OPEN-SOURCE SCRIPT

# Markov Chain Trend Indicator

Overview
The Markov Chain Trend Indicator utilizes the principles of Markov Chain processes to analyze stock price movements and predict future trends. By calculating the probabilities of transitioning between different market states (Uptrend, Downtrend, and Sideways), this indicator provides traders with valuable insights into market dynamics.

Key Features
• State Identification: Differentiates between Uptrend, Downtrend, and Sideways states based on price movements.
• Transition Probability Calculation: Calculates the probability of transitioning from one state to another using historical data.
• Real-time Dashboard: Displays the probabilities of each state on the chart, helping traders make informed decisions.
• Background Color Coding: Visually represents the current market state with background colors for easy interpretation.

Concepts Underlying the Calculations
• Markov Chains: A stochastic process where the probability of moving to the next state depends only on the current state, not on the sequence of events that preceded it.
• Logarithmic Returns: Used to normalize price changes and identify states based on significant movements.
• Transition Matrices: Utilized to store and calculate the probabilities of moving from one state to another.

How It Works
The indicator first calculates the logarithmic returns of the stock price to identify significant movements. Based on these returns, it determines the current state (Uptrend, Downtrend, or Sideways). It then updates the transition matrices to keep track of how often the price moves from one state to another. Using these matrices, the indicator calculates the probabilities of transitioning to each state and displays this information on the chart.

Traders can use the Markov Chain Trend Indicator to:
• Identify Market Trends: Quickly determine if the market is in an uptrend, downtrend, or sideways state.
• Predict Future Movements: Use the transition probabilities to forecast potential market movements and make informed trading decisions.
• Enhance Trading Strategies: Combine with other technical indicators to refine entry and exit points based on predicted trends.

Example Usage Instructions
2. Observe the background color to quickly identify the current market state:
Green for Uptrend, Red for Downtrend, Gray for Sideways
3. Check the dashboard label to see the probabilities of transitioning to each state.