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Transition probabilities encode the likelihood of staying in or switching between states. In the two-state volatility example, high self-loop probabilities (0.8 for Low, 0.7 for High) mean the system tends to remain in its current state.

Conditions: The market is modeled as a two-state Markov chain.; Self-transition probabilities are high relative to switching probabilities.

Transition probabilities encode the likelihood of staying in or switching between states. In the two-state volatility example, high self-loop probabilities (0.8 for Low, 0.7 for High) mean the system tends to remain in its current state.

Conditions: The market is modeled as a two-state Markov chain.; Self-transition probabilities are high relative to switching probabilities.

In practice, market regimes or states are rarely observed directly. They are hidden and must be inferred from noisy observable data, such as returns.

Conditions: Applies to Hidden Markov Models (HMMs) or latent variable models.; Observable outputs are noisy or smoothed.

In practice, market regimes or states are rarely observed directly. They are hidden and must be inferred from noisy observable data, such as returns.

Conditions: Applies to Hidden Markov Models (HMMs) or latent variable models.; Observable outputs are noisy or smoothed.