ssfortran.FilterResults#

class ssfortran.FilterResults(llf, llf_obs, nobs_diffuse, k_diffuse, t_steady, predicted_state, predicted_state_cov, predicted_diffuse_state_cov, filtered_state, filtered_state_cov, forecasts, forecasts_error, forecasts_error_cov, forecasts_error_diffuse_cov, forecasts_error_cov_inv, kalman_gain, standardized_forecasts_error, diagnostic_start)#

Output of the Kalman filter (DK §4.3, §5.2).

Arrays have time as the last axis and 0-based periods: column t of predicted_state is \(a_{t+1}\) in DK’s 1-based notation, and its last column is the one-step prediction past the sample.

Attributes:

llffloat: Log likelihood (DK eq. 7.2); the diffuse log likelihood (DK §7.2.2) with diffuse states.
llf_obsndarray, shape (n,): Contribution of each period to llf.
nobs_diffuseint: Number of periods with a diffuse state (DK’s d).
k_diffuseint: Rank of the diffuse part of the initial variance.
t_steadyint: First period (1-based) that used the steady-state shortcut, or 0.
predicted_statendarray, shape (m, n+1): \(a_t = E(\alpha_t | y_1, \dots, y_{t-1})\).
predicted_state_covndarray, shape (m, m, n+1): \(P_t\), or \(P_{*,t}\) in diffuse periods.
predicted_diffuse_state_covndarray, shape (m, m, n+1): \(P_{\infty,t}\); zero after the diffuse periods.
filtered_statendarray, shape (m, n): \(a_{t|t}\) (DK eq. 4.24).
filtered_state_covndarray, shape (m, m, n): \(P_{t|t}\).
forecastsndarray, shape (p, n): One-step predictions \(d_t + Z_t a_t\).
forecasts_errorndarray, shape (p, n): Innovations \(v_t\); NaN where y is missing.
forecasts_error_covndarray, shape (p, p, n): \(F_t\), in the original coordinates also in univariate periods.
forecasts_error_diffuse_covndarray, shape (p, p, n): \(F_{\infty,t} = Z_t P_{\infty,t} Z_t'\).
forecasts_error_cov_invndarray, shape (p, p, n): \(F_t^{-1}\) over the observed elements, zero-padded; NaN in periods processed element by element.
kalman_gainndarray, shape (m, p, n): \(K_t = T_t P_t Z_t' F_t^{-1}\); NaN in periods processed element by element.
standardized_forecasts_errorndarray, shape (p, n): \(L_t^{-1} v_t\) with \(F_t = L_t L_t'\) (DK §7.5); NaN where missing or diffuse.
diagnostic_startint: First 0-based period after the burn-in and the diffuse periods.