state_space: State-space representation of a solved model

In qpmR: Quarterly Projection Models for Monetary Policy Analysis

State-space representation of a solved model

Description

Exposes the exact matrices qpmR itself uses for filtering, so other estimators and filters can be built on top of a solved model. The representation (in deviations from steady state) is

a_t = T a_{t-1} + R e_t, e_t ~ N(0, Qc)

y_t = Z a_t + d + u_t, u_t ~ N(0, H)

with d the steady state of the observables and P1 the stationary (Lyapunov) covariance used to initialize the filter.

Usage

state_space(solution, observables = NULL, measurement_error = 0, kappa = 1e+06)

Arguments

solution	A qpm_solution.
observables	Character vector of observed variables (a subset of the declared variables). Default: all declared variables.
measurement_error	Measurement-error standard deviation(s): a scalar recycled over observables, or a named vector.
kappa	Diffuse-prior variance scale for unit-root directions (only used when the model has unit roots).

Details

For stationary models P1 is the exact stationary covariance. When the model has unit roots (random-walk trends), an approximate diffuse initialization is used: P1 solves the Lyapunov equation for the slightly damped transition sqrt(1 - 1/kappa) * T, which reproduces the stationary covariance in stable directions and a variance of order kappa in unit-root directions, with the exact cross-coupling. Exact Durbin-Koopman diffuse recursions are on the roadmap.

Value

A list with elements T, R, Z, d, Qc, H, P1, vars_all, observables, diffuse, n_unit.

Examples

sol <- qpm_solve(qpm_template("bkl"))
ss <- state_space(sol, observables = c("pi", "i", "q"))
dim(ss$T); ss$d

qpmR documentation built on Sept. 29, 2026, 5:10 p.m.