-time trend filter proposed by Alfred François Tagher in the “Trend Identification By Price And Time Filtering” article from the February 2024 edition of TASC's Traders' Tips . █ CONCEPTS In his article, Alfred François Tagher proposed a rule set designed to minimize the impact of stochastic price movements, facilitating the identification of larger-scale trends. The rules are: • If the most recent week's close exceeds the previous week's high, the trend is up. • If the most recent week's close is below the previous week's low, the trend is down. • The trend remains unchanged until one of the above conditions occurs. Similar rules can also apply to monthly bars. The author argues that this approach integrates characteristics of conventional price action and time dynamics filters, so he refers to it as price-time filtering . █ CALCULATIONS This script applies the above price-time filtering rules and offers multiple ways to view the results on a chart: • In the "Oscillator" view mode, the script counts and displays the number of bars in the uptrend and downtrend. • In the "Linebreak" view mode, the trend filter is presented in a format resembling a point-and-figure (P&F) chart , with the length of each bar corresponding to the high-low range of the respective trend. • In both view modes, the script offers bar coloring of the main chart based on the identified trend.
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TASC 2024.01 Gap Momentum System█ OVERVIEW TASC's January 2024 edition of Traders' Tips features an article titled “Gap Momentum” by Perry J. Kaufman. The article discusses how a trader might create a momentum strategy based on opening gap data. This script implements the Gap Momentum system presented therein. █ CONCEPTS In the article, Perry J. Kaufman introduces Gap Momentum as a cumulative series constructed in the same way as On-Balance Volume (OBV) , but using gap openings (today’s open minus yesterday’s close). To smoothen the resulting time series (i.e., obtain the " signal line "), the author applies a simple moving average . Subsequently, he proposes the following two trading rules for a long-only trading system: • Enter a long position when the signal line is moving higher. • Exit when the signal line is moving lower. █ CALCULATIONS The calculation of Gap Momentum involves the following steps: 1. Calculate the ratio of the sum of positive gaps over the past N days to the sum of negative gaps (absolute values) over the same time period. 2. Add the resulting gap ratio to the cumulative time series. This time series is the Gap Momentum. 3. Keep moving forward, as in an N-day moving average.
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TASC 2023.12 Growth and Value Switching System█ OVERVIEW This script implements a rotation system for trading value and growth ETFs, as developed by Markos Katsanos and detailed in the article titled 'Growth Or Value?' in TASC's December 2023 edition of Traders' Tips . The purpose of this script is to demonstrate how short-term momentum can be employed to track market trends and provide clarity on when to switch between value and growth. █ CONCEPTS The central concept of the presented rotation strategy is based on the observation that the stock market undergoes cycles favoring either growth or value stocks. Consequently, the script introduces a momentum trading system that is designed to switch between value and growth equities based on prevailing market conditions. Specifically tailored for long-term index investors, the system focuses on trading Vanguard's value and growth ETFs ( VTV and VUG ) on a weekly timeframe. To identify the ETF likely to outperform, the script uses a custom relative strength indicator applied to both VTV and VUG in comparison with an index ( SPY ). To minimize risk and drawdowns during bear markets, when both value and growth experience downtrends, the script employs the author's custom volume flow indicator (VFI) and blocks trades when its reading indicates money outflow . Positions are closed if the relative strength of the current open trade ETF falls below that of the other ETF for two consecutive weeks and is also below its moving average. Additionally, the script implements a stop-loss when the ETF is trading below its 40-week moving average, but only during bear markets. The script plots the relative strengths of the value and growth equities along with the signals triggered by the aforementioned rules. Information about the current readings of the relative strength and volume flow indicators, along with the current open position, is displayed in a table. █ CALCULATIONS The script uses the request.security() function to gather price data for both equities and the reference index. Custom relative strength and volume flow indicators are calculated based on the formulas presented in the original article. By default, the script employs the same parameters for these indicators as proposed in the original article for VTV and VUG on a weekly timeframe.
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TASC 2023.11 VAcc█ OVERVIEW The November 2023 edition of TASC's Traders' Tips features an article titled "VAcc: A Momentum Indicator Based On Velocity And Acceleration" by Scott Cong. This script implements the author's momentum indicator based on simple physics concepts. █ CONCEPTS The indicator is named VAcc as it is derived from the average velocity (V) and acceleration (Acc) over a specified lookback period. Consequently, its readings reflect two valuable characteristics of price data: rate (indicating the speed at which the price is moving) and rate of change (indicating whether the price is speeding up or slowing down). In the article, the author reports that for longer periods, VAcc behaves similarly to the MACD , albeit with a more responsive nature. For shorter periods, VAcc exhibits characteristics reminiscent of the stochastic oscillator , but it trends more prominently and is less prone to overbought/oversold saturation. To incorporate VAcc into trading strategies, the author suggests considering the following two permutations for the velocity and acceleration data series: Strong upward condition: Velocity is rising, and acceleration is rising above zero. Strong downward condition: Velocity is falling, and acceleration is falling. In the current implementation, the chart displays the average velocity as a line, while the average acceleration is presented as a histogram. █ CALCULATIONS The calculation of VAcc involves the following steps: For the current closing price, C , and for each bar C (i) within a specified lookback period from the current bar, the script calculates velocities, V (i) = ( C - C (i))/i. These velocities are then subjected to an exponential moving average to obtain the smoothed average velocity. Similarly, for each bar within the lookback period, accelerations are calculated as Acc (i) = ( V - V (i))/i and then averaged without smoothing.
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TASC 2023.10 COT Commercials Indicator█ OVERVIEW This script implements the COT Commercials Indicator introduced by Alfred François Tagher in an article featured in TASC's October 2023 edition of Traders' Tips . The indicator is designed for use in futures markets and represents a fast stochastic (%K) calculated based on the commercial open interest values of an asset derived from the weekly Commitments Of Traders (COT) report . █ CONCEPTS The COT report, issued by the Commodity ​Futures Trading Commission (CFTC) , presents a breakdown of reportable open interest positions held by various trader groups—commercial, noncommercial, and nonreportable (small traders). Open interest reflects the total number of derivative contracts entered by market participants but not yet settled. Consequently, it can serve as a measure of market activity and liquidity. The indicator showcased here aims to analyze changes in the reported net values of open interest for commercial traders/hedgers (often referred to as 'smart money', as they deal directly in underlying commodities). The net values are positive when the commercial traders have more long positions than short ones and negative when they hold more short positions than long ones. Positive net values indicate that commercial traders hold more long positions than short ones, while negative values indicate the opposite. Thus, overbought and oversold conditions of the COT Commercials Indicator potentially suggest collective bullish and bearish sentiments, respectively. █ CALCULATIONS The calculations involve these steps: 1. Net open interest values are extracted from COT data using the LibraryCOT library provided by TradingView. 2. A fast stochastic indicator (%K) is then applied to normalize these net values. The script also provides an option of calculating and plotting the indicator curve for noncommercial (speculators) open interest.
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TASC 2023.09 The Weekly Factor█ OVERVIEW TASC's September 2023 edition of Traders' Tips features an article written by Andrea Unger titled “The Weekly Factor", discussing the application of price patterns as filters for trade entries. This script implements a sample trading strategy presented in the article for demonstration purposes only. It explores how the strategy's equity curve might benefit from filtering trade entries using a specific price pattern. █ CONCEPTS Pattern filters represent valuable tools that assess current market conditions based on price movements and determine when those conditions become more favorable for trade entries. The filter used and tested in this article is a metric called the "weekly factor", which measures the price range over the last five trading days and compares it to the open of the session five days ago and the close of the session one day ago (i.e., the "body" of the five-day period). When the five-day body is small compared to the five-day range, this could indicate "indecision" or "compression", potentially followed by a price expansion. Thus, the weekly factor metric can help identify areas in the market where a period of compression might signal a potential breakout. This script demonstrates the use of the weekly factor for a sample intraday trading strategy (intended for educational and exploratory purposes only). In this strategy, the entry signal is triggered when a 15-minute bar breaks out of the previous day's high-low range, and the position is closed at the end of the day. █ CALCULATIONS The script uses two timeframes: • The strategy entries are processed on the 15-minute timeframe. • The weekly factor is obtained from the daily timeframe using the request.security function and the following formula: math.abs(open - close ) < RangeFilter * (ta.highest(5) - ta.lowest(5) ) Here, RangeFilter is an input that can be optimized to find the favorable ratio between the five-day body and the five-day range. Smaller RangeFilter values will lead to fewer trade entries. A RangeFilter value of 1 is equivalent to turning off the filtering altogether.
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TASC 2023.08 Channeling Your Inner Chartist█ OVERVIEW TASC's August 2023 edition of Traders' Tips features an article written by Stella Osoba titled “Using Price Channels.” The article offers a basic look at using price channels, with a primary focus on ​ Donchian channels . Following the article, the script provides an example of how to calculate and utilize the Donchian channel to gain insights into the price behavior and potential trend movements. █ CONCEPTS The use of price channels is a long-standing and fundamental charting technique commonly associated with trend-following trading strategies. Price channels help identify the trend on the chart and facilitate trading in its direction. The ​Donchian channel, in particular, consists of three lines. The upper line is conventionally calculated as the highest high over a specified lookback period, while the lower line is defined as the lowest low over the same period. The central line represents the midpoint between the upper and lower lines. The ​Donchian channel provides a simple and intuitive visual representation of price behavior. Breaking through the lower line, for instance, can indicate weakness and selling pressure, while breaking through the upper line can signal buying pressure. By observing these breakout points, one can gain insight into potential beginnings or endings of long-term trends. However, it is important to note that breakouts often lead to price reversals, so they should be carefully evaluated █ CALCULATIONS To illustrate a simple ​Donchian trading system, this script calculates and plots the channel lines, as well as potential entry points for long positions (green triangles) and short positions (red triangles).
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