Efficient — Indicators and Strategies

Efficient Work [LucF]█ OVERVIEW Efficient Work measures the ratio of price movement from close to close ( resulting work ) over the distance traveled to the high and low before settling down at the close ( total work ). The closer the two values are, the more Efficient Work approaches its maximum value of +1 for an up move or -1 for a down move. When price does not change, Efficient Work is zero. Higher values of Efficient Work indicate more efficient price travel between the close of two successive bars, which I interpret to be more significant, regardless of the move's amplitude. Because it measures the direction and strength of price changes rather than their amplitude, Efficient Work may be thought of as a sentiment indicator. █ CONCEPTS This oscillator's design stems from a few key concepts. Relative Levels Other than the centerline, relative rather than absolute levels are used to identify levels of interest. Accordingly, no fixed levels correspond to overbought/oversold conditions. Relative levels of interest are identified using: • A Donchian channel (historical highs/lows). • The oscillator's position relative to higher timeframe values. • Oscillator levels following points in time where a divergence is identified. Higher timeframes Two progressively higher timeframes are used to calculate larger-context values for the oscillator. The rationale underlying the use of timeframes higher than the chart's is that, while they change less frequently than the values calculated at the chart's resolution, they are more meaningful because more work (trader activity) is required to calculate them. Combining the immediacy of values calculated at the chart's resolution to higher timeframe values achieves a compromise between responsiveness and reliability. Divergences as points of interest rather than directional clues A very simple interpretation of what constitutes a divergence is used. A divergence is defined as a discrepancy between any bar's direction and the direction of the signal line on that same bar. No attempt is made to attribute a directional bias to divergences when they occur. Instead, the oscillator's level is saved and subsequent movement of the oscillator relative to the saved level is what determines the bullish/bearish state of the oscillator. Conservative coloring scheme Several additive coloring conditions allow the bull/bear coloring of the oscillator's main line to be restricted to specific areas meeting all the selected conditions. The concept is built on the premise that most of the time, an oscillator's value should be viewed as mere noise, and that somewhat like price, it only occasionally conveys actionable information. █ FEATURES Plots • Three lines can be plotted. They are named Main line , Line 2 and Line 3 . You decide which calculation to use for each line: • The oscillator's value at the chart's resolution. • The oscillator's value at a medium timeframe higher than the chart's resolution. • The oscillator's value at the highest timeframe. • An aggregate line calculated using a weighed average of the three previous lines (see the Aggregate Weights section of Inputs to configure the weights). • The coloring conditions, divergence levels and the Hi/Lo channel always apply to the Main line, whichever calculation you decide to use for it. • The color of lines 2 and 3 are fixed but can be set in the "Colors" section of Inputs. • You can change the thickness of each line. • When the aggregate line is displayed, higher timeframe values are only used in its calculation when they become available in the chart's history, otherwise the aggregate line would appear much later on the chart. To indicate when each higher timeframe value becomes available, a small label appears near the centerline. • Divergences can be shown as small dots on the centerline. • Divergence levels can be shown. The level and fill are determined by the oscillator's position relative to the last saved divergence level. • Bull/bear markers can be displayed. They occur whenever a new bull/bear state is determined by the "Main Line Coloring Conditions". • The Hi/Lo (Donchian) channel can be displayed, and its period defined. • The background can display the state of any one of 11 different conditions. • The resolutions used for the higher timeframes can be displayed to the right of the last bar's value. • Four key values are always displayed in the Data Window (fourth icon down to the right of your chart): oscillator values for the chart, medium and highest timeframes, and the oscillator's instant value before it is averaged. Main Line Coloring Conditions • Nine different conditions can be selected to determine the bull/bear coloring of the main line. All conditions set to "ON" must be met to determine the bull/bear state. • A volatility state can also be used to filter the conditions. • When the coloring conditions and the filter do not allow for a bull/bear state to be determined, the neutral color is used. Signal • Seven different averages can be used to calculate the average of the oscillator's value. • The average's period can be set. A period of one will show the instant value of the oscillator, provided you don't use linear regression or the Hull MA as they do not work with a period of one. • An external signal can be used as the oscillator's instant value. If an already averaged external value is used, set the period to one in this indicator. • For the cases where an external signal is used, a centerline value can be set. Higher Timeframes • The two higher timeframes are named Medium timeframe and Highest timeframe . They can be determined using one of three methods: • Auto-steps: the higher timeframes are determined using the chart's resolution. If the chart uses a seconds resolution, for example, the medium and highest resolutions will be 15 and 60 minutes. • Multiples: the timeframes are calculated using a multiple of the chart's resolution, which you can set. • Fixed: the set timeframes do not change with the chart's resolution. Repainting • Repainting can be controlled separately for the chart's value and the higher timeframe values. • The default is a repainting chart value and non-repainting higher timeframe values. The Aggregate line will thus repaint by default, as it uses the chart's value along with the higher timeframes values. Aggregate Weights • The weight of each component of the Aggregate line can be set. • The default is equal weights for the three components, meaning that the chart's value accounts for one third of the weight in the Aggregate. High Volatility • This provides control over the volatility filter used in the Main line's coloring conditions and the background display. • Volatility is determined to be high when the short-term ATR is greater than the long-term ATR. Colors • You can define your own colors for all of the oscillator's plots. • The default colors will perform well on both white and black chart backgrounds. Alerts • An alert can be defined for the script. The alert will trigger whenever a bull/bear marker appears in the indicator's display. The particular combination of coloring conditions and the display of bull/bear markers when you create the alert will thus determine when the alert triggers. Once the alerts are created, subsequent changes to the conditions controlling the display of markers will not affect the existing alert(s). • You can create multiple alerts from this script, each triggering on different conditions. Backtesting & Trading Engine Signal Line • An invisible plot named "BTE Signal" is provided. It can be used as an entry signal when connected to the PineCoders Backtesting & Trading Engine as an external input. It will generate an entry whenever a marker is displayed. █ NOTES • I do not know for sure if the calculations in Efficient Work are original. I apologize if they are not. • Because this version of Efficient Work only has access to OHLC information, it cannot measure the total distance traveled through all of a bar's ticks, but the indicator nonetheless behaves in a manner consistent with the intentions underlying its design. For Pine coders This code was written using the following standards: • The PineCoders Coding Conventions for Pine . • A modified version of the PineCoders MTF Oscillator Framework and MTF Selection Framework .

WMA/LSMA - Simplified Calculations Lots of moving averages are based on a weighted sum, the most common ones being the simple (arithmetic) and linearly weighted moving average. The problems with the weighted sum approach is that when your moving average is a FIR filter then the number of operations increase with higher values of length, and when the weights are based on a complex calculation this number of operations can increase drastically! For the common technical analyst the calculation time of moving averages can be an insignificant factor, even more when using higher time frames, however its always a good practice to seek better performances. The SMA has already a calculation where the number of operations is independent of its length, as such it can be easy to do the same for the linearly weighted moving average (WMA). This post will describe the process toward calculating a simple and efficient WMA which will then be used to provide an efficient calculation of the least squares moving average (LSMA). Carving Impulses Responses Remember that impulses responses fully describe the properties of moving averages, the impulse response of the WMA is a linearly decreasing function, so we'll try to calculate it without using a weighted sum. We first need to use a cumulative sum, the cumulative sum can be described as a summation from the first element of a series to the n th element of the series, where n is the current bar number, one could say that this operation is actually super inefficient, however this is not the case, as a cumulative sum can be calculated recursively as follows: y = y + x The cumulative sum can be described as an amplifier and posses the following impulse response: Once the cumulative sum receive the impulse signal as input the result will always be equal to 1. This will form the basis of our simplified calculation, all we need to do transform this response into a linearly decreasing one. The full process is as follows: Get the impulse response of the cumulative sum Subtract this response from a linearly increasing impulse response of size length Normalize the result such that the sum of the resulting response is equal to 1 We need a linearly increasing response of size length , this can be done by using a running sum of the original cumulative sum response, however we must make sure that the value of this response is 0 when the one of the cumulative sum is first equal to 1. Because the resulting response as a maximum value of length we need to multiply our cumulative sum response with length , then we proceed to subtraction. Finally we need to normalize the result, the sum of a linear sequence of values starting at 1 and ending at n is given by the explicit formula : n(n+1)/2 , which in our case give length*(length+1)/2 , we divide our previous response with this result and we end up with the impulse response of a WMA. This process can be graphically described as follows: We can then replace the impulse function by the closing price in order to get the WMA of the closing price. Advantages And Disadvantages The big advantage of this calculation is its efficiency, in its non functional form (you can see it in the code) the calculation of the WMA only require 9 operations regardless of the value of length against length*2 + 4 for the weighted sum approach, as such both methods are equally efficient in terms of operations as long as the length of a standard WMA is inferior to 3, which is ridiculous, as such our approach is more appropriate. Another advantage is that Pinescript does not allow for series as length arguments in the WMA function, however here we can have a variable length for the WMA. Of course there are disadvantages to this approach, in terms of code we require more variables for the non functional form, which create a lengthier scripts. Another disadvantage is that we can be prone to rounding errors due to the cumulative sum, however they shouldn't be significants in our case. Getting The Least Squares Moving Average The LSMA is one of my favorite moving averages, and it can derived from a linear combination between the WMA and SMA described as follows : 3WMA - 2SMA. Since we proposed an alternative calculation of the WMA we can then calculate the LSMA without even using the SMA, why ? because the SMA can be calculated by computing the changes over length period of the cumulative sum of an input, this result is then divided by length . Remember that the impulse response of a cumulative sum is just a rectangular function, all we need is to truncate it such that only length values of the response are equal to 1, this is done thanks to the change function in Pine. In Summary A more efficient calculations for both the WMA and LSMA have been presented, while this on itself isn't super important you have learned what is the process toward calculating a filter without relying on a weighted sum. This calculation will soon be included in the Pinecoders script allowing series as length argument. Thank you for reading, your interest is always appreciated !

Ultimate Momentum Indicator This is an indicator I've been playing with for a while, based on my previous MACD w/ RSI Warning indicator. This one takes it a step further, including information from MACD, RSI, ADX, and Parabolic SAR. These four indicators are represented in this indicator as follows: MACD: The histogram itself is a normal MACD histogram. Nothing strange about it, and you can adjust the settings for it just as you would a normal MACD. RSI: Any time the RSI is outside of normal ranges (which can be adjusted in the settings), the bar on the histogram will turn amber to warn you. The actual RSI value is also shown in a label to the left side of the indicator. ADX: Crosses are drawn along the 0 line to indicate ADX. Blue means the ADX is below the trending level (adjustable in the settings), and orange means it is above that level. Darker colors indicate the ADX has gone up since the previous bar, while lighter colors indicate it has gone down. The actual ADX value is also shown in the label to the left side of the indicator. Parabolic SAR: At the outside point of each bar in the histogram, a colored dot is drawn. If the dot is green, the Parabolic SAR (settings adjustable) is currently below the closing price. If the dot is red, the SAR is above the closing price. I must stress that this indicator is not a replacement for any one of the indicators it includes, as it's really only pulling small bits of information from each. The point of this indicator is to give a cohesive picture of momentum at a quick glance. I encourage you to continue to use the normal versions of whichever of the basic indicators you already use, especially if those indicators are a key part of your strategy. This indicator is designed purely as a way to get a bird's eye view of the momentum. Pretty much every normally adjustable value can be adjusted in the settings for each of the base indicators. You can also set: The RSI warning levels (30 and 70 by default) The ADX Crossover, i.e. the point at which you consider the ADX value to indicate a strong trend (25 by default) The offset for the label which shows the actual RSI & ADX values (109 by default, which happens to line up with my chart layout--yours will almost certainly need to be different to look clean) All of the colors, naturally As always, I am open to suggestions on how I might make the indicator look cleaner, or even other indicators I might try to include in the data this indicator produces. My choice of indicators to base this one from is entirely based on the ones I use and know, but I'm sure there are other great indicators that may improve this combination indicator even more!

Extended Recursive Bands - Maximum Efficiency With Extra Options Introducing A New Calculation For Efficient Bands Calculation ! Here it is ! The Recursive Bands Indicator, an indicator specially created to be extremely efficient, i think you already know that calculation time is extra important in algorithmic trading, and this is the principal motivation for the creation of the proposed indicator. Originally described in my paper "Pierrefeu, Alex (2019): Recursive Bands - A New Indicator For Technical Analysis" , the indicator framework has been widely used in my previous uploaded indicators, however it would have been a shame to not upload it, however user experience being a major concern for me, i decided to add extra options, which explain the term "extended". On The Indicator Calculation You can skip this part if it doesn't interest you. The calculation of the indicator is based on recursion, but i want to explain the mathematical formula described in the paper. I've seen some users trying to remake it from the calculations, however there was always something weird, and i understand, mathematical notations are always a bit weird, even myself don't always write them correctly/understand them, however this one is relatively simple to understand. First lets explain each elements of the calculation : α = smoothing constant, or 2/(length+1) max/min = maximum and minimum function, max return the greatest input value while min return the lowest one, for example : max(4,2) = 4 while min(4,2) = 2 the "||" notation mean taking the absolute value, for example : |-1| = abs(-1) = 1 The calculation after the max/min function is called the correction factor, and is the core of the indicator. The last two variables are just here to provide an initial value for upper and lower, basically when we start our calculations we will assign the value of the closing price for upper and lower. The motivation behind using a smoothing constant in range of (0,1) was to tell the reader that the indicator is easily made adaptive, this is what i did on my adaptive trailing stop indicator by using the efficiency ratio as smoothing variable, the user can use 1/length instead of the provided calculation for alpha. If you interested on the indicator main logic, it is actually really simple, by using upper = max(price,upper) and lower = min(price,lower) we would get the maximum/minimum price value at time t , therefore upper can only be greater or equal than its precedent value, while lower can only be lower or equal than its precedent value, in order to fix that we subtract/sum upper/lower with a value, this allow the upper band to be lower than its precedent value and lower to be greater than its precedent value, this is the role of the correction factor. The Indicator The indicator display one upper and one lower band, every common usages applied to bands indicators such as support/resistance, breakout, trailing stop...etc, can also be applied to this one. length control how reactive the bands are, higher values of length will make the bands cross the price less often. In order to provide more flexibility for the user i added the option to use various methods for the calculation of the indicator, therefore the indicator can use the average true range, standard deviation, average high-low range, and one totally exclusive method specially designed for this indicator. Classic Method This option make the indicator use its classical calculation, this is the most efficient method of all. Atr Method (atr) This method use the average true range as correction factor, notice that lower values of length can still produce wide band. Standard Deviation Method (stdev) This method use a biased estimate of the standard deviation as correction factor. The method produce smoother bands that converge more slowly toward the price in comparison with the classic correction factor. Average High-Low Range Method (ahlr) This method use the average of the high-low range as correction factor, extremely similar to the average true range. Rising Falling Volatility (rfv) Method A new method created for this indicator, this correction factor use the absolute prices changes when price value is greater/lower than any length past values of the price, this allow to have more boxy shaped bands, work best with greater values of length. The bands can be in contact with this method, a possible fix in the future. Conclusion The recursive band indicator is one of my greatest indicators in my opinion (i would love to have yours), as you can see the idea behind it is extremely simple and allow for a super efficient band indicator, which was the original motivation behind it, in order to provide more fun for the users i also added more option for the correction factor, this allow the user to be creative and not get stuck with the original calculation. Like the trend step indicator family we have almost ended our series on the recursive band framework, 1 more trailing stop will be added in the future, and then we'll have more "boring" stuff until i find something cool again, it shouldn't be long ;) Thanks for reading !

G-Channels - Efficient Calculation Of Upper/Lower Extremities Introduction Channels indicators are widely used in technical analysis, they provide lot of information. In general, technical indicators giving upper/lower extremities are calculated by adding/subtracting a volatility component to a central tendency estimator. This is the case with Bollinger bands, using the rolling standard deviation as volatility estimator and the simple moving average as central tendency estimator, or the Keltner channels using the exponential moving average and the average true range. Lots and lots and lots (i can go on) of those indicators have been made, they only really need a central tendency estimator, which can be obtained from pretty much any filter, however i find interesting to focus on the efficiency of those indicators, therefore i propose a super efficient channel indicator using recursion. The average resulting from the upper/lower extremity of the indicator provide a new efficient filter similar to the average highest/lowest. The calculation - How Does It Works Efficiency is often associated to recursion, this would allow us to use past output values as input, so how does the indicator is calculated? Lets look at the upper band calculation : a := max(src,nz(a(1))) - nz(a(1) - b(1))/length src is the closing price, a is upper extremity, b is the lower one. Here we only need 3 values, the previous values of a and b and the closing price. Basically a := max(src,nz(a(1))) mean : if the closing price is greater than the precedent value of a then output the closing price, else output the precedent value of a therefore a will never be inferior to its precedent value, this is useful for getting the maximum price value in our dataset however its not useful to make an upper band, therefore we subtract this to a correction factor defined as the difference between a and b , this force the upper band to have lower values thus acting like a band without loosing its "upper" property, a similar process is done with the lower band. Of course we could only use 2 values for making the indicator, thus ending with : a := max(src,nz(a(1))) - nz(abs(close - a(1))/length In fact this implementation is the same as the one proposed in my paper "Recursive Bands - A New Indicator For Technical Analysis", its also what i used for making the indicator "Adaptive Trailing Stop", this would be more efficient but i used the difference between the upper and lower extremities for a reason. The Central tendency Estimator This is the reason why i didn't implemented a more efficient version. Basically this central tendency estimator is just the average between the upper and lower extremities, it behave like the average of the highest/lowest over length period, its central plot in the Donchian channel indicator. Below is a comparison of both with length = 100 : But why is our average so "boxy"? The extremities are not boxy, so why the average is sometimes equal to its previous value? Explain! Its super easy to understand, imagine two lines, if their absolute change is the same and they follow an opposite direction, then their average is constant. the average of the green and red line is the orange line. If both lines follow the same direction then their average will also follow this direction. When both extremities follow the same direction, the average will also do the same, when both follow an opposite direction then the average will be equal to its precedent value, this is also due to the fact that both extremities are based on the same correction factor (a-b) , else the average wouldn't act that way, now you understand why i made this choice. Conclusion I proposed an efficient implementation of a channel indicator that provide an interesting central tendency estimator. This simple implementation would allow for tons of interesting concepts, some of my indicators use a similar approach and allow for great outputs, you'll see them soon enough. I hope this indicator find its use in the community, remember to ask before using this indicator in a script you want to publish. Thanks for reading ! If you want to discuss about anime stuff send me a pm but don't do it in the commend section.