Markov Chain Forecasting Model

Markov Chain Forecasting Model (Simplified)

Markov Chain Forecasting Model (Simplified)

Model Setup

Transition Probability Matrix (P)

Enter the probability of transitioning from ROW state to COLUMN state in one time step. Each row must sum to 1 (or 100%).

Initial State Vector (S0)

Enter the initial distribution of the system across states (probabilities or proportions). Must sum to 1 (or 100%).

Simplified Model: Assumes a time-homogeneous, first-order Markov chain. Matrix validation is basic.

Forecasted State Distributions & Steady State

Define model parameters and click "Run Forecast" to see results.

Forecasted State Probabilities Over Time

Steady-State Distribution (Long-Term Probabilities)

Calculated iteratively...
StateSteady-State Probability

Interpretation & Export

Interpreting Markov Chain Forecasts

A Markov chain models a sequence of possible events (states) where the probability of each event depends only on the state attained in the previous event.

  • Transition Probability Matrix (P): Shows the likelihood of moving from one state to another in a single time step. Pij is the probability of moving from state i to state j.
  • Initial State Vector (S0): Represents the distribution of the system across states at the beginning (time t=0).
  • Forecasted State Distributions (St): The vector St = S0 * Pt (or St = St-1 * P) shows the probability distribution of being in each state after t time steps.
  • Steady-State Distribution (π): If the chain is regular (ergodic), it will eventually reach a stable distribution where further transitions do not change the probabilities of being in each state (i.e., π = π * P). This represents the long-term behavior of the system.

Applications: Market share analysis, customer loyalty/churn, equipment reliability, weather forecasting, genetics, etc.

Export Results

© Markov Chain Forecasting Model (Simplified). For educational purposes.