Mean Shift Pivot ClusteringCore Concepts
According to Jeff Greenblatt in his book "Breakthrough Strategies for Predicting Any Market", Fibonacci and Lucas sequences are observed repeated in the bar counts from local pivot highs/lows. They occur from high to high, low to high, high to low, or low to high. Essentially, this phenomenon is observed repeatedly from any pivot points on any time frame. Greenblatt combines this observation with Elliott Waves to predict the price and time reversals. However, I am no Elliottician so it was not easy for me to use this in a practical manner. I decided to only use the bar count projections and ignore the price. I projected a subset of Fibonacci and Lucas sequences along with the Fibonacci ratios from each pivot point. As expected, a projection from each pivot point resulted in a large set of plotted data and looks like a huge gong show of lines. Surprisingly, I did notice clusters and have observed those clusters to be fairly accurate.
Fibonacci Sequence: 1, 2, 3, 5, 8, 13, 21, 34...
Lucas Sequence: 2, 1, 3, 4, 7, 11, 18, 29, 47...
Fibonacci Ratios (converted to whole numbers): 23, 38, 50, 61, 78, 127, 161...
Light Bulb Moment
My eyes may suck at grouping the lines together but what about clustering algorithms? I chose to use a gimped version of Mean Shift because it doesn't require me to know in advance how many lines to expect like K-Means. Mean shift is computationally expensive and with Pinescript's 500ms timeout, I had to make due without the KDE. In other words, I skipped the weighting part but I may try to incorporate it in the future. The code is from Harrison Kinsley . He's a fantastic teacher!
Usage
Search Radius: how far apart should the bars be before they are excluded from the cluster? Try to stick with a figure between 1-5. Too large a figure will give meaningless results.
Pivot Offset: looks left and right X number of bars for a pivot. Same setting as the default TradingView pivot high/low script.
Show Lines Back: show historical predicted lines. (These can change)
Use this script in conjunction with Fibonacci price retracement/extension levels and/or other support/resistance levels. If it's no where near a support/resistance and there's a projected time pivot coming up, it's probably a fake out.
Notes
Re-painting is intended. When a new pivot is found, it will project out the Fib/Lucas sequences so the algorithm will run again with additional information.
The script is for informational and educational purposes only.
Do not use this indicator by itself to trade!
Lucas
Lucas Numbers - Horizontal levels█ OVERVIEW
Lucas numbers are related to the Fibonacci numbers and calculated using them as well. It is an easy formula where you'd take the golden ration to the power of n which in the case of this script that would be the revolutions. This script plots Lucas numbers as horizontal price lines. To run this script, turn your "Auto" scale off, and keep your chart on "Log" scale. it is important to keep your "Auto" scale off to be able to view your chart without distortions.
Enjoy!
