Pips-Stepped, R-squared Adaptive T3 [Loxx]Pips-Stepped, R-squared Adaptive T3 is a a T3 moving average with optional adaptivity, trend following, and pip-stepping. This indicator also uses optional flat coloring to determine chops zones. This indicator is R-squared adaptive. This is also an experimental indicator.
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.
Included:
Bar coloring
Signals
Alerts
Flat coloring
Tilson
R-squared Adaptive T3 [Loxx]R-squared Adaptive T3 is an R-squared adaptive version of Tilson's T3 moving average. This adaptivity was originally proposed by mladen on various forex forums. This is considered experimental but shows how to use r-squared adapting methods to moving averages. In theory, the T3 is a six-pole non-linear Kalman filter.
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
VHF-Adaptive T3 w/ Expanded Source Types [Loxx]VHF-Adaptive T3 w/ Expanded Source Types is a T3 moving average with expanded source types and adaptive period inputs using a vertical horizontal filter
What is T3?
Developed by Tim Tillson, the T3 Moving Average is considered superior to traditional moving averages as it is smoother, more responsive and thus performs better in ranging market conditions as well.
What is VHF Adaptive Cycle?
Vertical Horizontal Filter (VHF) was created by Adam White to identify trending and ranging markets. VHF measures the level of trend activity, similar to ADX DI. Vertical Horizontal Filter does not, itself, generate trading signals, but determines whether signals are taken from trend or momentum indicators. Using this trend information, one is then able to derive an average cycle length.
Included
Bar coloring
Alerts
Loxx's Expanded Source Types
T3-Filterd SSL [Loxx]T3-Filterd SSL is an SSL indicator that is filtered with T3 moving average
What is SSL?
Known as the SSL , the Semaphore Signal Level channel chart alert is an indicator that combines moving averages to provide you with a clear visual signal of price movement dynamics. In short, it's designed to show you when a price trend is forming. For our purposes here, SSL has been modified to allow for different moving average selection and different closing price look back periods.
What is T3?
Developed by Tim Tillson, the T3 Moving Average is considered superior to traditional moving averages as it is smoother, more responsive and thus performs better in ranging market conditions as well.
Included
Bar coloring
Alerts
Signals
Tillson IE/2 [CC]The IE/2 was created by Tim Tillson (Stocks and Commodities Jan 1998) and this is a practically undiscovered gem because in that same article he goes on to to create the popular T3 moving average and the GDEma but practically no one seemed to notice the IE2 or maybe it is just my imagination. Anyway this indicator name is short for Integral of Linear Regression Slope + Endpoint Moving Average / 2 so you can why it was shortened to IE/2. Like the name implies this takes two variations of smoothing that complement each other and averages them together to in theory get the benefits of each. The EPMA is much noiser but follows the data more closely and the complete opposite for the ILRS so you can see the idea in action. Like all of my indicators I include strong buy and sell signals in addition to normal ones so strong signals are darker in color and normal signals are lighter in color. 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!
Trend Catcher BotTrend analysis strategy with entry filters such as MACD and Tilson T3. It will look at possible entry points and it can use MACD or TilsonT3 filters to decide whether or not enter in a new trade.
Notes:
- Results include a 0.075% Fee.
- Simulated leverage of 5x.
- Initial Capital of $1000.
- Uses a max order size of $200k per trade (Leverage included).
- Stop loss of 1.15%.
- The stop loss is moved to 0.4% Profit once the Trade reaches 1.15% profit.
- All settings adjustable.
- Non Repainting.
TKP T3 Trend With Psar BarcolorThis script is adapted from TKP's long/short indicator to initiate buy/sell indications when price crosses the T3 moving averages, and when the T3's themselves cross. Bars change colors based on price over/under T3 and T3 up or down or This allows for simple visual analysis of trend direction along with entries, exits, and stop loss values.
Renko Strategy T3 V1An interesting strategy using Renko calculations and Tilson T3 on normal charts targeted for cryptocurrencies but can work with different assets.
Tested on Daily but can work with lower frames using Renko Size and T3 Length adjustments.
== Description ==
Strategy get Renko close/open/high/low values and smooth them with T3 Tilson.
Base on these results the strategy triggers a long and short orders, where green uptrending and red downtrending.
Including Alerts
== Repaint ==
There seems to be some sort of inconsistency when doing 'Replay' function with the strategy, which means using Replay function won't trade like if you see the trading results without Replay. Regarding real time, it does not seem to repaint, besides that you need to wait for the last active bar to complete for it to give you indication.
You can disable strategy to use it has a sole indicator.
There might be a new strategy of Renko Strategy V2 in the future as i have an in progress prototype, Follow to get updated:
www.tradingview.com
Tilson T3Developed by Tim Tillson, the T3 Moving Average is considered superior to traditional moving averages as it is smoother, more responsive and thus performs better in ranging market conditions as well. However, it bears the disadvantage of overshooting the price as it attempts to realign itself to current market conditions (www.tradingpedia.com).
Heikin Ashi Trend IndicatorMy own implantation of Heikin Ashi which i call HAT.
The Heikin Ashi Trend Indicator (HAT) used to determine the price direction of an asset, as well as draw attention to when the price direction is changing.
The HAT indicator translates the current close/open/high/low into Heikin Ashi and smooths them a bit using Tilson T3 formula.
Buy signal when Heikin Ashi Close is bigger than Heikin Ashi Open with Tilson T3 smoothing.
Sell signal when Heikin Ashi Open is bigger than Heikin Ashi Close with Tilson T3 smoothing.
Set the 'percentSqueeze' percentage to display possible reversal with light Red/Green crosses.
Green - Up Trend
Light Green - Possible reversal is near
Red - Down Trend
Light Red - Possible reversal is near
Follow for more indicators: www.tradingview.com
KK_MA_MTFThis is multitimeframe Hull moving average
you can change offset to 0 if you want realtime data
Tilson T3 and MavilimW Triple Combined StrategyInspired by truly greatful Kivanç Ozbilgic (www.tradingview.com).
The strategy tries to combined three different moving average strategies into one.
Strategies covered are:
1. Tillson T3 Moving Average Strategy
Developed by Tim Tillson, the T3 Moving Average is considered superior to traditional moving averages as it is smoother, more responsive and thus performs better in ranging market conditions as well. However, it bears the disadvantage of overshooting the price as it attempts to realign itself to current market conditions.
It incorporates a smoothing technique which allows it to plot curves more gradual than ordinary moving averages and with a smaller lag. Its smoothness is derived from the fact that it is a weighted sum of a single EMA, double EMA, triple EMA and so on. When a trend is formed, the price action will stay above or below the trend during most of its progression and will hardly be touched by any swings. Thus, a confirmed penetration of the T3 MA and the lack of a following reversal often indicates the end of a trend. Here is what the calculation looks like:
T3 = c1*e6 + c2*e5 + c3*e4 + c4*e3, where:
– e1 = EMA (Close, Period)
– e2 = EMA (e1, Period)
– e3 = EMA (e2, Period)
– e4 = EMA (e3, Period)
– e5 = EMA (e4, Period)
– e6 = EMA (e5, Period)
– a is the volume factor, default value is 0.7 but 0.618 can also be used
– c1 = – a^3
– c2 = 3*a^2 + 3*a^3
– c3 = – 6*a^2 – 3*a – 3*a^3
– c4 = 1 + 3*a + a^3 + 3*a^2
T3 MovingThe T3 Moving Average generally produces entry signals similar to other moving averages and thus is traded largely in the same manner.
Strategy for Tillson T3 is if the close crossovers T3 line and for at least five bars the close was under the T3
2. Tillson T3 Fibonacci Cross
Kivanc Ozbilgic added a second T3 line with a volume factor of 0.618 (Fibonacci Ratio) and length of 3 (fibonacci number) which can be added by selecting the T3 Fibonacci Strategy input box.
Strategy for Tillson T3 Fibo is when the Fibo Line crossover the T3 it gives long signal vice versa.
3. MavilimW
MavilimW is originally a support and resistance indicator based on fibonacci injected weighted moving averages.
Strategy for MavilimW is is if the close crossovers T3 line and for at least five bars the close was under the T3
Hope you enjoy
TKP Short/Long IndicatorThis script uses T3 Moving averages and a modified Parabolic Sar Calculation to help Identify trend reversals, but can also keep you in the predominant direction of strong trending price action.
Briz 1D XMAs LOCKED to 1D - BitcoinA crazy bunch of MAs coded the way I wanted - Never was meant to be published but maybe it will help other tightwads out there that need many MAs in one indicator. These SMAs and EMAs are locked to the 1 day time frame. The PURGATORY line is a 666 day MA from 12 hour - thus, 333 1D. There is also a high and low Mayer Multiple built in, a Tilson MA, and a bubble top SMA.
T3+SMA This source code is subject to the terms of the Mozilla Public License 2.0 at mozilla.org
© 03.freeman
This strategy is based only on T3 moving average, but uses sma 200 as filter for enter long or short.
The default settings considers a daily timeframe.
The strategy is very simple: long if T3 increase, short if T3 decrease.
Note that if you set volume factor to 0 you will have an exponential moving average, while if you set to 1 you'll get a DEMA.
Yacine MA Bands ModMashed together the ema-bands from IvanLabrie with some moving average script stuff from ChrisMoody and LazyBear and this is the result. Credit goes to them, 'cause I don't know to how to code tbh. Just copy/pasted stuff untill I got the result I wanted.
Bands work as support/resistance among other things. You can use them to trade breakouts or reversals or whatever.
Combining them with a momentum indicator would probably be useful for timing divergence or OB/OS and stuff like that.
Included moving average types;
SMA
EMA
RMA
WMA
VWMA
HullMA
TilsonMA
TEMA
Not sure if all of them works as they should... y'know since I cant code/script. Looks good to me though.¨
Default should work pretty good for the DAX, But you'll probably want to fiddle a bit with the settings.
Here's a pic of how they can be used. Ofc everything looks simple in hindsight, but you get the point.
