Kaufman Adaptive Moving Average (KAMA) Strategy [TradeDots]"The Kaufman Adaptive Moving Average (KAMA) Strategy" is a trend-following system that leverages the adaptive qualities of the Kaufman Adaptive Moving Average (KAMA). This strategy is distinguished by its ability to adjust dynamically to market volatility, enhancing trading accuracy by minimizing the effects of false and delayed signals often associated with the Simple Moving Average (SMA).
HOW IT WORKS
This strategy is centered around use of the Kaufman Adaptive Moving Average (KAMA) indicator, which refines the principles of the Exponential Moving Average (EMA) with a superior smoothing technique.
KAMA distinguishes itself by its responsiveness to changes in market prices through an "Efficiency Ratio (ER)." This ratio is computed by dividing the recent absolute net price change by the cumulative sum of the absolute price changes over a specified period. The resulting ER value ranges between 0 and 1, where 0 indicates high market noise and 1 reflects stronger market momentum.
Using ER, we could get the smoothing constant (SC) for the moving average derived using the following formula:
fastest = 2/(fastma_length + 1)
slowest = 2/(slowma_length + 1)
SC = math.pow((ER * (fastest-slowest) + slowest), 2)
The KAMA line is then calculated by applying the SC to the difference between the current price and the previous KAMA.
APPLICATION
For entering long positions, this strategy initializes when there is a sequence of 10 consecutive rising KAMA lines. Conversely, a sequence of 10 consecutive falling KAMA lines triggers sell orders for long positions. The same logic applies inversely for short positions.
DEFAULT SETUP
Commission: 0.01%
Initial Capital: $10,000
Equity per Trade: 80%
Users are advised to adjust and personalize this trading strategy to better match their individual trading preferences and style.
RISK DISCLAIMER
Trading entails substantial risk, and most day traders incur losses. All content, tools, scripts, articles, and education provided by TradeDots serve purely informational and educational purposes. Past performances are not definitive predictors of future results.
Noisereduction
Nasan Rate of Change (ROC)**NOTE: FOR COMPARISON TRADITIONAL ROC IS PLOTTED WITH THE SAME ROC LENGTH OF 9. IT IS NOT PART OF THE INDICATOR"
The Nasan ROC indicator is smoothed version of the of the traditional ROC indicator. The Nasna ROC uses a triple pass moving average differencing strategy. A cumulative sum of the deviations obtained from the moving average differencing provides a smooth "noise free" trend and this cumulative sum of deviations is used for calculating ROC.
Let's break down the components and understand the indicator we discussed earlier:
Sequential Triple Pass Filter:
Three filters with lengths specified by length1, length2, and length3 are applied to the closing prices (close).
The filters involve calculating the cumulative sum of the differences between the closing prices and their respective moving averages.
The idea is to detrend the data and accumulate the deviations from the average over time, emphasizing longer-term trends.
Calculation of Rate of Change (ROC) of Cumulative Sum:
The Rate of Change (ROC) of the cumulative sum (rocCumulativeSum) is calculated using the ta.roc function with a specified length (rocLength).
ROC measures the percentage change in the cumulative sum over a specified period.
The ROC histogram provides insights into the momentum of the detrended series. Positive values suggest increasing momentum, while negative values suggest decreasing momentum.
Pay attention to the color of the histogram bars.
The histogram bars are colored green if the current ROC value is greater than or equal to the previous ROC value, and red otherwise.
This coloring is based on the concept that a positive ROC suggests upward momentum, while a negative ROC suggests downward momentum.
Volatility - Volume Impact:
The Average True Range (ATR) is calculated with a period of 14.
Volume strength is calculated as a factor (VCF) that considers the ratio of the simple moving average (SMA) of the current volume to the SMA of the volume over a longer period (144).
This volume factor (VCF) is then multiplied by ATR, creating a synergy with volatility and volume.
Visualization with Background Color Gradient:
A background color gradient is applied to the chart based on the calculated volume strength (f1).
The gradient color ranges from black (indicating low ATR and volume strength) to purple (indicating high ATR and volume strength). A low value indicates a ranging market with no significant price movements and it is safter to avoid signals generated from ROC histogram in these region.
Synergy of ROC and Volume Strength:
Observe how the ROC signals align with the background color gradient. For example, confirm whether positive ROC aligns with periods of high ATR and volume strength.
This synergy can provide confirmation or divergence signals, adding another layer of analysis.
Variety MA Cluster Filter Crosses [Loxx]What is a Cluster Filter?
One of the approaches to determining a useful signal (trend) in stream data. Small filtering (smoothing) tests applied to market quotes demonstrate the potential for creating non-lagging digital filters (indicators) that are not redrawn on the last bars.
Standard Approach
This approach is based on classical time series smoothing methods. There are lots of articles devoted to this subject both on this and other websites. The results are also classical:
1. The changes in trends are displayed with latency;
2. Better indicator (digital filter) response achieved at the expense of smoothing quality decrease;
3. Attempts to implement non-lagging indicators lead to redrawing on the last samples (bars).
And whereas traders have learned to cope with these things using persistence of economic processes and other tricks, this would be unacceptable in evaluating real-time experimental data, e.g. when testing aerostructures.
The Main Problem
It is a known fact that the majority of trading systems stop performing with the course of time, and that the indicators are only indicative over certain intervals. This can easily be explained: market quotes are not stationary. The definition of a stationary process is available in Wikipedia:
A stationary process is a stochastic process whose joint probability distribution does not change when shifted in time.
Judging by this definition, methods of analysis of stationary time series are not applicable in technical analysis. And this is understandable. A skillful market-maker entering the market will mess up all the calculations we may have made prior to that with regard to parameters of a known series of market quotes.
Even though this seems obvious, a lot of indicators are based on the theory of stationary time series analysis. Examples of such indicators are moving averages and their modifications. However, there are some attempts to create adaptive indicators. They are supposed to take into account non-stationarity of market quotes to some extent, yet they do not seem to work wonders. The attempts to "punish" the market-maker using the currently known methods of analysis of non-stationary series (wavelets, empirical modes and others) are not successful either. It looks like a certain key factor is constantly being ignored or unidentified.
The main reason for this is that the methods used are not designed for working with stream data. All (or almost all) of them were developed for analysis of the already known or, speaking in terms of technical analysis, historical data. These methods are convenient, e.g., in geophysics: you feel the earthquake, get a seismogram and then analyze it for few months. In other words, these methods are appropriate where uncertainties arising at the ends of a time series in the course of filtering affect the end result.
When analyzing experimental stream data or market quotes, we are focused on the most recent data received, rather than history. These are data that cannot be dealt with using classical algorithms.
Cluster Filter
Cluster filter is a set of digital filters approximating the initial sequence. Cluster filters should not be confused with cluster indicators.
Cluster filters are convenient when analyzing non-stationary time series in real time, in other words, stream data. It means that these filters are of principal interest not for smoothing the already known time series values, but for getting the most probable smoothed values of the new data received in real time.
Unlike various decomposition methods or simply filters of desired frequency, cluster filters create a composition or a fan of probable values of initial series which are further analyzed for approximation of the initial sequence. The input sequence acts more as a reference than the target of the analysis. The main analysis concerns values calculated by a set of filters after processing the data received.
In the general case, every filter included in the cluster has its own individual characteristics and is not related to others in any way. These filters are sometimes customized for the analysis of a stationary time series of their own which describes individual properties of the initial non-stationary time series. In the simplest case, if the initial non-stationary series changes its parameters, the filters "switch" over. Thus, a cluster filter tracks real time changes in characteristics.
Cluster Filter Design Procedure
Any cluster filter can be designed in three steps:
1. The first step is usually the most difficult one but this is where probabilistic models of stream data received are formed. The number of these models can be arbitrary large. They are not always related to physical processes that affect the approximable data. The more precisely models describe the approximable sequence, the higher the probability to get a non-lagging cluster filter.
2. At the second step, one or more digital filters are created for each model. The most general condition for joining filters together in a cluster is that they belong to the models describing the approximable sequence.
3. So, we can have one or more filters in a cluster. Consequently, with each new sample we have the sample value and one or more filter values. Thus, with each sample we have a vector or artificial noise made up of several (minimum two) values. All we need to do now is to select the most appropriate value.
An Example of a Simple Cluster Filter
For illustration, we will implement a simple cluster filter corresponding to the above diagram, using market quotes as input sequence. You can simply use closing prices of any time frame.
1. Model description. We will proceed on the assumption that:
The aproximate sequence is non-stationary, i.e. its characteristics tend to change with the course of time.
The closing price of a bar is not the actual bar price. In other words, the registered closing price of a bar is one of the noise movements, like other price movements on that bar.
The actual price or the actual value of the approximable sequence is between the closing price of the current bar and the closing price of the previous bar.
The approximable sequence tends to maintain its direction. That is, if it was growing on the previous bar, it will tend to keep on growing on the current bar.
2. Selecting digital filters. For the sake of simplicity, we take two filters:
The first filter will be a variety filter calculated based on the last closing prices using the slow period. I believe this fits well in the third assumption we specified for our model.
Since we have a non-stationary filter, we will try to also use an additional filter that will hopefully facilitate to identify changes in characteristics of the time series. I've chosen a variety filter using the fast period.
3. Selecting the appropriate value for the cluster filter.
So, with each new sample we will have the sample value (closing price), as well as the value of MA and fast filter. The closing price will be ignored according to the second assumption specified for our model. Further, we select the МА or ЕМА value based on the last assumption, i.e. maintaining trend direction:
For an uptrend, i.e. CF(i-1)>CF(i-2), we select one of the following four variants:
if CF(i-1)fastfilter(i), then CF(i)=slowfilter(i);
if CF(i-1)>slowfilter(i) and CF(i-1)slowfilter(i) and CF(i-1)>fastfilter(i), then CF(i)=MAX(slowfilter(i),fastfilter(i)).
For a downtrend, i.e. CF(i-1)slowfilter(i) and CF(i-1)>fastfilter(i), then CF(i)=MAX(slowfilter(i),fastfilter(i));
if CF(i-1)>slowfilter(i) and CF(i-1)fastfilter(i), then CF(i)=fastfilter(i);
if CF(i-1)<slowfilter(i) and CF(i-1)<fastfilter(i), then CF(i)=MIN(slowfilter(i),fastfilter(i)).
Where:
CF(i) – value of the cluster filter on the current bar;
CF(i-1) and CF(i-2) – values of the cluster filter on the previous bars;
slowfilter(i) – value of the slow filter
fastfilter(i) – value of the fast filter
MIN – the minimum value;
MAX – the maximum value;
What is Variety MA Cluster Filter Crosses?
For this indicator we calculate a fast and slow filter of the same filter and then we run a cluster filter between the fast and slow filter outputs to detect areas of chop/noise. The output is the uptrend is denoted by green color, downtrend by red color, and chop/noise/no-trade zone by white color. As a trader, you'll likely want to avoid trading during areas of chop/noise so you'll want to avoid trading when the color turns white.
Extras
Bar coloring
Alerts
Loxx's Expanded Source Types, see here:
Loxx's Moving Averages, see here:
An example of filtered chop, see the yellow circles. The cluster filter identifies chop zones so you don't get stuck in a sideways market.
End-pointed SSA of Williams %R [Loxx]End-pointed SSA of Williams %R is an indicator that runes Williams %R SSA calculation through a Singular Spectrum Analysis (SSA) algorithm to derive a smoother final output. The reduction in noise from the traditional Williams %R is significant.
What is Williams %R?
Williams %R , also known as the Williams Percent Range, is a type of momentum indicator that moves between 0 and -100 and measures overbought and oversold levels. The Williams %R may be used to find entry and exit points in the market. The indicator is very similar to the Stochastic oscillator and is used in the same way. It was developed by Larry Williams and it compares a stock’s closing price to the high-low range over a specific period, typically 14 days or periods.
What is Singular Spectrum Analysis ( SSA )?
Singular spectrum analysis ( SSA ) is a technique of time series analysis and forecasting. It combines elements of classical time series analysis, multivariate statistics, multivariate geometry, dynamical systems and signal processing. SSA aims at decomposing the original series into a sum of a small number of interpretable components such as a slowly varying trend, oscillatory components and a ‘structureless’ noise. It is based on the singular value decomposition ( SVD ) of a specific matrix constructed upon the time series. Neither a parametric model nor stationarity-type conditions have to be assumed for the time series. This makes SSA a model-free method and hence enables SSA to have a very wide range of applicability.
For our purposes here, we are only concerned with the "Caterpillar" SSA . This methodology was developed in the former Soviet Union independently (the ‘iron curtain effect’) of the mainstream SSA . The main difference between the main-stream SSA and the "Caterpillar" SSA is not in the algorithmic details but rather in the assumptions and in the emphasis in the study of SSA properties. To apply the mainstream SSA , one often needs to assume some kind of stationarity of the time series and think in terms of the "signal plus noise" model (where the noise is often assumed to be ‘red’). In the "Caterpillar" SSA , the main methodological stress is on separability (of one component of the series from another one) and neither the assumption of stationarity nor the model in the form "signal plus noise" are required.
"Caterpillar" SSA
The basic "Caterpillar" SSA algorithm for analyzing one-dimensional time series consists of:
Transformation of the one-dimensional time series to the trajectory matrix by means of a delay procedure (this gives the name to the whole technique);
Singular Value Decomposition of the trajectory matrix;
Reconstruction of the original time series based on a number of selected eigenvectors.
This decomposition initializes forecasting procedures for both the original time series and its components. The method can be naturally extended to multidimensional time series and to image processing.
The method is a powerful and useful tool of time series analysis in meteorology, hydrology, geophysics, climatology and, according to our experience, in economics, biology, physics, medicine and other sciences; that is, where short and long, one-dimensional and multidimensional, stationary and non-stationary, almost deterministic and noisy time series are to be analyzed.
Included:
Bar coloring
[*Alerts
[*Signals
[*Loxx's Expanded Source Types
Related Williams %R Indicators
Williams %R on Chart w/ Dynamic Zones
Williams %R w/ Bollinger Bands
Intermediate Williams %R w/ Discontinued Signal Lines
Related SSA Indicators
End-pointed SSA of FDASMA
End-pointed SSA of Normalized Price Oscillator
Digital Kahler CCI [Loxx]Digital Kahler CCI is a Digital Kahler filtered CCI. This modification significantly reduces noise.
What is Digital Kahler?
From Philipp Kahler's article for www.traders-mag.com, August 2008. "A Classic Indicator in a New Suit: Digital Stochastic"
Digital Indicators
Whenever you study the development of trading systems in particular, you will be struck in an extremely unpleasant way by the seemingly unmotivated indentations and changes in direction of each indicator. An experienced trader can recognise many false signals of the indicator on the basis of his solid background; a stupid trading system usually falls into any trap offered by the unclear indicator course. This is what motivated me to improve even further this and other indicators with the help of a relatively simple procedure. The goal of this development is to be able to use this indicator in a trading system with as few additional conditions as possible. Discretionary traders will likewise be happy about this clear course, which is not nerve-racking and makes concentrating on the essential elements of trading possible.
How Is It Done?
The digital stochastic is a child of the original indicator. We owe a debt of gratitude to George Lane for his idea to design an indicator which describes the position of the current price within the high-low range of the historical price movement. My contribution to this indicator is the changed pattern which improves the quality of the signal without generating too long delays in giving signals. The trick used to generate this “digital” behavior of the indicator. It can be used with most oscillators like RSI or CCI .
First of all, the original is looked at. The indicator always moves between 0 and 100. The precise position of the indicator or its course relative to the trigger line are of no interest to me, I would just like to know whether the indicator is quoted below or above the value 50. This is tantamount to the question of whether the market is just trading above or below the middle of the high-low range of the past few days. If the market trades in the upper half of its high-low range, then the digital stochastic is given the value 1; if the original stochastic is below 50, then the value –1 is given. This leads to a sequence of 1/-1 values – the digital core of the new indicator. These values are subsequently smoothed by means of a short exponential moving average . This way minor false signals are eliminated and the indicator is given its typical form.
Calculation
The calculation is simple
Step1 : create the CCI
Step 2 : Use CCI as Fast MA and smoothed CCI as Slow MA
Step 3 : Multiple the Slow and Fast MAs by their respective input ratios, and then divide by their sum. if the result is greater than 0, then the result is 1, if it's less than 0 then the result is -1, then chart the data
if ((slowr * slow_k + fastr * fast_k) / (fastr + slowr) > 50.0)
temp := 1
if ((slowr * slow_k + fastr * fast_k) / (fastr + slowr) < 50.0)
temp := -1
Step 4 : Profit
Other implementations of Digital Kahler
This is to better understand the process the DK process and it's result, and furthermore, I'm linking these because for many in the Forex community, they see DK filtered indicators as the best implementations of standard indicators.
MACD
VHF-Adaptive, Digital Kahler Variety RSI w/ Dynamic Zones
Included:
Bar coloring
Signals
Alerts
Loxx's Expanded Source Types
Loxx's Moving Averages
