109 lines
3.2 KiB
Python
109 lines
3.2 KiB
Python
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"""
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Example: Hidden Markov Model for Regime Detection
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=================================================
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This example demonstrates using HMM to detect market regimes in synthetic data.
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"""
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import numpy as np
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import matplotlib.pyplot as plt
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from optimizr import HMM
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# Generate synthetic data with regime changes
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np.random.seed(42)
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# Regime 1: Bull market (positive drift, low volatility)
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bull_returns = np.random.normal(0.01, 0.015, 500)
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# Regime 2: Bear market (negative drift, high volatility)
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bear_returns = np.random.normal(-0.008, 0.03, 500)
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# Regime 3: Sideways (no drift, medium volatility)
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sideways_returns = np.random.normal(0.001, 0.02, 500)
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# Combine regimes
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returns = np.concatenate([bull_returns, bear_returns, sideways_returns])
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# True regime labels (for comparison)
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true_regimes = np.concatenate([
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np.zeros(500, dtype=int),
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np.ones(500, dtype=int),
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np.full(500, 2, dtype=int)
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])
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print("="*70)
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print("HMM Regime Detection Example")
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print("="*70)
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print(f"\nGenerated {len(returns)} returns across 3 regimes")
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print(f"Regime 1 (Bull): μ=0.01, σ=0.015")
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print(f"Regime 2 (Bear): μ=-0.008, σ=0.03")
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print(f"Regime 3 (Sideways): μ=0.001, σ=0.02")
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# Fit HMM
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print("\nFitting HMM with 3 states...")
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hmm = HMM(n_states=3)
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hmm.fit(returns, n_iterations=100, tolerance=1e-6)
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print("\nLearned Parameters:")
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print(f"Emission means: {hmm.emission_means_}")
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print(f"Emission stds: {hmm.emission_stds_}")
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print(f"\nTransition Matrix:")
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print(hmm.transition_matrix_)
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# Decode states
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print("\nDecoding state sequence...")
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predicted_states = hmm.predict(returns)
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# Compute accuracy (accounting for permutation)
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from scipy.stats import mode
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best_accuracy = 0
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best_mapping = {}
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import itertools
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for perm in itertools.permutations([0, 1, 2]):
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mapping = {i: perm[i] for i in range(3)}
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mapped_predictions = np.array([mapping[s] for s in predicted_states])
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accuracy = np.mean(mapped_predictions == true_regimes)
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if accuracy > best_accuracy:
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best_accuracy = accuracy
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best_mapping = mapping
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print(f"\nBest accuracy: {best_accuracy*100:.1f}%")
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print(f"State mapping: {best_mapping}")
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# Plot results
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fig, axes = plt.subplots(3, 1, figsize=(12, 10))
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# Plot returns
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axes[0].plot(returns, alpha=0.7, linewidth=0.5)
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axes[0].set_title("Synthetic Returns", fontsize=14, fontweight='bold')
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axes[0].set_ylabel("Return")
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axes[0].grid(True, alpha=0.3)
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# Plot true regimes
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for regime in range(3):
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mask = true_regimes == regime
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axes[1].fill_between(np.where(mask)[0], 0, 1, alpha=0.3, label=f'Regime {regime}')
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axes[1].set_title("True Regimes", fontsize=14, fontweight='bold')
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axes[1].set_ylabel("State")
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axes[1].set_ylim(-0.1, 1.1)
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axes[1].legend(loc='upper right')
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axes[1].grid(True, alpha=0.3)
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# Plot detected regimes
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for regime in range(3):
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mask = predicted_states == regime
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axes[2].fill_between(np.where(mask)[0], 0, 1, alpha=0.3, label=f'State {regime}')
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axes[2].set_title("Detected States (HMM)", fontsize=14, fontweight='bold')
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axes[2].set_xlabel("Time")
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axes[2].set_ylabel("State")
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axes[2].set_ylim(-0.1, 1.1)
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axes[2].legend(loc='upper right')
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axes[2].grid(True, alpha=0.3)
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plt.tight_layout()
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plt.savefig("hmm_regime_detection.png", dpi=150, bbox_inches='tight')
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print("\n✓ Plot saved to: hmm_regime_detection.png")
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plt.show()
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