Generalized Step Moving Average w/ Pips Filter [Loxx]Generalized Step Moving Average w/ Pips Filter is a stepping function on source input to derive a moving average. This general form the stepping can also be applied to any other input such as EMA, SMA, HMA, WMA, etc.. This moving average employ a filtering system based on the following:
Core filter, both min and max value: pips * (multiplier) or the (average of momentum) * (multiplier).
Post processing filter: pips * (multiplier)
These filtering options require trend to shift by the above values before changing direction thereby reducing noise and yielding a better defined trend.
Things to note
This indicator requires fine tuning to make it work on all tickers. If you place this on a chart and it shows all green or red candles, then you must adjust the indicator to coincide with the pip movement of that ticker.
This indicator can be used on any timeframe.
Included
Bar coloring
Signals
Alerts
Loxx's Expanded Source Types
Pipsstepped
Pips-Stepped, Adaptive-ER DSEMA w/ DSL [Loxx]Pips-Stepped, Adaptive-ER DSEMA w/ DSL is an Efficiency-Ratio-Adaptive, Double-Smoothed EMA with Pips Stepping and Discontinued Signal Lines. This combination reduces noise and improves signal quality.
What is Double Smoothed Exponential Moving Average (DSEMA) ?
The Double Smoothed Exponential Moving Average is a lot less laggy compared to a traditional EMA . It's also considered a leading indicator compared to the EMA , and is best utilized whenever smoothness and speed of reaction to market changes are required.
What is the efficiency ratio?
In statistical terms, the Efficiency Ratio tells us the fractal efficiency of price changes. ER fluctuates between 1 and 0, but these extremes are the exception, not the norm. ER would be 1 if prices moved up 10 consecutive periods or down 10 consecutive periods. ER would be zero if price is unchanged over the 10 periods.
Included:
Bar coloring
Signals
Alerts
EMA and FEMA Signal/ DSL smoothing
Loxx's Expanded Source Types
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
Pips-Stepped PDFMA [Loxx]Pips-Stepped PDFMA is and Pips-stepped moving average that uses a probability density function moving average. This is tuned for Forex. You must adjust the step size to extreme levels for this to work for crypto or stocks. Try 30000 for BTC on the daily chart, for example.
What is Probability Density Function?
Probability density function based MA is a sort of weighted moving average that uses probability density function to calculate the weights.
Included:
Bar coloring
Alerts
Expanded source types
Signals
Flat-level coloring for scalping
Pips-Stepped, OMA-Filtered, Ocean NMA [Loxx]Pips-Stepped, OMA-Filtered, Ocean NMA is an Ocean Natural Moving Average Filter that is pre-filtered using One More Moving Average (OMA) and then post-filtered using stepping by pips. This indicator is quadruple adaptive depending on the settings used:
OMA adaptive
Hiekin-Ashi Better Source Input Adaptive (w/ AMA of Kaufman smoothing)
Ocean NMA adaptive
Pips adaptive
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
What is the Ocean Natural Moving Average?
Created by Jim Sloman, the NMA is a moving average that automatically adjusts to volatility without being programed to do so. For more info, read his guide "Ocean Theory, an Introduction"
What's the difference between this indicator and Sloan's original NMA?
Sloman's original calculation uses the natural log of price as input into the NMA , here we use moving averages of price as the input for NMA . As such, this indicator applies a certain level of Ocean theory adaptivity to moving average filter used.
Included:
Bar coloring
Alerts
Expanded source types
Signals
Flat-level coloring for scalping
Stepped Heiken Ashi Moving Average w/ Jurik Filtering [Loxx]Stepped Heiken Ashi Moving Average w/ Jurik Filtering is a Heiken Ashi moving average with Jurik Filtering and stepping by pips. This can be used as a moving average channel.
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:
Toggle fill color
Toggle bar color
Toggle candles
