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SteadyStateBVAR: Bayesian Vector Autoregressions with Steady-State Priors

Source: R/SteadyStateBVAR-package.R
SteadyStateBVAR-package.Rd

Provides estimation of Bayesian vector autoregression (BVAR) models with steady-state priors via 'Stan', along with functions for unconditional and conditional forecasting, as well as impulse response analysis. For details on the steady-state BVAR model see Villani (2009) doi:10.1002/jae.1065 .

Details

The steady-state BVAR model takes the form

$$y_t = \Psi d_t + \Pi_1(y_{t-1}-\Psi d_{t-1})+\dots+\Pi_p(y_{t-p}-\Psi d_{t-p})+u_t$$

where \(y_t\) is an \(k\)-dimensional vector of endogenous variables at time \(t\), and \(d_t\) is a \(q\)-dimensional vector of deterministic (exogenous) variables at time \(t\). Here \(\Pi_\ell\) for \(\ell=1,\dots,p\) is a \((k \times k)\) matrix of autoregressive parameters, and \(\Psi\) is a \((k \times q)\) matrix of steady-state parameters. Now

$$\mathrm{E}(y_t)=\mu_t=\Psi d_t$$

is the unconditional mean, or the steady state of the process.

Regarding the (reduced-form) innovations \(u_t\), this package supports three specifications

  1. \(u_t \overset{\text{iid}}{\sim} \mathrm{N_k}(0,\Sigma_u)\)

  2. \(u_t \sim \mathrm{N_k}(0,\Sigma_{u,t})\), where \(\Sigma_{u,t}\) is driven by a latent Random Walk process (stochastic volatility)

  3. \(u_t \sim \mathrm{N_k}(0,\Sigma_{u,t})\), where \(\Sigma_{u,t}\) is driven by a latent AR(1) process (stochastic volatility)

For more information, please see the package vignettes

  1. vignette("SteadyStateBVAR-intro")

  2. vignette("Homoscedastic-steady-state-BVAR")

  3. vignette("RW-stochastic-volatility-steady-state-BVAR")

  4. vignette("AR1-stochastic-volatility-steady-state-BVAR")

References

Villani, M. (2009). Steady-state priors for vector autoregressions. Journal of Applied Econometrics, 24(4), pp. 630–650.

See also

Useful links:

Author

Maintainer: Mark Becker mark.jw.becker@gmail.com [copyright holder]

Authors: