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"""
Regime-Switching Models for detecting structural breaks and transitions.
"""
import numpy as np
from typing import Dict, List, Optional, Tuple
from scipy import stats
class RegimeSwitchingModel:
"""
Markov Regime-Switching Model.
Models systems that switch between different regimes (e.g., peace/war,
stable/unstable) with different dynamics in each regime.
"""
def __init__(self, n_regimes: int, n_features: int):
"""
Initialize regime-switching model.
Parameters
----------
n_regimes : int
Number of regimes
n_features : int
Number of features
"""
self.n_regimes = n_regimes
self.n_features = n_features
# Regime-specific parameters
self.means = np.random.randn(n_regimes, n_features)
self.covariances = np.array([np.eye(n_features) for _ in range(n_regimes)])
# Transition matrix
self.transition_matrix = np.random.dirichlet(np.ones(n_regimes), size=n_regimes)
def set_parameters(
self,
means: np.ndarray,
covariances: np.ndarray,
transition_matrix: np.ndarray
) -> None:
"""
Set model parameters.
Parameters
----------
means : np.ndarray, shape (n_regimes, n_features)
Mean for each regime
covariances : np.ndarray, shape (n_regimes, n_features, n_features)
Covariance for each regime
transition_matrix : np.ndarray, shape (n_regimes, n_regimes)
Regime transition probabilities
"""
self.means = means
self.covariances = covariances
self.transition_matrix = transition_matrix
def fit(self, data: np.ndarray, max_iter: int = 100) -> None:
"""
Fit model using EM algorithm.
Parameters
----------
data : np.ndarray, shape (n_samples, n_features)
Time series data
max_iter : int
Maximum EM iterations
"""
n_samples = len(data)
for iteration in range(max_iter):
# E-step: compute regime probabilities
regime_probs = self._compute_regime_probabilities(data)
# M-step: update parameters
for k in range(self.n_regimes):
weights = regime_probs[:, k]
total_weight = weights.sum()
if total_weight > 0:
# Update mean
self.means[k] = np.sum(weights[:, np.newaxis] * data, axis=0) / total_weight
# Update covariance
diff = data - self.means[k]
self.covariances[k] = (weights[:, np.newaxis, np.newaxis] * \
(diff[:, :, np.newaxis] @ diff[:, np.newaxis, :])).sum(axis=0) / total_weight
# Update transition matrix
for i in range(self.n_regimes):
for j in range(self.n_regimes):
numerator = 0
denominator = 0
for t in range(n_samples - 1):
numerator += regime_probs[t, i] * regime_probs[t + 1, j]
denominator += regime_probs[t, i]
if denominator > 0:
self.transition_matrix[i, j] = numerator / denominator
# Normalize transition matrix rows
self.transition_matrix = self.transition_matrix / \
self.transition_matrix.sum(axis=1, keepdims=True)
def _compute_regime_probabilities(self, data: np.ndarray) -> np.ndarray:
"""
Compute regime probabilities using filtering.
Parameters
----------
data : np.ndarray
Data
Returns
-------
np.ndarray
Regime probabilities for each time step
"""
n_samples = len(data)
probs = np.zeros((n_samples, self.n_regimes))
# Compute likelihoods
likelihoods = np.zeros((n_samples, self.n_regimes))
for k in range(self.n_regimes):
likelihoods[:, k] = stats.multivariate_normal.pdf(
data,
mean=self.means[k],
cov=self.covariances[k]
)
# Forward filtering
probs[0] = likelihoods[0]
probs[0] /= probs[0].sum()
for t in range(1, n_samples):
probs[t] = likelihoods[t] * (probs[t-1] @ self.transition_matrix)
probs[t] /= probs[t].sum()
return probs
def predict_regime(self, data: np.ndarray) -> np.ndarray:
"""
Predict most likely regime at each time step.
Parameters
----------
data : np.ndarray
Time series data
Returns
-------
np.ndarray
Most likely regime at each time step
"""
probs = self._compute_regime_probabilities(data)
return np.argmax(probs, axis=1)
def detect_regime_shifts(
self,
data: np.ndarray,
confidence_threshold: float = 0.8
) -> List[Dict[str, any]]:
"""
Detect regime shifts in data.
Parameters
----------
data : np.ndarray
Time series data
confidence_threshold : float
Minimum confidence for regime shift
Returns
-------
list
List of detected shifts
"""
regimes = self.predict_regime(data)
probs = self._compute_regime_probabilities(data)
shifts = []
for t in range(1, len(regimes)):
if regimes[t] != regimes[t-1]:
confidence = probs[t, regimes[t]]
if confidence >= confidence_threshold:
shifts.append({
'time': t,
'from_regime': regimes[t-1],
'to_regime': regimes[t],
'confidence': confidence
})
return shifts
def forecast(
self,
current_regime: int,
n_steps: int,
n_simulations: int = 1000
) -> Tuple[np.ndarray, np.ndarray]:
"""
Forecast future states using Monte Carlo.
Parameters
----------
current_regime : int
Current regime
n_steps : int
Forecast horizon
n_simulations : int
Number of simulations
Returns
-------
tuple
(forecasts, regime_paths)
"""
forecasts = np.zeros((n_simulations, n_steps, self.n_features))
regime_paths = np.zeros((n_simulations, n_steps), dtype=int)
for sim in range(n_simulations):
regime = current_regime
for t in range(n_steps):
# Generate observation from current regime
forecasts[sim, t] = np.random.multivariate_normal(
self.means[regime],
self.covariances[regime]
)
regime_paths[sim, t] = regime
# Transition to next regime
regime = np.random.choice(
self.n_regimes,
p=self.transition_matrix[regime]
)
return forecasts, regime_paths
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