Kalman Filter Trend BreakersThe Kalman filter is a recursive algorithm developed in 1960 by Rudolf E. Kálmán, a Hungarian-American engineer and mathematician, that provides optimal estimates of a system's state by combining noisy measurements with a predictive model. It is widely used in control systems, signal processing, and finance for tracking and forecasting.
In trading, KF might be a good replacement for a moving average, as it reacts to price changes in a different way. Not only it follows price direction, but can also track the velocity of price change. This specific behaviour of KF is used in this indicator to track changes in trends.
Trend is characterized by price moving directionally, however, any trend comes to pause or complete stop and reversal, as the price changes more slowly (a trend fades into a sideways movement for a while) or the price movement changes direction, thus making a reversal.
This indicator detects the points where such changes occur (trend breaker points), and produces signals, which serve as points of current trend pausing or reversing. By applying different settings for KF calculation, you can produce less or more signals that indicate change in trend character, and either detect only significant trends changes, or less and shorter trends changes as well.
The signals do not differentiate the exact type of a trend change (it can be a brief trend pause followed by a continuation, as well as a complete reversal). However, once you are in a trend, the significant velocity change indicates a change in trend structure. In this sense, trend breaker signals should not be followed blindly, and can be used only as trend (and subsequently, position) exit confirmations, but not the entry contrarian confirmations.
For better visual representation, you can use chart signals attached to bars, and additionally paint a vertical gradient at each signal which shows significant trend deceleration.
Kalman filter calculations used in this indicator are partially based on an open-source code from @loxx which was published in 2022 as Kalman filter overlay .
Velocity
Glitch IndexGlitch Index is an oscillator from an unknown origin that is discovered in 2013 as a lua indicator taken from MetaStock days and we are not really sure how far back the original idea goes.
How it Works?
As I found this indicator and looking at it's code in different platform I can see it comes back from a basic idea of getting a price value, calculating it's smoothed average with a set multiplier and getting the difference then presenting it on a simplified scale. It appears to be another interpretation of figuring out price acceleration and velocity. The main logic is calculated as below:
price = priceSet(priceType)
_ma = getAverageName(price, MaMethod, MaPeriod)
rocma = ((_ma - _ma ) * 0.1) + 1
maMul = _ma * rocma
diff = price - maMul
gli_ind = (diff / price) * -10
How to Use?
Glitch Index can be used based on different implementations and along with your already existing trading system as a confirmation. Yoıu can use it as a Long signal when the histogram crosses inner levels or you can use it as an overbough and oversold signals when the histogram crosses above outter levels and gets back in the range between outter and inner levels.
You can customise the settings and set your prefered inner and outter levels in indicator settings along with gradient or static based coloring and modify the code as you see fit. The coloring code is set below:
gli_col = gli_ind > outterLevel ? color.green : gli_ind < -outterLevel ? color.red : gli_ind > innerLevel ? color.rgb(106, 185, 109, 57) : gli_ind < -innerLevel ? color.rgb(233, 111, 111, 40) : color.new(color.yellow, 60)
gradcol = color.from_gradient(gli_ind, -outterLevel, outterLevel, color.red, color.green)
colorSelect = colorType == "Gradient" ? gradcol : gli_col
Velocity and Acceleration SignalsThe "Velocity and Acceleration Signals" indicator is a versatile tool designed to provide traders with valuable insights into price momentum and acceleration. By harnessing the power of mathematics and visualization, this indicator helps traders make informed decisions in the fast-paced world of financial markets.
Crunching the Numbers: How It Works
At its core, the indicator relies on two key concepts: velocity and acceleration. Here's how it operates:
-- Velocity Calculation : The indicator takes a step back in time, considering a user-defined historical period (typically around 14 bars). It calculates the velocity of price movements during this period. Velocity represents the speed at which an asset's price is changing and is derived by examining how much the price has moved between bars. Specifically, it computes the rate of change in price over time.
-- Acceleration Calculation : Building upon velocity, the indicator goes one step further and calculates acceleration. Acceleration signifies how quickly the velocity is changing. It quantifies whether the price is speeding up or slowing down in its ascent or descent.
-- Smoothing with EMA : To enhance clarity and reduce noise, the indicator smooths the velocity using an Exponential Moving Average (EMA) with a user-defined length. This smoothed velocity provides a more comprehensive view of the price momentum trend.
Visualizing Market Dynamics
The indicator doesn't just crunch numbers; it also paints a vivid picture of market sentiment:
-- Coloration : The indicator employs a color scheme to visualize market conditions. It uses lime for positive acceleration and fuchsia for negative acceleration. The color green represents positive smoothed velocity, while red denotes negative smoothed velocity. A gray hue signals a neutral or transitional phase.
-- Plotting Velocity and Acceleration : The indicator provides visual representations of both smoothed velocity and acceleration. Smoothed velocity is depicted as columns, with green or red coloring indicating the direction. Acceleration is displayed as a histogram, with lime or fuchsia bars showcasing bullish or bearish momentum. A gray zero line offers a reference point for changes in momentum direction.
-- Strong Up and Strong Down Conditions : For traders seeking distinctive signals, the indicator identifies "Strong Up" and "Strong Down" conditions. A "Strong Up" occurs when smoothed velocity crosses above a user-defined threshold, coupled with positive acceleration. Conversely, a "Strong Down" emerges when smoothed velocity crosses below another threshold, accompanied by negative acceleration. These conditions are marked with prominent triangular shapes.
Unlocking Trading Potential
Now, let's explore how traders can leverage the indicator:
-- Trend Confirmation : Traders can use this indicator to validate the prevailing market trend. A robust smoothed velocity, combined with acceleration in the same direction, can confirm the current trend.
-- Contrarian Signals : Extreme conditions signaled by a strong crossover or crossunder of the smoothed velocity threshold, along with appropriate acceleration, can hint at potential trend reversals.
-- Divergence Analysis : Savvy traders can employ this indicator to identify divergences between price movements and momentum. If the price exhibits higher highs while the indicator shows lower highs (or vice versa), it may signify a weakening or strengthening trend.
Navigating Limitations
As with any trading tool, it's essential to acknowledge the indicator's limitations:
-- Lookback Period : The indicator's effectiveness may vary based on the chosen historical period. Longer periods smooth out fluctuations but may lag in capturing recent changes in sentiment.
-- Threshold Sensitivity : Interpreting threshold crossovers or crossunders can be subjective. Traders should carefully fine-tune these threshold values based on their trading strategy and market conditions.
-- Context Matters : The indicator focuses solely on velocity and acceleration signals and does not incorporate other critical factors such as trading volume, market news, or fundamental analysis. Therefore, traders should use it in conjunction with additional indicators and analysis techniques.
While the primary focus is on trend and momentum analysis, this indicator indirectly provides information about volatility as well. Rapid changes in velocity and acceleration can indicate increasing volatility in the market, which may be of interest to traders looking for opportunities during volatile conditions.
However, this indicator doesn't directly measure volume. To incorporate volume analysis into your trading strategy, you may want to combine this indicator with volume-based indicators or consider other tools specifically designed for volume analysis.
In conclusion, this indicator is a valuable ally for traders looking to decode market dynamics and make data-driven trading decisions. While it offers powerful insights, it's crucial to recognize its limitations and deploy it as part of a comprehensive trading strategy.
Velocity Acceleration Convergence Divergence Indicator [CC]I created the Velocity Acceleration Convergence Divergence Indicator, and it is quite a mouthful if I do say so. I based this script on my two previous scripts: Velocity Indicator and Velocity Acceleration Indicator . This acts like a typical MACD but is much faster with the responses. This indicator is created by finding the difference between the Velocity Indicator and Velocity Acceleration Indicator to determine the overall trend strength of the underlying stock. Like the other scripts, I coded the general buy and sell signals the same, so you would want to buy when the indicator crosses over above the zero midline and sell when it crosses below the zero midline. I have also used the same colors, so darker colors for strong signals and lighter colors for normal signals.
Please let me know if you would like me to publish another script or if you want something custom done!
Velocity Acceleration Indicator [CC]The Velocity Acceleration Indicator was created by Scott Cong (Stocks and Commodities Sep 2023, pgs 8-15). This is another personal variation of his formula designed to capture the overall velocity acceleration of the underlying stock by applying the velocity formula to the original indicator to find the acceleration of the underlying velocity. I changed a few things around and managed actually to get less lag and quicker signals for this version, so make sure you compare the Velocity Indicator script that I published yesterday. This indicator is also visually similar to a typical stochastic indicator but uses a different underlying calculation. This works well as a momentum indicator, and the values are completely unbounded, so the best ways to determine bullish or bearish trends is either by using a crossover or crossunder between the indicator and the midline or to buy or sell the indicator when it reaches a high or low point and starts to fall or rise respectively. I used the zero line for my default version to help determine the bullish or bearish trends. I have also included multiple colors to differentiate between very strong signals and normal signals, so very strong signals are darker in color, and normal signals use lighter colors. Buy when the line turns green and sell when it turns red.
Let me know if there are any other indicators or scripts you would like to see me publish! I will have some more new scripts in the next week or so.
Velocity Indicator [CC]The Velocity Indicator was created by Scott Cong (Stocks and Commodities Sep 2023, pgs 8-15). This is my variation of his formula designed to capture the overall velocity of the underlying stock by applying the typical velocity formula. This indicator is visually similar to a typical stochastic indicator but uses a different underlying calculation. This works well as a momentum indicator, and the values are completely unbounded, so the best ways to determine bullish or bearish trends is either by using a crossover or crossunder between the indicator and the midline or to buy or sell the indicator when it reaches a high or low point and starts to fall or rise respectively. For my default version, I used the zero line to help determine the bullish or bearish trends. I have also included multiple colors to differentiate between very strong signals and normal signals, so very strong signals are darker in color, and normal signals use lighter colors. Buy when the line turns green and sell when it turns red.
Let me know if there are any other indicators or scripts you would like to see me publish! I will have some more new scripts in the next week or so.
Display Trade Volume with MA Angle and Price VelocityThis Pine Script indicator is designed to provide traders with a visual representation of trade volume, moving average (MA) angle, and price velocity on a chart. The primary components of this indicator are:
Trade Volume: The indicator compares the current bar's trade volume with the average volume over a user-defined lookback period. The volume is displayed as either "Low" or "Trade" in a table, with red or green background color, respectively, to indicate whether it's below or above the average volume.
MA Angle: The indicator calculates the angle of the moving average (either Simple, Exponential, or Hull) over a user-defined length. A positive angle is shown in green, while a negative angle is shown in red. The angle is displayed in degrees in the table.
Price Velocity: This component calculates the velocity of price movement by comparing the difference between high and low prices over a user-defined lookback period. It then displays the velocity as either "Slow" or "Fast" in the table, with red or green background color, respectively, depending on whether it's below or above the average difference.
The indicator also includes alert conditions for high and low volume situations, notifying the trader when the current bar's volume is significantly higher or lower than the average volume.
Super 6x: RSI, MACD, Stoch, Loxxer, CCI, & Velocity [Loxx]Super 6x: RSI , MACD , Stoch , Loxxer, CCI , & Velocity is a combination of 6 indicators into one histogram. This includes the option to allow repainting.
What is MACD?
Moving average convergence divergence ( MACD ) is a trend-following momentum indicator that shows the relationship between two moving averages of a security’s price. The MACD is calculated by subtracting the 26-period exponential moving average ( EMA ) from the 12-period EMA .
What is CCI?
The Commodity Channel Index ( CCI ) measures the current price level relative to an average price level over a given period of time. CCI is relatively high when prices are far above their average. CCI is relatively low when prices are far below their average. Using this method, CCI can be used to identify overbought and oversold levels.
What is RSI?
The relative strength index is a technical indicator used in the analysis of financial markets. It is intended to chart the current and historical strength or weakness of a stock or market based on the closing prices of a recent trading period. The indicator should not be confused with relative strength .
What is Stochastic?
The stochastic oscillator, also known as stochastic indicator, is a popular trading indicator that is useful for predicting trend reversals. It also focuses on price momentum and can be used to identify overbought and oversold levels in shares, indices, currencies and many other investment assets.
What is Loxxer?
The Loxxer indicator is a technical analysis tool that compares the most recent maximum and minimum prices to the previous period's equivalent price to measure the demand of the underlying asset.
What is Velocity?
In simple words, velocity is the speed at which something moves in a particular direction. For example as the speed of a car travelling north on a highway, or the speed a rocket travels after launching.
How to use
Long signal: All 4 indicators turn green
Short signal: All 4 indicators turn red
Included
Bar coloring
Alerts
Normalized Velocity [Loxx]Velocity (which is often called a "smoother momentum" since it is much smoother than momentum without lagging at all) with an addition of ATR normalization
Since velocity is (even when normalization is applied) is not an indicator with fixed bounds, this indicator is uses floating levels for what is usually called overbought and oversold levels (+ a floating "zero" line is added). Something that would look like a "fixed levels" is easily achieved if you use long floating levels period in which case those levels are quite similar to fixed levels.
This indicator can be used like any momentum indicator (in that case recommended coloring mode is to use either slope coloring or "zero" middle level crossing coloring) or it can be used as a "trending" indicator in which case it is better to use coloring on outer level cross, and longer calculation periods are advised in that case.
Included:
Bar coloring
3 signal variations w/ alerts
Loxx's Expanded Source Types
Alerts
T3 Velocity Candles [Loxx]T3 Velocity Candles is a candle coloring overlay that calculates its gradient coloring using T3 velocity.
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.
QQE of Parabolic-Weighted Velocity [Loxx]QQE of Parabolic-Weighted Velocity is a QQE indicator that takes as its input parabolic-weighted velocity calculation. This version can help in determining trend. Adjust the calculating period to your trading style: longer - to trend traders, shorter - for scalping.
What is Qualitative Quantitative Estimation (QQE)?
The Qualitative Quantitative Estimation (QQE) indicator works like a smoother version of the popular Relative Strength Index ( RSI ) indicator. QQE expands on RSI by adding two volatility based trailing stop lines. These trailing stop lines are composed of a fast and a slow moving Average True Range (ATR).
There are many indicators for many purposes. Some of them are complex and some are comparatively easy to handle. The QQE indicator is a really useful analytical tool and one of the most accurate indicators. It offers numerous strategies for using the buy and sell signals. Essentially, it can help detect trend reversal and enter the trade at the most optimal positions.
Included:
Loxx's Expanded Source Types
Alerts
Signals
Bar coloring
CFB-Adaptive Velocity Histogram [Loxx]CFB-Adaptive Velocity Histogram is a velocity indicator with One-More-Moving-Average Adaptive Smoothing of input source value and Jurik's Composite-Fractal-Behavior-Adaptive Price-Trend-Period input with Dynamic Zones. All Juirk smoothing allows for both single and double Jurik smoothing passes. Velocity is adjusted to pips but there is no input value for the user. This indicator is tuned for Forex but can be used on any time series data.
What is Composite Fractal Behavior ( CFB )?
All around you mechanisms adjust themselves to their environment. From simple thermostats that react to air temperature to computer chips in modern cars that respond to changes in engine temperature, r.p.m.'s, torque, and throttle position. It was only a matter of time before fast desktop computers applied the mathematics of self-adjustment to systems that trade the financial markets.
Unlike basic systems with fixed formulas, an adaptive system adjusts its own equations. For example, start with a basic channel breakout system that uses the highest closing price of the last N bars as a threshold for detecting breakouts on the up side. An adaptive and improved version of this system would adjust N according to market conditions, such as momentum, price volatility or acceleration.
Since many systems are based directly or indirectly on cycles, another useful measure of market condition is the periodic length of a price chart's dominant cycle, (DC), that cycle with the greatest influence on price action.
The utility of this new DC measure was noted by author Murray Ruggiero in the January '96 issue of Futures Magazine. In it. Mr. Ruggiero used it to adaptive adjust the value of N in a channel breakout system. He then simulated trading 15 years of D-Mark futures in order to compare its performance to a similar system that had a fixed optimal value of N. The adaptive version produced 20% more profit!
This DC index utilized the popular MESA algorithm (a formulation by John Ehlers adapted from Burg's maximum entropy algorithm, MEM). Unfortunately, the DC approach is problematic when the market has no real dominant cycle momentum, because the mathematics will produce a value whether or not one actually exists! Therefore, we developed a proprietary indicator that does not presuppose the presence of market cycles. It's called CFB (Composite Fractal Behavior) and it works well whether or not the market is cyclic.
CFB examines price action for a particular fractal pattern, categorizes them by size, and then outputs a composite fractal size index. This index is smooth, timely and accurate
Essentially, CFB reveals the length of the market's trending action time frame. Long trending activity produces a large CFB index and short choppy action produces a small index value. Investors have found many applications for CFB which involve scaling other existing technical indicators adaptively, on a bar-to-bar basis.
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.
Ideally, you would like a filtered signal to be both smooth and lag-free. Lag causes delays in your trades, and increasing lag in your indicators typically result in lower profits. In other words, late comers get what's left on the table after the feast has already begun.
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
3 signal variations w/ alerts
Divergences w/ alerts
Loxx's Expanded Source Types
T3 Velocity [Loxx]T3 Velocity is a simple velocity indicator using T3 moving average that uses gradient colors to better identify trends.
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.
Included:
Bar coloring
Signals
Alerts
Loxx's Expanded Source Types
Carrey's Velocity and AccelerationThis is initially based on the MA Speed indicator from TradeStation () and expanded upon greatly. This implements 3 different variable MAs and calculates and plots both speed and acceleration of each. Also, a single line composite option is included for both speed and acceleration that changes color based on directional confluence of each MA's speed/acceleration. Additionally, optional labels are included to show where the 3 MAs are clustered, and a volatile move is expected, and where they are more distributed, expecting a temporary reversal.
The additional acceleration concept comes from kinematics in physics. Utilizing time-based derivatives, we can calculate the velocity and acceleration of the moving averages, which can help us identify momentum of price action and locate reversals sooner.
Adaptive, One More Moving Average (OMA) [Loxx]Adaptive, One More Moving Average (OMA) is an adaptive moving average created by Mladen Rakic that changes shape with volatility and momentum
What is the One More Moving Average (OMA)?
The usual story goes something like this : which is the best moving average? Everyone that ever started to do any kind of technical analysis was pulled into this "game". Comparing, testing, looking for new ones, testing ...
The idea of this one is simple: it should not be itself, but it should be a kind of a chameleon - it should "imitate" as much other moving averages as it can. So the need for zillion different moving averages would diminish. And it should have some extra, of course:
The extras:
it has to be smooth
it has to be able to "change speed" without length change
it has to be able to adapt or not (since it has to "imitate" the non-adaptive as well as the adaptive ones)
The steps:
Smoothing - compared are the simple moving average (that is the basis and the first step of this indicator - a smoothed simple moving average with as little lag added as it is possible and as close to the original as it is possible) Speed 1 and non-adaptive are the reference for this basic setup.
Speed changing - same chart only added one more average with "speeds" 2 and 3 (for comparison purposes only here)
Finally - adapting : same chart with SMA compared to one more average with speed 1 but adaptive (so this parameters would make it a "smoothed adaptive simple average") Adapting part is a modified Kaufman adapting way and this part (the adapting part) may be a subject for changes in the future (it is giving satisfactory results, but if or when I find a better way, it will be implemented here)
Some comparisons for different speed settings (all the comparisons are without adaptive turned on, and are approximate. Approximation comes from a fact that it is impossible to get exactly the same values from only one way of calculation, and frankly, I even did not try to get those same values).
speed 0.5 - T3 (0.618 Tilson)
speed 2.5 - T3 (0.618 Fulks/Matulich)
speed 1 - SMA, harmonic mean
speed 2 - LWMA
speed 7 - very similar to Hull and TEMA
speed 8 - very similar to LSMA and Linear regression value
Parameters:
Length - length (period) for averaging
Source - price to use for averaging
Speed - desired speed (i limited to -1.5 on the lower side but it even does not need that limit - some interesting results with speeds that are less than 0 can be achieved)
Adaptive - does it adapt or not
Jurik Velocity ("smoother moment") [Loxx]Jurik Velocity ("smoother moment") is a very simple and very useful calculation. This indicator was created to expose this calculation to folks who might find it useful in their own indicators and strategies.
What is velocity?
Velocity is a vector quantity that refers to "the rate at which an object changes its position." Imagine a person moving rapidly - one step forward and one step back - always returning to the original starting position. While this might result in a frenzy of activity, it would result in a zero velocity. Because the person always returns to the original position, the motion would never result in a change in position. Since velocity is defined as the rate at which the position changes, this motion results in zero velocity. If a person in motion wishes to maximize their velocity, then that person must make every effort to maximize the amount that they are displaced from their original position. Every step must go into moving that person further from where he or she started. For certain, the person should never change directions and begin to return to the starting position.
Velocity is a vector quantity. As such, velocity is direction aware. When evaluating the velocity of an object, one must keep track of direction. It would not be enough to say that an object has a velocity of 55 mi/hr. One must include direction information in order to fully describe the velocity of the object. For instance, you must describe an object's velocity as being 55 mi/hr, east. This is one of the essential differences between speed and velocity. Speed is a scalar quantity and does not keep track of direction; velocity is a vector quantity and is direction aware.
Included:
-Toggle on/off bar coloring
Happy trading!
Money Velocity Population Adjusted (MVPA)MVPA=GDPPC/( M2 /POP). An adaptation to normal Money Velocity, taking into account populations for more volatile plots/different perspective. Major world economy's money supply velocity. Compare how each country's monetary policy has played out and current trajectory in comparison to others. The velocity of money is a measure of the number of times that the average unit of currency is used to purchase goods and services within a given time period. The concept relates the size of economic activity to a given money supply, and the speed of money exchange is one of the variables that determine inflation .
Money Velocity(GDP/M2)V=GDP/M2
Major world economy's money supply velocity. Compare how each country's monetary policy has played out and current trajectory in comparison to others. The velocity of money is a measure of the number of times that the average unit of currency is used to purchase goods and services within a given time period. The concept relates the size of economic activity to a given money supply, and the speed of money exchange is one of the variables that determine inflation.
StrengthA mathematically elegant, native & modern way how to measure velocity/ strength/ momentum. As you can see it looks like MACD, but !suddenly! has N times shorter code (disregard the functions), and only 1 parameter instead of 3. OMG HOW DID HE DO IT?!?
MACD: "Let's take one filter (1 parameter), than another filter (2 parameters), then let's take dem difference, then let's place another filter over the difference (3rd parameter + introduction of a nested calculation), and let's write a whole book about it, make thousands of multi-hours YouTube videos about it, and let's never mention about the amount of uncertainty being introduced by multiple parameters & introduction of the nested calculation."
Strength: "let's get real, let's drop a weighted linear regression & usual linear regression over the data of the same length, take dem slopes, then make the difference over these slopes, all good. And then share it with people w/o putting an ® sign".
Fyi, regressions were introduced centuries ago, maybe decades idk, the point is long time ago, and computational power enough to calculate what I'm saying is slightly more than required for macd.
Rationale.
Linearly weighted linear regression has steeper slope (W) than the usual linear regression slope (S) due to the fact that the recent datapoints got more weight. This alone is enough of a metric to measure velocity. But still I've recalled macd and decided to make smth like it cuz I knew it'll might make you happy. I realized that S can be used instead of smoothing the W, thus eliminating the nested calculation and keeping entropy & info loss in place. And see, what we get is natural, simple, makes sense and brings flex. I also wanna remind you that by applying regression we maximize the info gain by using all the data in the window, instead of taking difference between the first and the last datapoints.
This script is dedicated to my friend Fabien. Man, you were the light in the darkness in that company. You'll get your alien green Lambo if you'll really want it, no doubts on my side bout that.
Good hunting
