Parabolic SAR of KAMA [Loxx]

Parabolic SAR of KAMA attempts to reduce noise and volatility from regular Parabolic SAR in order to derive more accurate trends. In addition, and to further reduce noise and enhance trend identification, PSAR of KAMA includes two calculations of efficiency ratio: 1) price change adjusted for the daily volatility; or, 2) Jurik Fractal Dimension Adaptive (explained below)

What is PSAR?
The parabolic SAR indicator, developed by J. Wells Wilder, is used by traders to determine trend direction and potential reversals in price. The indicator uses a trailing stop and reverse method called "SAR," or stop and reverse, to identify suitable exit and entry points. Traders also refer to the indicator as to the parabolic stop and reverse, parabolic SAR, or PSAR.

What is KAMA?
Developed by Perry Kaufman, Kaufman's Adaptive Moving Average (KAMA) is a moving average designed to account for market noise or volatility. KAMA will closely follow prices when the price swings are relatively small and the noise is low. KAMA will adjust when the price swings widen and follow prices from a greater distance. This trend-following indicator can be used to identify the overall trend, time turning points and filter price movements.

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.

What is Jurik Fractal Dimension?
There is a weak and a strong way to measure the random quality of a time series.

The weak way is to use the random walk index (RWI). You can download it from the Omega web site. It makes the assumption that the market is moving randomly with an average distance D per move and proposes an amount the market should have changed over N bars of time. If the market has traveled less, then the action is considered random, otherwise it's considered trending.

The problem with this method is that taking the average distance is valid for a Normal (Gaussian) distribution of price activity. However, price action is rarely Normal, with large price jumps occuring much more frequently than a Normal distribution would expect. Consequently, big jumps throw the RWI way off, producing invalid results.

The strong way is to not make any assumption regarding the distribution of price changes and, instead, measure the fractal dimension of the time series. Fractal Dimension requires a lot of data to be accurate. If you are trading 30 minute bars, use a multi-chart where this indicator is running on 5 minute bars and you are trading on 30 minute bars.

Conclusion from the combined efforts explained above:
-PSAR is a tool that identifies trends
-To reduce noise and identify trends during periods of low volatility, we calculate a PSAR on KAMA
-To enhance noise and reduction and trend identification, we attempt to derive an efficiency ratio that is less reliant on a Normal (Gaussian) distribution of price

Included:
-Customization of all variables
-Select from two different ER calculation styles
-Multiple timeframe enabled

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What's new:
-Added a baseline. This baseline operates as a trend confirmation with PSAR of KAMA and vice versa. When the the baseline trend doesn't agree with the PSAR of KAMA trend, or vice versa, both the baseline and PSAR of KAMA's color turns white. This helps identify chop and no trade zones

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Small update to comment sections

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Add option to color bars

Here's an example of identifying a chop zone. This is one of various methods to identify sideways price movement.

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Small updates