Regime Switching Deep Dive

Markets alternate between distinct economic regimes. A 2-state Hamilton model assigns each period to a hidden state — calm / bull vs crisis / bear — with Markov transition probabilities.

Crisis share

Ergodic π(calm)

70.0%

Avg calm run

33 d

Avg crisis run

14 d

Return Series Coloured by Regime

Cumulative Return by Regime

Bimodal Return Distribution

Transition Matrix Heatmap

μ₀ (calm mean)0.04

σ₀ (calm vol)0.60

μ₁ (crisis mean)-0.08

σ₁ (crisis vol)1.80

p₀₀ (stay calm)0.970

p₁₁ (stay crisis)0.930

Observations1000

Seed42

r_{t} ∣ S_{t} = j \sim N (μ_{j}, σ_{j}^{2})

P (S_{t} = j ∣ S_{t - 1} = i) = p_{ij}; P = (p_{00} 1 - p_{11} 1 - p_{00} p_{11})

π_{0} = \frac{1 - p _{11}}{2 - p _{00} - p _{11}}; E [calm duration] = \frac{1}{1 - p _{00}}

Reduce p₀₀ to trigger frequent switches from calm to crisis. The bimodal histogram reveals well-separated distributions when σ₁ ≫ σ₀. The transition matrix heatmap summarises the full Markov dynamics at a glance.

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