[SGM Markov Chain]Introduction
A Markov chain is a mathematical model that describes a system evolving over time among a finite number of states. This model is based on the assumption that the future state of the system depends only on the current state and not on previous states, the so-called Markov property. In the context of financial markets, Markov chains can be used to model transitions between different market conditions, for example, the probability of a price going up after going up, or going down after going down.
Script Description
This script uses a Markov chain to calculate closing price transition probabilities across the entire accessible chart. It displays the probabilities of the following transitions:
- Up after Up (HH): Probability that the price rises after going up.
- Down after Down (BB): Probability that the price will go down after going down.
- Up after Down (HB): Probability that the price goes up after going down.
- Down after Up (BH): Probability that the price will go down after going up.
Features
- Color customization: Choose colors for each transition type.
- Table Position: Select the position of the probability display table (top/left, top/right, bottom/left, bottom/right).
Markovchain
Markov Chain Trend IndicatorOverview
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.
How Traders Can Use It
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
Add the Markov Chain Trend Indicator to your TradingView chart.
Observe the background color to quickly identify the current market state:
Green for Uptrend, Red for Downtrend, Gray for Sideways
Check the dashboard label to see the probabilities of transitioning to each state.
Use these probabilities to anticipate market movements and adjust your trading strategy accordingly.
Combine the indicator with other technical analysis tools for more robust decision-making.
Function - simple* Markov Chain Monte Carlo Simulation (MCMC)Example function of a markov chain monte carlo simulation.
