fit_kalman¶

Defined in fynance.features.filters

fit_kalman(y, G, F, *, fit_W=True, fit_V=True, W0=None, V0=None, m0=None, C0=None)[source]

Estimate Kalman filter noise covariances by maximum likelihood.

Optimises W and/or V via the prediction-error log-likelihood computed by kalman_loglikelihood. Parameters are searched in log-space to guarantee positive-definiteness for diagonal matrices.

Only diagonal W and V are supported for estimation. Pass fixed non-diagonal matrices through W0 / V0 with fit_W=False / fit_V=False.

Parameters:

ynp.ndarray of shape (T, n): Observed data.
Gnp.ndarray of shape (n, n): State transition matrix (fixed).
Fnp.ndarray of shape (n, n): Observation matrix (fixed).
fit_Wbool, optional: Whether to estimate W (default True).
fit_Vbool, optional: Whether to estimate V (default True).
W0np.ndarray of shape (n, n), optional: Initial / fixed W. If fit_W=False this value is used as-is. Defaults to identity.
V0np.ndarray of shape (n, n), optional: Initial / fixed V. If fit_V=False this value is used as-is. Defaults to identity.
m0np.ndarray of shape (n,), optional: Initial state mean (default: zeros).
C0np.ndarray of shape (n, n), optional: Initial state covariance (default: identity).

Returns:

dict with keys:

'W' : np.ndarray — estimated (or fixed) process noise covariance.
'V' : np.ndarray — estimated (or fixed) observation noise covariance.
'loglik' : float — log-likelihood at the optimum.
'success' : bool — whether the optimizer converged.

Examples

>>> import numpy as np
>>> rng = np.random.default_rng(42)
>>> n, T = 1, 200
>>> W_true = np.eye(n) * 0.5
>>> V_true = np.eye(n) * 1.0
>>> x = np.cumsum(rng.multivariate_normal(np.zeros(n), W_true, T), axis=0)
>>> y = x + rng.multivariate_normal(np.zeros(n), V_true, T)
>>> G = F = np.eye(n)
>>> result = fit_kalman(y, G, F)
>>> result['success']
True
>>> result['W'].shape
(1, 1)