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Jurik Composite Fractal Behavior (CFB) on EMA [Loxx]

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Jurik Composite Fractal Behavior (CFB) on EMA [Loxx] is an exponential moving average with adaptive price trend duration inputs. This purpose of this indicator is to introduce the formulas for the calculation Composite Fractal Behavior. As you can see from the chart above, price reacts wildly to shifts in volatility--smoothing out substantially while riding a volatility wave and cutting sharp corners when volatility drops. Notice the chop zone on BTC around August 2021, this was a time of extremely low relative volatility.

This indicator uses three previous indicators from my public scripts. These are:

JCFBaux Volatility [Loxx]
Jurik Filter [Loxx]
Jurik Volty [Loxx]

The CFB is also related to the following indicator
Jurik Velocity ("smoother moment") [Loxx]

Now let's dive in...

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.

Modifications and improvements
1. Jurik's original calculation for CFB only allowed for depth lengths of 24, 48, 96, and 192. For theoretical purposes, this indicator allows for up to 20 different depth inputs to sample volatility. These depth lengths are

2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 512, 768, 1024, 1536

Including these additional length inputs is arguable useless, but they are are included for completeness of the algorithm.

2. The result of the CFB calculation is forced to be an integer greater than or equal to 1.

3. The result of the CFB calculation is double filtered using an advanced, (and adaptive itself) filtering algorithm called the Jurik Filter. This filter and accompanying internal algorithm are discussed above.

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