Text

Enforcing Stationarity through the Prior in Vector Autoregressions

Stationarity is a very common assumption in time series analysis. A vector autoregressive process is stable if and only if the roots of its characteristic equation lie outside the unit circle, constraining the autoregressive coefficient matrices to lie in the stationary region. However, the stationary region has a highly complex geometry which impedes specification of a prior distribution. In this work, an unconstrained reparameterization of a stationary vector autoregression is presented. The new parameters are partial autocorrelation matrices, which are interpretable, and can be transformed bijectively to the space of unconstrained square matrices through a simple mapping of their singular values. This transformation preserves various structural forms of the partial autocorrelation matrices and readily facilitates specification of a prior. Properties of this prior are described along with an important special case which is exchangeable with respect to the order of the elements in the observation vector. Posterior inference and computation are described and implemented using Hamiltonian Monte Carlo via Stan. The prior and inferential procedures are illustrated with an application to a macroeconomic time series which highlights the benefits of enforcing stationarity and encouraging shrinkage toward a sensible parametric structure. Supplementary materials for this article are available online.

Ketersediaan

Informasi Detail

Judul Seri

JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS; Vol.32 No.1 March 2023

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 74-83

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

VECTOR AUTOREGRESSIVE MODEL
STAN
PARTIAL AUTOCORRELATION MATRIX
UNCONSTRAINED REPARAMETERIZATION

Info Detail Spesifik

https://doi.org/10.1080/10618600.2022.2079648

Pernyataan Tanggungjawab

Sarah E. Heaps

Versi lain/terkait

Lampiran Berkas

Komentar