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标准差(StdDev)

STD-Filtered, N-Pole Gaussian Filter [Loxx]This is a Gaussian Filter with Standard Deviation Filtering that works for orders (poles) higher than the usual 4 poles that was originally available in Ehlers Gaussian Filter formulas. Because of that, it is a sort of generalized Gaussian filter that can calculate arbitrary (order) pole Gaussian Filter and which makes it a sort of a unique indicator. For this implementation, the practical mathematical maximum is 15 poles after which the precision of calculation is useless--the coefficients for levels above 15 poles are so high that the precision loss actually means very little. Despite this maximal precision utility, I've left the upper bound of poles open-ended so you can try poles of order 15 and above yourself. The default is set to 5 poles which is 1 pole greater than the normal maximum of 4 poles. The purpose of the standard deviation filter is to filter out noise by and by default it will filter 1 standard deviation. Adjust this number and the filter selections (price, both, GMA, none) to reduce the signal noise. What is Ehlers Gaussian filter? This filter can be used for smoothing. It rejects high frequencies (fast movements) better than an EMA and has lower lag. published by John F. Ehlers in "Rocket Science For Traders". A Gaussian filter is one whose transfer response is described by the familiar Gaussian bell-shaped curve. In the case of low-pass filters, only the upper half of the curve describes the filter. The use of gaussian filters is a move toward achieving the dual goal of reducing lag and reducing the lag of high-frequency components relative to the lag of lower-frequency components. A gaussian filter with... One Pole: f = alpha*g + (1-alpha)f Two Poles: f = alpha*2g + 2(1-alpha)f - (1-alpha)2f Three Poles: f = alpha*3g + 3(1-alpha)f - 3(1-alpha)2f + (1-alpha)3f Four Poles: f = alpha*4g + 4(1-alpha)f - 6(1-alpha)2f + 4(1-alpha)3f - (1-alpha)4f and so on... For an equivalent number of poles the lag of a Gaussian is about half the lag of a Butterworth filters: Lag = N*P / pi^2, where, N is the number of poles, and P is the critical period Special initialization of filter stages ensures proper working in scans with as few bars as possible. From Ehlers Book: "The first objective of using smoothers is to eliminate or reduce the undesired high-frequency components in the eprice data. Therefore these smoothers are called low-pass filters, and they all work by some form of averaging. Butterworth low-pass filters can do this job, but nothing comes for free. A higher degree of filtering is necessarily accompanied by a larger amount of lag. We have come to see that is a fact of life." References John F. Ehlers: "Rocket Science For Traders, Digital Signal Processing Applications", Chapter 15: "Infinite Impulse Response Filters" Included Loxx's Expanded Source Types Signals Alerts Bar coloring Related indicators STD-Filtered, Gaussian Moving Average (GMA) STD-Filtered, Gaussian-Kernel-Weighted Moving Average One-Sided Gaussian Filter w/ Channels Fisher Transform w/ Dynamic Zones R-sqrd Adapt. Fisher Transform w/ D. Zones & Divs .
Pine Script™指标
由loxx提供
49
STD-Filtered, Gaussian Moving Average (GMA) [Loxx]STD-Filtered, Gaussian Moving Average (GMA) is a 1-4 pole Ehlers Gaussian Filter with standard deviation filtering. This indicator should perform similar to Ehlers Fisher Transform. The purpose of the standard deviation filter is to filter out noise by and by default it will filter 1 standard deviation. Adjust this number and the filter selections (price, both, GMA, none) to reduce the signal noise. What is Ehlers Gaussian filter? This filter can be used for smoothing. It rejects high frequencies (fast movements) better than an EMA and has lower lag. published by John F. Ehlers in "Rocket Science For Traders". First implemented in Wealth-Lab by Dr René Koch. A Gaussian filter is one whose transfer response is described by the familiar Gaussian bell-shaped curve. In the case of low-pass filters, only the upper half of the curve describes the filter. The use of gaussian filters is a move toward achieving the dual goal of reducing lag and reducing the lag of high-frequency components relative to the lag of lower-frequency components. A gaussian filter with... one pole is equivalent to an EMA filter. two poles is equivalent to EMA(EMA()) three poles is equivalent to EMA(EMA(EMA())) and so on... For an equivalent number of poles the lag of a Gaussian is about half the lag of a Butterworth filters: Lag = N * P / (2 * ¶2), where, N is the number of poles, and P is the critical period Special initialization of filter stages ensures proper working in scans with as few bars as possible. From Ehlers Book: "The first objective of using smoothers is to eliminate or reduce the undesired high-frequency components in the eprice data. Therefore these smoothers are called low-pass filters, and they all work by some form of averaging. Butterworth low-pass filtters can do this job, but nothing comes for free. A higher degree of filtering is necessarily accompanied by a larger amount of lag. We have come to see that is a fact of life." References John F. Ehlers: "Rocket Science For Traders, Digital Signal Processing Applications", Chapter 15: "Infinite Impulse Response Filters" Included Loxx's Expanded Source Types Signals Alerts Bar coloring Related indicators STD-Filtered, Gaussian-Kernel-Weighted Moving Average One-Sided Gaussian Filter w/ Channels Fisher Transform w/ Dynamic Zones R-sqrd Adapt. Fisher Transform w/ D. Zones & Divs.
Pine Script™指标
由loxx提供
5
Improved Z-Score OverlayLast month I published an improved z-score script that goes underneath your chart, which helps to highlight overbought or oversold regimes. It is customizable, and allows changing the periods, whether smoothing capability is desired, whether to use simple or exponential moving averages, and which data source to use (open, high, low, close, ohlc4). Some individuals may find that it is most useful not only to have the z-score visible underneath their price chart, but have the sigma values clearly visible on the chart itself to determine overbought or oversold levels. Therefore, this improved z-score overlay script will place the centerline of price on the chart, and +3/+2/+1/0/-1/-2/-3 sigma. These can be disabled if some values do not want to be shown, and the colors / opacity can be changed. Additionally, you could also put this into a new pane below your chart and disable all of the +3 to -3 sigma values, and enable the "Z-Score" button. This will allow you to replicate the original Improved Z-Score Script. If anyone has questions or would like to have any improvements made, let me know :) - Jim Bosse
Pine Script™指标
由jlb05013提供
STD-Filtered, Gaussian-Kernel-Weighted Moving Average BT [Loxx]STD-Filtered, Gaussian-Kernel-Weighted Moving Average BT is the backtest for the following indicator Included: This backtest uses a special implementation of ATR and ATR smoothing called "True Range Double" which is a range calculation that accounts for volatility skew. You can set the backtest to 1-2 take profits with stop-loss Signals can't exit on the same candle as the entry, this is coded in a way for 1-candle delay post entry This should be coupled with the INDICATOR version linked above for the alerts and signals. Strategies won't paint the signal "L" or "S" until the entry actually happens, but indicators allow this, which is repainting on current candle, but this is an FYI if you want to get serious with Pinescript algorithmic botting You can restrict the backtest by dates It is advised that you understand what Heikin-Ashi candles do to strategies, the default settings for this backtest is NON Heikin-Ashi candles but you have the ability to change that in the source selection This is a mathematically heavy, heavy-lifting strategy. Make sure you do your own research so you understand what is happening here. STD-Filtered, Gaussian-Kernel-Weighted Moving Average is a moving average that weights price by using a Gaussian kernel function to calculate data points. This indicator also allows for filtering both source input price and output signal using a standard deviation filter. Purpose This purpose of this indicator is to take the concept of Kernel estimation and apply it in a way where instead of predicting past values, the weighted function predicts the current bar value at each bar to create a moving average that is suitable for trading. Normally this method is used to create an array of past estimators to model past data but this method is not useful for trading as the past values will repaint. This moving average does NOT repaint, however you much allow signals to close on the current bar before taking the signal. You can compare this to Nadaraya-Watson Estimator wherein they use Nadaraya-Watson estimator method with normalized kernel weighted function to model price. What are Kernel Functions? A kernel function is used as a weighing function to develop non-parametric regression model is discussed. In the beginning of the article, a brief discussion about properties of kernel functions and steps to build kernels around data points are presented. Kernel Function In non-parametric statistics, a kernel is a weighting function which satisfies the following properties. A kernel function must be symmetrical. Mathematically this property can be expressed as K (-u) = K (+u). The symmetric property of kernel function enables its maximum value (max(K(u)) to lie in the middle of the curve. The area under the curve of the function must be equal to one. Mathematically, this property is expressed as: integral −∞ + ∞ ∫ K(u)d(u) = 1 Value of kernel function can not be negative i.e. K(u) ≥ 0 for all −∞ < u < ∞. Kernel Estimation In this article, Gaussian kernel function is used to calculate kernels for the data points. The equation for Gaussian kernel is: K(u) = (1 / sqrt(2pi)) * e^(-0.5 *(j / bw )^2) Where xi is the observed data point. j is the value where kernel function is computed and bw is called the bandwidth. Bandwidth in kernel regression is called the smoothing parameter because it controls variance and bias in the output.
Pine Script™策略
由loxx提供
7
STD-Filtered, Gaussian-Kernel-Weighted Moving Average [Loxx]STD-Filtered, Gaussian-Kernel-Weighted Moving Average is a moving average that weights price by using a Gaussian kernel function to calculate data points. This indicator also allows for filtering both source input price and output signal using a standard deviation filter. Purpose This purpose of this indicator is to take the concept of Kernel estimation and apply it in a way where instead of predicting past values, the weighted function predicts the current bar value at each bar to create a moving average that is suitable for trading. Normally this method is used to create an array of past estimators to model past data but this method is not useful for trading as the past values will repaint. This moving average does NOT repaint, however you much allow signals to close on the current bar before taking the signal. You can compare this to Nadaraya-Watson Estimator wherein they use Nadaraya-Watson estimator method with normalized kernel weighted function to model price. What are Kernel Functions? A kernel function is used as a weighing function to develop non-parametric regression model is discussed. In the beginning of the article, a brief discussion about properties of kernel functions and steps to build kernels around data points are presented. Kernel Function In non-parametric statistics, a kernel is a weighting function which satisfies the following properties. A kernel function must be symmetrical. Mathematically this property can be expressed as K (-u) = K (+u). The symmetric property of kernel function enables its maximum value (max(K(u)) to lie in the middle of the curve. The area under the curve of the function must be equal to one. Mathematically, this property is expressed as: integral −∞ + ∞ ∫ K(u)d(u) = 1 Value of kernel function can not be negative i.e. K(u) ≥ 0 for all −∞ < u < ∞. Kernel Estimation In this article, Gaussian kernel function is used to calculate kernels for the data points. The equation for Gaussian kernel is: K(u) = (1 / sqrt(2pi)) * e^(-0.5 *(j / bw)^2) Where xi is the observed data point. j is the value where kernel function is computed and bw is called the bandwidth. Bandwidth in kernel regression is called the smoothing parameter because it controls variance and bias in the output. The effect of bandwidth value on model prediction is discussed later in this article. Included Loxx's Expanded Source types Signals Alerts Bar coloring
Pine Script™指标
由loxx提供
2
Strength Volatility Killer - The Quant ScienceStrength Volatility Killer - The Quant Science™ is based on a special version of RSI (Relative Strength Index), created with the simple average and standard deviation. DESCRIPTION The algorithm analyses the market and opens positions following three different volatility entry conditions. Each entry has a specific and personal exit condition. The user can setting trailing stop loss from user interface. USER INTERFACE SETTING Configures the algorithm from the user interface. AUTO TRADING COMPLIANT With the user interface, the trader can easily set up this algorithm for automatic trading. BACKTESTING INCLUDED The trader can adjust the backtesting period of the strategy before putting it live. Analyze large periods such as years or months or focus on short-term periods. NO LIMIT TIMEFRAME This algorithm can be used on all timeframes. GENERAL FEATURES Multi-strategy:  the algorithm can apply long strategy or short strategy. Built-in alerts:  the algorithm contains alerts that can be customized from the user interface. Integrated indicator: indicator is included. Backtesting included:  quickly automatic backtesting of the strategy. Auto-trading compliant:  functions for auto trading are included. ABOUT BACKTESTING Backtesting refers to the period 13 June 2022 - today, ticker: AVAX/USDT, timeframe 5 minutes. Initial capital: $1000.00 Commission per trade: 0.03%
Pine Script™策略
由thequantscience提供
BTMM|TDIThis is the trader's dynamic index inspired by Steve Mauro's BTMM strategy. In addition to the RSI, Trendline, Baseline, Volatility Bands I have also included additional trend biases that are painted in the background to provide more confluence when the markets break out in either direction. For convenience, a position size calculator is included for all users to quickly calculate lot sizes on forex pairs with difference account balance currencies. The calculator works accurately on forex pairs. DO NOT USE for crypto or indices as some brokers have unique contract sizes that could not be fully incorporated into the tool. There is also data table that displays historical values of the RSI, Trendline, Baseline, and an EMA vs Price scoring procedure that covers the current candle (t0) and up to 3 candles back. The table is meant to provide a snapshot view of either bullish or bearish dominance that can be deciphered with a quick glance.
Pine Script™指标
由The_Trading_Jedi提供
11
Dap's Oscillator- Short Term Momentum and Trend. BINANCE:BTCUSDT BYBIT:BTCUSDT BYBIT:ETHUSDT BINANCE:ETHUSDT DAP's OSCILLATOR: WHAT IS IT? This Oscillator was created to inspire confidence in the short-term trend of traders. This will work very well with a volatility metric (I recommend BBWP by @The_Caretaker) WHAT IS IT MADE OF? 1. Consists of a series of equations (mainly the difference between simple to exponential moving averages) and Standard deviations of these moving average differences (length equivalent to the length of sampled ma's) 2. These equations are then boiled down through an averaging process array, after averaging the covariants are equated against the variants of the positive side of the array. This is what is presented as the aqua line. 3. The RC average (yellow) is the sma following the DAP'S Oscillator at a specified length 4. The most important part of this indicator is simply the momentum oscillator represented as a green or red line based on the value relative to the Oscillators. HOW DO I USE THIS? As I mentioned before mixed with a volatility metric, it should set you up for a good decision based on short-term trends. I would say to be careful for periods of consolidation, with the consolidation the momentum often meets hands with DAP's Oscillator and can cause fake-outs. You want to spot divergences from the price to the momentum difference, as well as room to work down or upward to secure a good entry on a position. CHEAT CODE'S NOTES: I appreciate everyone who has boosted my previous scripts, it means a lot. If you want to translate words to pine script onto a chart, feel free to PM me. I would be happy to help bring an indicator to life. I may take a quick break but will be back shortly to help create more cheat codes for yall. Thanks! -Cheat Code
Pine Script™指标
由CheatCode1提供
4
STD-Stepped Fast Cosine Transform Moving Average [Loxx]STD-Stepped Fast Cosine Transform Moving Average is an experimental moving average that uses Fast Cosine Transform to calculate a moving average. This indicator has standard deviation stepping in order to smooth the trend by weeding out low volatility movements. What is the Discrete Cosine Transform? A discrete cosine transform (DCT) expresses a finite sequence of data points in terms of a sum of cosine functions oscillating at different frequencies. The DCT, first proposed by Nasir Ahmed in 1972, is a widely used transformation technique in signal processing and data compression. It is used in most digital media, including digital images (such as JPEG and HEIF, where small high-frequency components can be discarded), digital video (such as MPEG and H.26x), digital audio (such as Dolby Digital, MP3 and AAC), digital television (such as SDTV, HDTV and VOD), digital radio (such as AAC+ and DAB+), and speech coding (such as AAC-LD, Siren and Opus). DCTs are also important to numerous other applications in science and engineering, such as digital signal processing, telecommunication devices, reducing network bandwidth usage, and spectral methods for the numerical solution of partial differential equations. The use of cosine rather than sine functions is critical for compression, since it turns out (as described below) that fewer cosine functions are needed to approximate a typical signal, whereas for differential equations the cosines express a particular choice of boundary conditions. In particular, a DCT is a Fourier-related transform similar to the discrete Fourier transform (DFT), but using only real numbers. The DCTs are generally related to Fourier Series coefficients of a periodically and symmetrically extended sequence whereas DFTs are related to Fourier Series coefficients of only periodically extended sequences. DCTs are equivalent to DFTs of roughly twice the length, operating on real data with even symmetry (since the Fourier transform of a real and even function is real and even), whereas in some variants the input and/or output data are shifted by half a sample. There are eight standard DCT variants, of which four are common. The most common variant of discrete cosine transform is the type-II DCT, which is often called simply "the DCT". This was the original DCT as first proposed by Ahmed. Its inverse, the type-III DCT, is correspondingly often called simply "the inverse DCT" or "the IDCT". Two related transforms are the discrete sine transform (DST), which is equivalent to a DFT of real and odd functions, and the modified discrete cosine transform (MDCT), which is based on a DCT of overlapping data. Multidimensional DCTs (MD DCTs) are developed to extend the concept of DCT to MD signals. There are several algorithms to compute MD DCT. A variety of fast algorithms have been developed to reduce the computational complexity of implementing DCT. One of these is the integer DCT (IntDCT), an integer approximation of the standard DCT, : ix, xiii, 1, 141–304  used in several ISO/IEC and ITU-T international standards. Notable settings windowper = period for calculation, restricted to powers of 2: "16", "32", "64", "128", "256", "512", "1024", "2048", this reason for this is FFT is an algorithm that computes DFT (Discrete Fourier Transform) in a fast way, generally in 𝑂(𝑁⋅log2(𝑁)) instead of 𝑂(𝑁2). To achieve this the input matrix has to be a power of 2 but many FFT algorithm can handle any size of input since the matrix can be zero-padded. For our purposes here, we stick to powers of 2 to keep this fast and neat. read more about this here: Cooley–Tukey FFT algorithm smthper = smoothing count, this smoothing happens after the first FCT regular pass. this zeros out frequencies from the previously calculated values above SS count. the lower this number, the smoother the output, it works opposite from other smoothing periods Included Alerts Signals Loxx's Expanded Source Types Additional reading A Fast Computational Algorithm for the Discrete Cosine Transform by Chen et al. Practical Fast 1-D DCT Algorithms With 11 Multiplications by Loeffler et al. Cooley–Tukey FFT algorithm
Pine Script™指标
由loxx提供
9
[KRONOS] DeviationsDescription This indicator calculates the differences between the current price and the local support or resistance, and normalizes it into a range. The value basis is calculated from a defined period of time that is then multiplied to get a standard deviations and a max. and min. value subtracted and divided into a final value. It includes Extreme zones. This value appears as blue and red lines which deviates from the oversold to overbought range. Momentum. Lower time frame momentum is represented by a gray histogram as well as a signal line oscillating from a red to blue color. Strong reversal. Red ( bearish ) and blue ( bullish ) columns will appear on the histogram when our algorithm detects that the strength of momentum is coming to an end indicative of a trend reversal. Trend confirmation. Red or blue arrows will act as a trend confirmation. Support and resistance . The zero line will frequently serve as a S/R area. Divergences. You can use this indicator to detect potential pivot areas. How to use? Sell/Short when the histogram shows a red column and the signal line is in or above the overbought area (colored in red). Buy/Long when the histogram shows a blue column and the signal line is in or below the oversold area (colored in blue). extra tip: if you entered a trade based on the above conditions, you can partially increase your position each time you see a confirmation arrow.
Pine Script™指标
由kronos-algo提供
EMA-Deviation-Corrected Super Smoother [Loxx]This indicator is using the modified "correcting" method. Instead of using standard deviation for calculation, it is using EMA deviation and is applied to Ehlers' Super Smoother. What is EMA-Deviation? By definition, the Standard Deviation (SD, also represented by the Greek letter sigma σ or the Latin letter s) is a measure that is used to quantify the amount of variation or dispersion of a set of data values. In technical analysis we usually use it to measure the level of current volatility. Standard Deviation is based on Simple Moving Average calculation for mean value. This version is not doing that. It is, instead, using the properties of EMA to calculate what can be called a new type of deviation, and since it is based on EMA. It is similar to Standard Deviation, but on a first glance you shall notice that it is "faster" than the Standard Deviation and that makes it useful when the speed of reaction to volatility is expected from any code or trading system. What is Ehlers Super Smoother? The Super Smoother filter uses John Ehlers’s “Super Smoother” which consists of a a Two-pole Butterworth filter combined with a 2-bar SMA (Simple Moving Average) that suppresses the 22050 Hz Nyquist frequency: A characteristic of a sampler, which converts a continuous function or signal into a discrete sequence. Things to know The yellow and fuchsia thin line is the original Super Smoother The green and red line is the Corrected Super Smoother When the original Super Smoother crosses above the Corrected Super Smoother line, its a long, when it crosses below, its a short Included Alerts Signals Bar coloring
Pine Script™指标
由loxx提供
6
Corrected JMA [Loxx]This indicator uses the Juirk Moving Average to calculate price deviations from the JMA and if the changes are not significant, then the value is "flattened". That way we can easily see both trends and potential chop zones. This uses the regular JMA as a trigger. What is Jurik Volty used in the Juirk Filter? One of the lesser known qualities of Juirk smoothing is that the Jurik smoothing process is adaptive. "Jurik Volty" (a sort of market volatility ) is what makes Jurik smoothing adaptive. The Jurik Volty calculation can be used as both a standalone indicator and to smooth other indicators that you wish to make adaptive. What is the Jurik Moving Average? Have you noticed how moving averages add some lag (delay) to your signals? ... especially when price gaps up or down in a big move, and you are waiting for your moving average to catch up? Wait no more! JMA eliminates this problem forever and gives you the best of both worlds: low lag and smooth lines. Included: Bar coloring
Pine Script™指标
由loxx提供
1
The Trading CurrentAlthough we cannot take credit for inventing the bell curve, our trading indicator called, The Trading Current has some very novel & one of a kind features. The Current is inspired from standard deviation channels and the investment premise that statistical outliers occur, but are not sustainable movements. We have created a unique indicator to assist you in taking advantage of those outlier moves. The most unique proprietary feature of The Current is its alert functionality. On as many time frames as you want, The Current will notify you of standard deviation line crosses. Even more impressive is the alert functionalities ability to take into consideration Pearsons Coefficient. For example... Lets say that you as a trader ONLY like to short a strong down trend or long a strong uptrend; you dont trade horizontal range type of price action. You can set a custom multi-time-frame alert on The Current such as... "Alert me when price crosses above +2 Standard Deviations away from the mean, but only if Pearsons Coefficient is greater than 85% in a downtrend. This type of alert can be set on multiple time frames all at once and you dont even need to keep the channels overlayed on your chart. This type of alert functionality is ideal for all traders. Pick and choose your spots and live your life without having to stare at the screen until price crosses the line that you're watching. We hope you enjoy!
Pine Script™指标
由max7882提供
5
STD-Filterd, R-squared Adaptive T3 w/ Dynamic Zones BT [Loxx]STD-Filterd, R-squared Adaptive T3 w/ Dynamic Zones BT is the backtest strategy for "STD-Filterd, R-squared Adaptive T3 w/ Dynamic Zones " seen below: Included: This backtest uses a special implementation of ATR and ATR smoothing called "True Range Double" which is a range calculation that accounts for volatility skew. You can set the backtest to 1-2 take profits with stop-loss Signals can't exit on the same candle as the entry, this is coded in a way for 1-candle delay post entry This should be coupled with the INDICATOR version linked above for the alerts and signals. Strategies won't paint the signal "L" or "S" until the entry actually happens, but indicators allow this, which is repainting on current candle, but this is an FYI if you want to get serious with Pinescript algorithmic botting You can restrict the backtest by dates It is advised that you understand what Heikin-Ashi candles do to strategies, the default settings for this backtest is NON Heikin-Ashi candles but you have the ability to change that in the source selection This is a mathematically heavy, heavy-lifting strategy with multi-layered adaptivity. Make sure you do your own research so you understand what is happening here. This can be used as its own trading system without any other oscillators, moving average baselines, or volatility/momentum confirmation indicators. What is the T3 moving average? Better Moving Averages Tim Tillson November 1, 1998 Tim Tillson is a software project manager at Hewlett-Packard, with degrees in Mathematics and Computer Science. He has privately traded options and equities for 15 years. Introduction "Digital filtering includes the process of smoothing, predicting, differentiating, integrating, separation of signals, and removal of noise from a signal. Thus many people who do such things are actually using digital filters without realizing that they are; being unacquainted with the theory, they neither understand what they have done nor the possibilities of what they might have done." This quote from R. W. Hamming applies to the vast majority of indicators in technical analysis . Moving averages, be they simple, weighted, or exponential, are lowpass filters; low frequency components in the signal pass through with little attenuation, while high frequencies are severely reduced. "Oscillator" type indicators (such as MACD , Momentum, Relative Strength Index ) are another type of digital filter called a differentiator. Tushar Chande has observed that many popular oscillators are highly correlated, which is sensible because they are trying to measure the rate of change of the underlying time series, i.e., are trying to be the first and second derivatives we all learned about in Calculus. We use moving averages (lowpass filters) in technical analysis to remove the random noise from a time series, to discern the underlying trend or to determine prices at which we will take action. A perfect moving average would have two attributes: It would be smooth, not sensitive to random noise in the underlying time series. Another way of saying this is that its derivative would not spuriously alternate between positive and negative values. It would not lag behind the time series it is computed from. Lag, of course, produces late buy or sell signals that kill profits. The only way one can compute a perfect moving average is to have knowledge of the future, and if we had that, we would buy one lottery ticket a week rather than trade! Having said this, we can still improve on the conventional simple, weighted, or exponential moving averages. Here's how: Two Interesting Moving Averages We will examine two benchmark moving averages based on Linear Regression analysis. In both cases, a Linear Regression line of length n is fitted to price data. I call the first moving average ILRS, which stands for Integral of Linear Regression Slope. One simply integrates the slope of a linear regression line as it is successively fitted in a moving window of length n across the data, with the constant of integration being a simple moving average of the first n points. Put another way, the derivative of ILRS is the linear regression slope. Note that ILRS is not the same as a SMA ( simple moving average ) of length n, which is actually the midpoint of the linear regression line as it moves across the data. We can measure the lag of moving averages with respect to a linear trend by computing how they behave when the input is a line with unit slope. Both SMA (n) and ILRS(n) have lag of n/2, but ILRS is much smoother than SMA . Our second benchmark moving average is well known, called EPMA or End Point Moving Average. It is the endpoint of the linear regression line of length n as it is fitted across the data. EPMA hugs the data more closely than a simple or exponential moving average of the same length. The price we pay for this is that it is much noisier (less smooth) than ILRS, and it also has the annoying property that it overshoots the data when linear trends are present. However, EPMA has a lag of 0 with respect to linear input! This makes sense because a linear regression line will fit linear input perfectly, and the endpoint of the LR line will be on the input line. These two moving averages frame the tradeoffs that we are facing. On one extreme we have ILRS, which is very smooth and has considerable phase lag. EPMA has 0 phase lag, but is too noisy and overshoots. We would like to construct a better moving average which is as smooth as ILRS, but runs closer to where EPMA lies, without the overshoot. A easy way to attempt this is to split the difference, i.e. use (ILRS(n)+EPMA(n))/2. This will give us a moving average (call it IE /2) which runs in between the two, has phase lag of n/4 but still inherits considerable noise from EPMA. IE /2 is inspirational, however. Can we build something that is comparable, but smoother? Figure 1 shows ILRS, EPMA, and IE /2. Filter Techniques Any thoughtful student of filter theory (or resolute experimenter) will have noticed that you can improve the smoothness of a filter by running it through itself multiple times, at the cost of increasing phase lag. There is a complementary technique (called twicing by J.W. Tukey) which can be used to improve phase lag. If L stands for the operation of running data through a low pass filter, then twicing can be described by: L' = L(time series) + L(time series - L(time series)) That is, we add a moving average of the difference between the input and the moving average to the moving average. This is algebraically equivalent to: 2L-L(L) This is the Double Exponential Moving Average or DEMA , popularized by Patrick Mulloy in TASAC (January/February 1994). In our taxonomy, DEMA has some phase lag (although it exponentially approaches 0) and is somewhat noisy, comparable to IE /2 indicator. We will use these two techniques to construct our better moving average, after we explore the first one a little more closely. Fixing Overshoot An n-day EMA has smoothing constant alpha=2/(n+1) and a lag of (n-1)/2. Thus EMA (3) has lag 1, and EMA (11) has lag 5. Figure 2 shows that, if I am willing to incur 5 days of lag, I get a smoother moving average if I run EMA (3) through itself 5 times than if I just take EMA (11) once. This suggests that if EPMA and DEMA have 0 or low lag, why not run fast versions (eg DEMA (3)) through themselves many times to achieve a smooth result? The problem is that multiple runs though these filters increase their tendency to overshoot the data, giving an unusable result. This is because the amplitude response of DEMA and EPMA is greater than 1 at certain frequencies, giving a gain of much greater than 1 at these frequencies when run though themselves multiple times. Figure 3 shows DEMA (7) and EPMA(7) run through themselves 3 times. DEMA^3 has serious overshoot, and EPMA^3 is terrible. The solution to the overshoot problem is to recall what we are doing with twicing: DEMA (n) = EMA (n) + EMA (time series - EMA (n)) The second term is adding, in effect, a smooth version of the derivative to the EMA to achieve DEMA . The derivative term determines how hot the moving average's response to linear trends will be. We need to simply turn down the volume to achieve our basic building block: EMA (n) + EMA (time series - EMA (n))*.7; This is algebraically the same as: EMA (n)*1.7-EMA( EMA (n))*.7; I have chosen .7 as my volume factor, but the general formula (which I call "Generalized Dema") is: GD (n,v) = EMA (n)*(1+v)-EMA( EMA (n))*v, Where v ranges between 0 and 1. When v=0, GD is just an EMA , and when v=1, GD is DEMA . In between, GD is a cooler DEMA . By using a value for v less than 1 (I like .7), we cure the multiple DEMA overshoot problem, at the cost of accepting some additional phase delay. Now we can run GD through itself multiple times to define a new, smoother moving average T3 that does not overshoot the data: T3(n) = GD ( GD ( GD (n))) In filter theory parlance, T3 is a six-pole non-linear Kalman filter. Kalman filters are ones which use the error (in this case (time series - EMA (n)) to correct themselves. In Technical Analysis , these are called Adaptive Moving Averages; they track the time series more aggressively when it is making large moves. What is R-squared Adaptive? One tool available in forecasting the trendiness of the breakout is the coefficient of determination ( R-squared ), a statistical measurement. The R-squared indicates linear strength between the security's price (the Y - axis) and time (the X - axis). The R-squared is the percentage of squared error that the linear regression can eliminate if it were used as the predictor instead of the mean value. If the R-squared were 0.99, then the linear regression would eliminate 99% of the error for prediction versus predicting closing prices using a simple moving average . R-squared is used here to derive a T3 factor used to modify price before passing price through a six-pole non-linear Kalman filter. What are Dynamic Zones? As explained in "Stocks & Commodities V15:7 (306-310): Dynamic Zones by Leo Zamansky, Ph .D., and David Stendahl" Most indicators use a fixed zone for buy and sell signals. Here’ s a concept based on zones that are responsive to past levels of the indicator. One approach to active investing employs the use of oscillators to exploit tradable market trends. This investing style follows a very simple form of logic: Enter the market only when an oscillator has moved far above or below traditional trading lev- els. However, these oscillator- driven systems lack the ability to evolve with the market because they use fixed buy and sell zones. Traders typically use one set of buy and sell zones for a bull market and substantially different zones for a bear market. And therein lies the problem. Once traders begin introducing their market opinions into trading equations, by changing the zones, they negate the system’s mechanical nature. The objective is to have a system automatically define its own buy and sell zones and thereby profitably trade in any market — bull or bear. Dynamic zones offer a solution to the problem of fixed buy and sell zones for any oscillator-driven system. An indicator’s extreme levels can be quantified using statistical methods. These extreme levels are calculated for a certain period and serve as the buy and sell zones for a trading system. The repetition of this statistical process for every value of the indicator creates values that become the dynamic zones. The zones are calculated in such a way that the probability of the indicator value rising above, or falling below, the dynamic zones is equal to a given probability input set by the trader. To better understand dynamic zones, let's first describe them mathematically and then explain their use. The dynamic zones definition: Find V such that: For dynamic zone buy: P{X <= V}=P1 For dynamic zone sell: P{X >= V}=P2 where P1 and P2 are the probabilities set by the trader, X is the value of the indicator for the selected period and V represents the value of the dynamic zone. The probability input P1 and P2 can be adjusted by the trader to encompass as much or as little data as the trader would like. The smaller the probability, the fewer data values above and below the dynamic zones. This translates into a wider range between the buy and sell zones. If a 10% probability is used for P1 and P2, only those data values that make up the top 10% and bottom 10% for an indicator are used in the construction of the zones. Of the values, 80% will fall between the two extreme levels. Because dynamic zone levels are penetrated so infrequently, when this happens, traders know that the market has truly moved into overbought or oversold territory. Calculating the Dynamic Zones The algorithm for the dynamic zones is a series of steps. First, decide the value of the lookback period t. Next, decide the value of the probability Pbuy for buy zone and value of the probability Psell for the sell zone. For i=1, to the last lookback period, build the distribution f(x) of the price during the lookback period i. Then find the value Vi1 such that the probability of the price less than or equal to Vi1 during the lookback period i is equal to Pbuy. Find the value Vi2 such that the probability of the price greater or equal to Vi2 during the lookback period i is equal to Psell. The sequence of Vi1 for all periods gives the buy zone. The sequence of Vi2 for all periods gives the sell zone. In the algorithm description, we have: Build the distribution f(x) of the price during the lookback period i. The distribution here is empirical namely, how many times a given value of x appeared during the lookback period. The problem is to find such x that the probability of a price being greater or equal to x will be equal to a probability selected by the user. Probability is the area under the distribution curve. The task is to find such value of x that the area under the distribution curve to the right of x will be equal to the probability selected by the user. That x is the dynamic zone. Included: Bar coloring Signals Alerts Loxx's Expanded Source Types
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STD-Filterd, R-squared Adaptive T3 w/ Dynamic Zones [Loxx]STD-Filterd, R-squared Adaptive T3 w/ Dynamic Zones is a standard deviation filtered R-squared Adaptive T3 moving average with dynamic zones. What is the T3 moving average? Better Moving Averages Tim Tillson November 1, 1998 Tim Tillson is a software project manager at Hewlett-Packard, with degrees in Mathematics and Computer Science. He has privately traded options and equities for 15 years. Introduction "Digital filtering includes the process of smoothing, predicting, differentiating, integrating, separation of signals, and removal of noise from a signal. Thus many people who do such things are actually using digital filters without realizing that they are; being unacquainted with the theory, they neither understand what they have done nor the possibilities of what they might have done." This quote from R. W. Hamming applies to the vast majority of indicators in technical analysis . Moving averages, be they simple, weighted, or exponential, are lowpass filters; low frequency components in the signal pass through with little attenuation, while high frequencies are severely reduced. "Oscillator" type indicators (such as MACD , Momentum, Relative Strength Index ) are another type of digital filter called a differentiator. Tushar Chande has observed that many popular oscillators are highly correlated, which is sensible because they are trying to measure the rate of change of the underlying time series, i.e., are trying to be the first and second derivatives we all learned about in Calculus. We use moving averages (lowpass filters) in technical analysis to remove the random noise from a time series, to discern the underlying trend or to determine prices at which we will take action. A perfect moving average would have two attributes: It would be smooth, not sensitive to random noise in the underlying time series. Another way of saying this is that its derivative would not spuriously alternate between positive and negative values. It would not lag behind the time series it is computed from. Lag, of course, produces late buy or sell signals that kill profits. The only way one can compute a perfect moving average is to have knowledge of the future, and if we had that, we would buy one lottery ticket a week rather than trade! Having said this, we can still improve on the conventional simple, weighted, or exponential moving averages. Here's how: Two Interesting Moving Averages We will examine two benchmark moving averages based on Linear Regression analysis. In both cases, a Linear Regression line of length n is fitted to price data. I call the first moving average ILRS, which stands for Integral of Linear Regression Slope. One simply integrates the slope of a linear regression line as it is successively fitted in a moving window of length n across the data, with the constant of integration being a simple moving average of the first n points. Put another way, the derivative of ILRS is the linear regression slope. Note that ILRS is not the same as a SMA ( simple moving average ) of length n, which is actually the midpoint of the linear regression line as it moves across the data. We can measure the lag of moving averages with respect to a linear trend by computing how they behave when the input is a line with unit slope. Both SMA (n) and ILRS(n) have lag of n/2, but ILRS is much smoother than SMA . Our second benchmark moving average is well known, called EPMA or End Point Moving Average. It is the endpoint of the linear regression line of length n as it is fitted across the data. EPMA hugs the data more closely than a simple or exponential moving average of the same length. The price we pay for this is that it is much noisier (less smooth) than ILRS, and it also has the annoying property that it overshoots the data when linear trends are present. However, EPMA has a lag of 0 with respect to linear input! This makes sense because a linear regression line will fit linear input perfectly, and the endpoint of the LR line will be on the input line. These two moving averages frame the tradeoffs that we are facing. On one extreme we have ILRS, which is very smooth and has considerable phase lag. EPMA has 0 phase lag, but is too noisy and overshoots. We would like to construct a better moving average which is as smooth as ILRS, but runs closer to where EPMA lies, without the overshoot. A easy way to attempt this is to split the difference, i.e. use (ILRS(n)+EPMA(n))/2. This will give us a moving average (call it IE /2) which runs in between the two, has phase lag of n/4 but still inherits considerable noise from EPMA. IE /2 is inspirational, however. Can we build something that is comparable, but smoother? Figure 1 shows ILRS, EPMA, and IE /2. Filter Techniques Any thoughtful student of filter theory (or resolute experimenter) will have noticed that you can improve the smoothness of a filter by running it through itself multiple times, at the cost of increasing phase lag. There is a complementary technique (called twicing by J.W. Tukey) which can be used to improve phase lag. If L stands for the operation of running data through a low pass filter, then twicing can be described by: L' = L(time series) + L(time series - L(time series)) That is, we add a moving average of the difference between the input and the moving average to the moving average. This is algebraically equivalent to: 2L-L(L) This is the Double Exponential Moving Average or DEMA , popularized by Patrick Mulloy in TASAC (January/February 1994). In our taxonomy, DEMA has some phase lag (although it exponentially approaches 0) and is somewhat noisy, comparable to IE /2 indicator. We will use these two techniques to construct our better moving average, after we explore the first one a little more closely. Fixing Overshoot An n-day EMA has smoothing constant alpha=2/(n+1) and a lag of (n-1)/2. Thus EMA (3) has lag 1, and EMA (11) has lag 5. Figure 2 shows that, if I am willing to incur 5 days of lag, I get a smoother moving average if I run EMA (3) through itself 5 times than if I just take EMA (11) once. This suggests that if EPMA and DEMA have 0 or low lag, why not run fast versions (eg DEMA (3)) through themselves many times to achieve a smooth result? The problem is that multiple runs though these filters increase their tendency to overshoot the data, giving an unusable result. This is because the amplitude response of DEMA and EPMA is greater than 1 at certain frequencies, giving a gain of much greater than 1 at these frequencies when run though themselves multiple times. Figure 3 shows DEMA (7) and EPMA(7) run through themselves 3 times. DEMA^3 has serious overshoot, and EPMA^3 is terrible. The solution to the overshoot problem is to recall what we are doing with twicing: DEMA (n) = EMA (n) + EMA (time series - EMA (n)) The second term is adding, in effect, a smooth version of the derivative to the EMA to achieve DEMA . The derivative term determines how hot the moving average's response to linear trends will be. We need to simply turn down the volume to achieve our basic building block: EMA (n) + EMA (time series - EMA (n))*.7; This is algebraically the same as: EMA (n)*1.7-EMA( EMA (n))*.7; I have chosen .7 as my volume factor, but the general formula (which I call "Generalized Dema") is: GD (n,v) = EMA (n)*(1+v)-EMA( EMA (n))*v, Where v ranges between 0 and 1. When v=0, GD is just an EMA , and when v=1, GD is DEMA . In between, GD is a cooler DEMA . By using a value for v less than 1 (I like .7), we cure the multiple DEMA overshoot problem, at the cost of accepting some additional phase delay. Now we can run GD through itself multiple times to define a new, smoother moving average T3 that does not overshoot the data: T3(n) = GD ( GD ( GD (n))) In filter theory parlance, T3 is a six-pole non-linear Kalman filter. Kalman filters are ones which use the error (in this case (time series - EMA (n)) to correct themselves. In Technical Analysis , these are called Adaptive Moving Averages; they track the time series more aggressively when it is making large moves. What is R-squared Adaptive? One tool available in forecasting the trendiness of the breakout is the coefficient of determination ( R-squared ), a statistical measurement. The R-squared indicates linear strength between the security's price (the Y - axis) and time (the X - axis). The R-squared is the percentage of squared error that the linear regression can eliminate if it were used as the predictor instead of the mean value. If the R-squared were 0.99, then the linear regression would eliminate 99% of the error for prediction versus predicting closing prices using a simple moving average . R-squared is used here to derive a T3 factor used to modify price before passing price through a six-pole non-linear Kalman filter. What are Dynamic Zones? As explained in "Stocks & Commodities V15:7 (306-310): Dynamic Zones by Leo Zamansky, Ph .D., and David Stendahl" Most indicators use a fixed zone for buy and sell signals. Here’ s a concept based on zones that are responsive to past levels of the indicator. One approach to active investing employs the use of oscillators to exploit tradable market trends. This investing style follows a very simple form of logic: Enter the market only when an oscillator has moved far above or below traditional trading lev- els. However, these oscillator- driven systems lack the ability to evolve with the market because they use fixed buy and sell zones. Traders typically use one set of buy and sell zones for a bull market and substantially different zones for a bear market. And therein lies the problem. Once traders begin introducing their market opinions into trading equations, by changing the zones, they negate the system’s mechanical nature. The objective is to have a system automatically define its own buy and sell zones and thereby profitably trade in any market — bull or bear. Dynamic zones offer a solution to the problem of fixed buy and sell zones for any oscillator-driven system. An indicator’s extreme levels can be quantified using statistical methods. These extreme levels are calculated for a certain period and serve as the buy and sell zones for a trading system. The repetition of this statistical process for every value of the indicator creates values that become the dynamic zones. The zones are calculated in such a way that the probability of the indicator value rising above, or falling below, the dynamic zones is equal to a given probability input set by the trader. To better understand dynamic zones, let's first describe them mathematically and then explain their use. The dynamic zones definition: Find V such that: For dynamic zone buy: P{X <= V}=P1 For dynamic zone sell: P{X >= V}=P2 where P1 and P2 are the probabilities set by the trader, X is the value of the indicator for the selected period and V represents the value of the dynamic zone. The probability input P1 and P2 can be adjusted by the trader to encompass as much or as little data as the trader would like. The smaller the probability, the fewer data values above and below the dynamic zones. This translates into a wider range between the buy and sell zones. If a 10% probability is used for P1 and P2, only those data values that make up the top 10% and bottom 10% for an indicator are used in the construction of the zones. Of the values, 80% will fall between the two extreme levels. Because dynamic zone levels are penetrated so infrequently, when this happens, traders know that the market has truly moved into overbought or oversold territory. Calculating the Dynamic Zones The algorithm for the dynamic zones is a series of steps. First, decide the value of the lookback period t. Next, decide the value of the probability Pbuy for buy zone and value of the probability Psell for the sell zone. For i=1, to the last lookback period, build the distribution f(x) of the price during the lookback period i. Then find the value Vi1 such that the probability of the price less than or equal to Vi1 during the lookback period i is equal to Pbuy. Find the value Vi2 such that the probability of the price greater or equal to Vi2 during the lookback period i is equal to Psell. The sequence of Vi1 for all periods gives the buy zone. The sequence of Vi2 for all periods gives the sell zone. In the algorithm description, we have: Build the distribution f(x) of the price during the lookback period i. The distribution here is empirical namely, how many times a given value of x appeared during the lookback period. The problem is to find such x that the probability of a price being greater or equal to x will be equal to a probability selected by the user. Probability is the area under the distribution curve. The task is to find such value of x that the area under the distribution curve to the right of x will be equal to the probability selected by the user. That x is the dynamic zone. Included: Bar coloring Signals Alerts Loxx's Expanded Source Types
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Visible Range Mean Deviation Histogram [LuxAlgo]This script displays a histogram from the mean and standard deviation of the visible price values on the chart. Bin counting is done relative to high/low prices instead of counting the price values within each bin, returning a smoother histogram as a result. Settings Bins Per Side: Number of bins computed above and below the price mean Deviation Multiplier: Standard deviation multiplier Style Relative: Determines whether the bins length is relative to the maximum bin count, with a length controlled with the width settings to the left. Bin Colors: Bin/POC Lines colors Show POCs: Shows point of controls Usage Histograms are generally used to estimate the underlying distribution of a series of observations, their construction is generally done taking into account the overall price range. The proposed histogram construct N intervals above*below the mean of the visible price, with each interval having a size of: σ × Mult / N , where σ is the standard deviation and N the number of Bins per side and is determined by the user. The standard deviation multipliers are highlighted at the left side of each bin. A high bin count reflects a higher series of observations laying within that specific interval, this can be useful to highlight ranging price areas. POCs highlight the most significant bins and can be used as potential support/resistances.
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由LuxAlgo提供
18
Standard-Deviation Adaptive Smoother MA [Loxx]Standard-Deviation Adaptive Smoother MA is a Smoother moving average with standard deviation adaptivity. What is the Smoother Moving Average? The Smoother filter is a faster-reacting smoothing technique which generates considerably less lag than the SMMA ( Smoothed Moving Average ). It gives earlier signals but can also create false signals due to its earlier reactions. This filter is sometimes wrongly mistaken for the superior Jurik Smoothing algorithm. Included: Bar coloring
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Williams Vix Fix Bottoms and TopsThis indicator uses the very popular Williams Vix Fix for Bottoms by Chris Moody but not only does it search for bottoms, it can also be switch to work for tops for those who look to short the market. I've also added in a few options like flipping the indicator, color adjustments on the settings page, as well as cut a few of the options I feel did not need to be in which cluttered the screen when the settings were opened. In his later revisions of the Williams Vix Fix, CM took out the functions which draw the high/low ranges as well as the standard deviation which is what this indicator uses to show entry points. I have added options back on to draw these, I think it's useful. To be honest, I have not messed around with the number settings much so I am not sure how adjusting the look back range or going for smaller / bigger percentage changes would change how well the indicator works. It seems to work very well at its default settings. With the Bollinger Band deviation, you have to remember that it looks back at the set amount of candles (20 by default) and uses those for the standard deviation: 1 dev = 68%, 2 dev = 95%, 3 dev = 99.7% These percentages mean that at 2 dev, 95% of the last 20 candles will remain within the boundaries of the Bollinger Bands. Three tends to be too high, one is usually too low. Two is pretty good. The lowest percentile option probably won't change much other than bring up the bottom line which doesn't effect the alerts or signals, just something to observe. The highest percentile option makes a difference similar to the stand deviation and Bollinger Band. The higher you put it, the less likely it will get triggered but the more reliant it of a signal it should be. As always, I have left notes throughout the code and I did leave in the code that was original but commented it out as I don't believe it's worth having. I like to have the high/lows drawn, as well as the standard deviation. Then I find that the filtered entries are most accurate signals to follow. Simple entry is hit or miss, Aggressive entry is always early but sometimes that's not a great thing.
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由theehoganator提供
22
[Sidders]Std. Deviation from Mean/MA (Z-score)This indicator visualizes in a straight forward way the distance price is away from the mean in absolute standard deviations (Z-score) over a certain lookback period (can be configured). Additionally I've included a moving average of the distance, the MA type can be configured in the settings. Personally using this indicator for some of my algo mean reversion strategies. Price reaching the extreme treshold (can be configured in settings, standard is 3) could be seen as a point where price will revert to the mean. I've included alerts for when price crosses into extreme areas, as well as alerts for when crosses back into 'normal' territory again. Both are also plotted on the indicator through background coloring/shapes. Since I've learned so much from other developers I've decided to open source the code. Let me know if you have any ideas on how to improve, I'll see if I can implement them. Enjoy!
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由Sidders提供
1
Volatility Ratio Adaptive RSX [Loxx]Volatility Ratio Adaptive RSX this indicator adds volatility ratio adapting and speed value to RSX in order to make it more responsive to market condition changes at the times of high volatility, and to make it smoother in the times of low volatility What is RSX? RSI is a very popular technical indicator, because it takes into consideration market speed, direction and trend uniformity. However, the its widely criticized drawback is its noisy (jittery) appearance. The Jurik RSX retains all the useful features of RSI, but with one important exception: the noise is gone with no added lag. Included: -Toggle on/off bar coloring
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SigmaSpikes Background Highlight [vnhilton]SigmaSpikes is an indicator created by Adam H Grimes. It's a volatility indicator which applies a standard deviation measure on candles for a set period of time, in order to find big candles/moves relative to the other candles. These big moves could be the outcome of setups being traded by market players, large market orders put in by big money players, &/or HFT algorithms reacting to events (usually fundamental events). These big moves can also be seen as inefficient as it doesn't fit in with the mostly efficient market - this is very similar to gaps of which price would want to fill as they're inefficient, in order to "restore order" to the market. This indicator attempts to give better information at a glance, by highlighting the background of candles that have sigma spikes over the set standard deviation threshold. In the chart snapshot image above featuring EURUSD, we can see at 24/06/22 3PM BST, a big move has occurred (highlighted in green showing upward move) leaving an inefficiency area that needs to be filled. The high end of the inefficiency area was reached in the following candle as there was no gap between that candle's open & the previous big candle's close. The low end of the inefficiency area was finally reached almost 4 hours later, at 6:55PM BST.
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由vnhilton提供
STD Stepped Ehlers Optimal Tracking Filter MTF w/ Alerts [Loxx]STD Stepped Ehlers Optimal Tracking Filter MTF w/ Alerts is the traditional Ehlers Optimal Tracking Filter but with stepped price levels, access to multiple time frames, and alerts. What is Ehlers Optimal Tracking Filter? From "OPTIMAL TRACKING FILTERS" by John Ehlers: "Dr. R.E. Kalman introduced his concept of optimum estimation in 1960. Since that time, his technique has proven to be a powerful and practical tool. The approach is particularly well suited for optimizing the performance of modern terrestrial and space navigation systems. Many traders not directly involved in system analysis have heard about Kalman filtering and have expressed an interest in learning more about it for market applications. Although attempts have been made to provide simple, intuitive explanations, none has been completely successful. Almost without exception, descriptions have become mired in the jargon and state-space notation of the “cult”. Surprisingly, in spite of the obscure-looking mathematics (the most impenetrable of which can be found in Dr. Kalman’s original paper), Kalman filtering is a fairly direct and simple concept. In the spirit of being pragmatic, we will not deal with the full-blown matrix equations in this description and we will be less than rigorous in the application to trading. Rigorous application requires knowledge of the probability distributions of the statistics. Nonetheless we end with practically useful results. We will depart from the classical approach by working backwards from Exponential Moving Averages. In this process, we introduce a way to create a nearly zero lag moving average. From there, we will use the concept of a Tracking Index that optimizes the filter tracking for the given uncertainty in price movement and the uncertainty in our ability to measure it." Included: -Standard deviation stepping filter, price is required to exceed XX deviations before the moving average line shifts direction -Selection of filtering based on source price, the moving average, or both; you can also set the Filter deviations to 0 for no filtering at all -Toggle on/off bar coloring -Toggle on/off signals -Long/Short alerts
Pine Script™指标
由loxx提供
6