Leavitt Convolution Probability

Technical Analysis of Markets with Leavitt Market Projections and Associated Convolution Probability

The aim of this study is to present an innovative approach to market analysis based on the research "Leavitt Market Projections." This technical tool combines one indicator and a probability function to enhance the accuracy and speed of market forecasts.

Key Features

Advanced Indicators: the script includes the Convolution line and a probability oscillator, designed to anticipate market changes. These indicators provide timely signals and offer a clear view of price dynamics.

Convolution Probability Function: The Convolution Probability (CP) is a key element of the script. A significant increase in this probability often precedes a market decline, while a decrease in probability can signal a bullish move. The Convolution Probability Function:

• At each bar, i, the linear regression routine finds the two parameters for the straight line: y=mi​x+bi​.
  
• Standard deviations can be calculated from the sequence of slopes, {mi​}, and intercepts, {bi​}.
  
• Each standard deviation has a corresponding probability.
  
• Their adjusted product is the Convolution Probability, CP. The construction of the Convolution Probability is straightforward. The adjusted product is the probability of one times 1− the probability of the other.
  

Customizable Settings: Users can define oversold and overbought levels, as well as set an offset for the linear regression calculation. These options allow for tailoring the script to individual trading strategies and market conditions.

Statistical Analysis: Each analyzed bar generates regression parameters that allow for the calculation of standard deviations and associated probabilities, providing an in-depth view of market dynamics.

The results from applying this technical tool show increased accuracy and speed in market forecasts. The combination of Convolution indicator and the probability function enables the identification of turning points and the anticipation of market changes.

Additional information:

• Leavitt, in his study, considers the SPY chart.
  
• When the Convolution Probability (CP) is high, it indicates that the probability P1​ (related to the slope) is high, and conversely, when CP is low, P1​ is low and P2 is high.
  
• For the calculation of probability, an approximate formula of the Cumulative Distribution Function (CDF) has been used, which is given by: CDF(x)=21​(1+erf(σ2​x−μ​)) where μ is the mean and σ is the standard deviation.
  
• For the calculation of probability, the formula used in this script is: 0.5 * (1 + (math.sign(zSlope) * math.sqrt(1 - math.exp(-0.5 * zSlope * zSlope))))
  

Conclusions

This study presents the approach to market analysis based on the research "Leavitt Market Projections." The script combines Convolution indicator and a Probability function to provide more precise trading signals. The results demonstrate greater accuracy and speed in market forecasts, making this technical tool a valuable asset for market participants.