Markov Chain Trend ProbabilityA Markov Chain is a mathematical model that predicts future states based on the current state, assuming that the future depends only on the present (not the past). Originally developed by Russian mathematician Andrey Markov, this concept is widely used in:
Finance: Risk modeling, portfolio optimization, credit scoring, algorithmic trading
Weather Forecasting: Predicting sunny/rainy days, temperature patterns, storm tracking
Here's an example of a Markov chain: If the weather is sunny, the probability that will be sunny 30 min later is say 90%. However, if the state changes, i.e. it starts raining, how the probability that will be raining 30 min later is say 70% and only 30% sunny.
Similar concept can be applied to markets price action and trends.
Mathematical Foundation
The core principle follows the Markov Property: P(X_{t+1}|X_t, X_{t-1}, ..., X_0) = P(X_{t+1}|X_t)
Transition Matrix :
-------------Next State
Current----
--------P11 P12
-----P21 P22
Probability Calculations:
P(Up→Up) = Count(Up→Up) / Count(Up states)
P(Down→Down) = Count(Down→Down) / Count(Down states)
Steady-state probability: π = πP (where π is the stationary distribution)
State Definition:
State = UPTREND if (Price_t - Price_{t-n})/ATR > threshold
State = DOWNTREND if (Price_t - Price_{t-n})/ATR < -threshold
How It Works in Trading
This indicator applies Markov Chain theory to market trends by:
Defining States: Classifies market conditions as UPTREND or DOWNTREND based on price movement relative to ATR (Average True Range)
Learning Transitions: Analyzes historical data to calculate probabilities of moving from one state to another
Predicting Probabilities: Estimates the likelihood of future trend continuation or reversal
How to Use
Parameters:
Lookback Period: Number of bars to analyze for trend detection (default: 14)
ATR Threshold: Sensitivity multiplier for state changes (default: 0.5)
Historical Periods: Sample size for probability calculations (default: 33)
Trading Applications:
Trend confirmation for entry/exit decisions
Risk assessment through probability analysis
Market regime identification
Early warning system for potential trend reversals
The indicator works on any timeframe and asset class. Enjoy!
