Musashi_Fractal_Dimension === Musashi-Fractal-Dimension ===
This tool is part of my research on the fractal nature of the markets and understanding the relation between fractal dimension and chaos theory.
To take full advantage of this indicator, you need to incorporate some principles and concepts:
- Traditional Technical Analysis is linear and Euclidean, which makes very difficult its modeling.
- Linear techniques cannot quantify non-linear behavior
- Is it possible to measure accurately a wave or the surface of a mountain with a simple ruler?
- Fractals quantify what Euclidean Geometry can’t, they measure chaos, as they identify order in apparent randomness.
- Remember: Chaos is order disguised as randomness.
- Chaos is the study of unstable aperiodic behavior in deterministic non-linear dynamic systems
- Order and randomness can coexist, allowing predictability.
- There is a reason why Fractal Dimension was invented, we had no way of measuring fractal-based structures.
- Benoit Mandelbrot used to explain it by asking: How do we measure the coast of Great Britain?
- An easy way of getting the need of a dimension in between is looking at the Koch snowflake.
- Market prices tend to seek natural levels of ranges of balance. These levels can be described as attractors and are determinant.
Fractal Dimension Index ('FDI')
Determines the persistence or anti-persistence of a market.
- A persistent market follows a market trend. An anti-persistent market results in substantial volatility around the trend (with a low r2), and is more vulnerable to price reversals
- An easy way to see this is to think that fractal dimension measures what is in between mainstream dimensions. These are:
- One dimension: a line
- Two dimensions: a square
- Three dimensions: a cube.
--> This will hint you that at certain moment, if the market has a Fractal Dimension of 1.25 (which is low), the market is behaving more “line-like”, while if the market has a high Fractal Dimension, it could be interpreted as “square-like”.
- 'FDI' is trend agnostic, which means that doesn't consider trend. This makes it super useful as gives you clean information about the market without trying to include trend stuff.
Question: If we have a game where you must choose between two options.
1. a horizontal line
2. a vertical line.
Each iteration a Horizontal Line or a Square will appear as continuation of a figure. If it that iteration shows a square and you bet vertical you win, same as if it is horizontal and it is a line.
- Wouldn’t be useful to know that Fractal dimension is 1.8? This will hint square. In the markets you can use 'FD' to filter mean-reversal signals like Bollinger bands, stochastics, Regular RSI divergences, etc.
- Wouldn’t be useful to know that Fractal dimension is 1.2? This will hint Line. In the markets you can use 'FD' to confirm trend following strategies like Moving averages, MACD, Hidden RSI divergences.
Calculation method:
Fractal dimension is obtained from the ‘hurst exponent’.
'FDI' = 2 - 'Hurst Exponent'
Musashi version of the Classic 'OG' Fractal Dimension Index ('FDI')
- By default, you get 3 fast 'FDI's (11,12,13) + 1 Slow 'FDI' (21), their interaction gives useful information.
- Fast 'FDI' cross will give you gray or red dots while Slow 'FDI' cross with the slowest of the fast 'FDI's will give white and orange dots. This are great to early spot trend beginnings or trend ends.
- A baseline (purple) is also provided, this is calculated using a 21 period Bollinger bands with 1.618 'SD', once calculated, you just take midpoint, this is the 'TDI's (Traders Dynamic Index) way. The indicator will print purple dots when Slow 'FDI' and baseline crosses, I see them as Short-Term cycle changes.
- Negative slope 'FDI' means trending asset.
- Positive most of the times hints correction, but if it got overextended it might hint a rocket-shot.
TDI Ranges:
- 'FDI' between 1.0≤ 'FDI' ≤1.4 will confirm trend following continuation signals.
- 'FDI' between 1.6≥ 'FDI' ≥2.0 will confirm reversal signals.
- 'FDI' == 1.5 hints a random unpredictable market.
Fractal Attractors
- As you must know, fractals tend orbit certain spots, this are named Attractors, this happens with any fractal behavior. The market of course also shows them, in form of Support & Resistance, Supply Demand, etc. It’s obvious they are there, but now we understand that they’re not linear, as the market is fractal, so simple trendline might not be the best tool to model this.
- I’ve noticed that when the Musashi version of the 'FDI' indicator start making a cluster of multicolor dots, this end up being an attractor, I tend to draw a rectangle as that area as price tend to come back (I still researching here).
Extra useful stuff
- Momentum / speed: Included by checking RSI Study in the indicator properties. This will add two RSI’s (9 and a 7 periods) plus a baseline calculated same way as explained for 'FDI'. This gives accurate short-term trends. It also includes RSI divergences (regular and hidden), deactivate with a simple check in the RSI section of the properties.
- BBWP (Bollinger Bands with Percentile): Efficient way of visualizing volatility as the percentile of Bollinger bands expansion. This line varies color from Iced blue when low volatility and magma red when high. By default, comes with the High vols deactivated for better view of 'FDI' and RSI while all studies are included. DDWP is trend agnostic, just like 'FDI', which make it very clean at providing information.
- Ultra Slow 'FDI': I noticed that while using BBWP and RSI, the indicator gets overcrowded, so there is the possibility of adding only one 'FDI' + its baseline.
Final Note: I’ve shown you few ways of using this indicator, please backtest before using in real trading. As you know trading is more about risk and trade management than the strategy used. This still a work in progress, I really hope you find value out of it. I use it combination with a tool named “Musashi_Katana” (also found in TradingView).
Best!
Musashi
FDI
FDI-Adaptive Non-Lag Moving Average [Loxx]FDI-Adaptive Non-Lag Moving Average is a Fractal Dimension Index adaptive Non-Lag moving Average. This acts more like a trend coloring indictor with gradient coloring.
What is the Fractal Dimension Index?
The goal of the fractal dimension index is to determine whether the market is trending or in a trading range. It does not measure the direction of the trend. A value less than 1.5 indicates that the price series is persistent or that the market is trending. Lower values of the FDI indicate a stronger trend. A value greater than 1.5 indicates that the market is in a trading range and is acting in a more random fashion.
Included
Bar coloring
Loxx's Expanded Source Types
Fractal-Dimension-Index-Adaptive Trend Cipher Candles [Loxx]Fractal-Dimension-Index-Adaptive Trend Cipher Candles is a candle coloring indicator that shows both trend and trend exhaustion using Fractal Dimension Index Adaptivity. To do this, we first calculate the dynamic period outputs from the FDI algorithm and then we injection those period inputs into a correlation function that correlates price input price to the candle index. The closer the correlation is to 1, the lighter the green color until the color turns yellow, sometimes, indicating upward price exhaustion. The closer the correlation is to -1, the lighter the red color until it reaches Fuchsia color indicating downward price exhaustion. Green means uptrend, red means downtrend, yellow means reversal from uptrend to downtrend, fuchsia means reversal from downtrend to uptrend.
What is the Fractal Dimension Index?
The goal of the fractal dimension index is to determine whether the market is trending or in a trading range. It does not measure the direction of the trend. A value less than 1.5 indicates that the price series is persistent or that the market is trending. Lower values of the FDI indicate a stronger trend. A value greater than 1.5 indicates that the market is in a trading range and is acting in a more random fashion.
Included
Loxx's Expanded Source Types
Related indicators:
Adaptive Trend Cipher loxx]
CFB-Adaptive Trend Cipher Candles
Dynamic Zones Polychromatic Momentum Candles
RSI Precision Trend Candles
FDI-Adaptive Fisher Transform [Loxx]FDI-Adaptive Fisher Transform is a Fractal Dimension Adaptive Fisher Transform indicator.
What is the Fractal Dimension Index?
The goal of the fractal dimension index is to determine whether the market is trending or in a trading range. It does not measure the direction of the trend. A value less than 1.5 indicates that the price series is persistent or that the market is trending. Lower values of the FDI indicate a stronger trend. A value greater than 1.5 indicates that the market is in a trading range and is acting in a more random fashion.
What is Fisher Transform?
The Fisher Transform is a technical indicator created by John F. Ehlers that converts prices into a Gaussian normal distribution.
The indicator highlights when prices have moved to an extreme, based on recent prices. This may help in spotting turning points in the price of an asset. It also helps show the trend and isolate the price waves within a trend.
Included:
Zero-line and signal cross options for bar coloring
Customizable overbought/oversold thresh-holds
Alerts
Signals
End-pointed SSA of FDASMA [Loxx]End-pointed SSA of FDASMA is a modification of Fractal-Dimension-Adaptive SMA (FDASMA) using End-Pointed Singular Spectrum Analysis. This is a multilayer adaptive indicator.
What is the Fractal Dimension Index?
The goal of the fractal dimension index is to determine whether the market is trending or in a trading range. It does not measure the direction of the trend. A value less than 1.5 indicates that the price series is persistent or that the market is trending. Lower values of the FDI indicate a stronger trend. A value greater than 1.5 indicates that the market is in a trading range and is acting in a more random fashion.
See here for more info:
Fractal-Dimension-Adaptive SMA (FDASMA) w/ DSL
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
Fractal Dimension Index Adaptive Period [Loxx]Fractal Dimension Index Adaptive Period is the adaptive period out of Fractal Dimension Index Adaptivity. This isn't an indicator that shows a signal, instead, it's to be used as auxiliary support and an educational tool to create other indicators. This value can be injected into other indicators to make those indicators Fractal Dimension Index Adaptive.
What is the Fractal Dimension Index?
The goal of the fractal dimension index is to determine whether the market is trending or in a trading range. It does not measure the direction of the trend. A value less than 1.5 indicates that the price series is persistent or that the market is trending. Lower values of the FDI indicate a stronger trend. A value greater than 1.5 indicates that the market is in a trading range and is acting in a more random fashion.
Included
Loxx's Expanded Source Types
Fractal-Dimension-Adaptive SMA (FDASMA) w/ DSL [Loxx]Fractal-Dimension-Adaptive SMA (FDASMA) w/ DSL is a fractal-dimension-index-adaptive SMA. The SMA is accelerated during a trend and slowed down during a sideways market, so as to avoid false signals. This indicator uses the fractal dimension to compute an ingest period length into the SMA to output the FDASMA.
What is the Fractal Dimension Index?
The goal of the fractal dimension index is to determine whether the market is trending or in a trading range. It does not measure the direction of the trend. A value less than 1.5 indicates that the price series is persistent or that the market is trending. Lower values of the FDI indicate a stronger trend. A value greater than 1.5 indicates that the market is in a trading range and is acting in a more random fashion.
What are DSL Discontinued Signal Line?
A lot of indicators are using signal lines in order to determine the trend (or some desired state of the indicator) easier. The idea of the signal line is easy : comparing the value to it's smoothed (slightly lagging) state, the idea of current momentum/state is made.
Discontinued signal line is inheriting that simple signal line idea and it is extending it : instead of having one signal line, more lines depending on the current value of the indicator.
"Signal" line is calculated the following way :
When a certain level is crossed into the desired direction, the EMA of that value is calculated for the desired signal line
When that level is crossed into the opposite direction, the previous "signal" line value is simply "inherited" and it becomes a kind of a level
This way it becomes a combination of signal lines and levels that are trying to combine both the good from both methods.
In simple terms, DSL uses the concept of a signal line and betters it by inheriting the previous signal line's value & makes it a level.
Included
2 Signal types
Alerts
Loxx's Expanded Source Types
Bar coloring
