Volatility clustering arises from simple state dependence in a Markov chain. It does not require heavy-tailed return distributions or complex non-linear dynamics.
Conditions: The underlying process follows a Markov chain with distinct states.; Returns within each state follow the same distribution.
Volatility clustering arises from simple state dependence in a Markov chain. It does not require heavy-tailed return distributions or complex non-linear dynamics.
Conditions: The underlying process follows a Markov chain with distinct states.; Returns within each state follow the same distribution.
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.