dot-postARp: Draws from the posterior of the autoregressive paramteres of...

In RGAP: Production Function Output Gap Estimation

Draws from the posterior of the autoregressive paramteres of a stationary AR(p), p > 1 process without starting values.

Description

Draws from the posterior of the autoregressive paramteres of a stationary AR(p), p > 1 process without starting values.

Usage

.postARp(Y, phi, phi0, Q0, sigma, lb = -Inf, ub = Inf)

Arguments

Y	A Tn x 1 vector with the time series.
phi	a 1 x p vector containing the last draw of the autoregressive parameters \phi. p has to be larger than one.
phi0	a 1 x p vector containing the prior mean for phi.
Q0	a p x p matrix containing the prior precision for phi.
sigma	a scalar containing the innovation variance.
lb	(optional) 1 x p vector with lower bounds for phi.
ub	(optional) 1 x p vector with upper bounds for phi.

Details

The corresponding model is given by Y_t = \phi_1 Y_{t-1} + ... + \phi_p Y_{t-p} + e_t, where e_t ~ N(0, \sigma) with prior distribution p(\phi) = N(\phi_0, 1/Q_0 ).

The posterior draw is obtained via a Metropolis Hastings step with proposal density q = \prod_{t=p+1}^Tn p(Y_t, \phi, \sigma, Y_{t-1}, ..., Y_{t-p} ) which is known due to conjugacy. The acceptance probability is given by \alpha = \min{1, p(Y_1, ... Y_p | \phi_r, \sigma) / p(Y_1, ... Y_p | \phi_{r-1}, \sigma)} where the subscript r denotes the r-th draw. p(Y_1, ... Y_p | \phi_r, \sigma) is itself normal.

Stationarity and box constraints are enforced. If the constraints are not fulfilled, the last draw is returned.

RGAP documentation built on Nov. 2, 2023, 6:02 p.m.