bvarsv (version 1.0)

sim.var1.sv.tvp: Simulate from a VAR(1) with Stochastic Volatility and Time-Varying Parameters

Description

Simulate from a VAR(1) with Stochastic Volatility and Time-Varying Parameters

Usage

sim.var1.sv.tvp(B0 = NULL, A0 = NULL, Sig0 = NULL, Q = NULL, 
S = NULL, W = NULL, t = 500, init = 1000)

Arguments

B0

Initial values of mean parameters: Matrix of dimension $[M, M+1]$, where the first column holds the intercept vector and the other columns hold the matrix of first-order autoregressive coefficients. By default (NULL), B0 corresponds to $M = 2

A0

Initial values for (transformed) error correlation parameters: Vector of length $0.5*M*(M-1)$. Defaults to a vector of zeros.

Sig0

Initial values for log error term volatility parameters: Vector of length $M$. Defaults to a vector of zeros.

Q, S, W

Covariance matrices for the innovation terms in the time-varying parameters ($B, A, Sig$). The matrices are symmetric, with dimensions equal to the number of elements in $B, A$ and $Sig$, respectively. Default to diagonal matrices with very small terms (<

t

Number of time periods to simulate.

init

Number of draws to initialize simulation (to decrease the impact of starting values).

Value

• data
  Simulated data, with rows corresponding to time and columns corresponding to the $M$ system variables.
• Beta
  Array of dimension $[M, M+1, t]$. Submatrix $[,,l]$ holds the parameter matrix for time period $l$.
• H
  Array of dimension $[M, M, t]$. Submatrix $[,,l]$ holds the error term covariance matrix for period $l$.

References

Primiceri, G. (2005): ``Time Varying Structural Vector Autoregressions and Monetary Policy'', Review of Economic Studies 72, 821-852.

See Also

bvar.sv.tvp can be used to fit a model on data generated by sim.var1.sv.tvp. This can be a useful way to analyze the performance of the estimation methods.

Examples

# Generate data from a model with moderate time variation in the parameters 
# and error term variances
set.seed(5813)
sim <- sim.var1.sv.tvp(Q = 1e-5*diag(6), S = 1e-5*diag(1), W = 1e-5*diag(2))
# Plot both series
matplot(sim$data, type = "l")
# Plot AR(1) parameters of both equations
matplot(cbind(sim$Beta[1,2,], sim$Beta[2,3,]), type = "l")