gmvarkit (version 1.0.3)

simulateGMVAR: Simulate from GMVAR process

Description

simulateGMVAR simulates observations from GMVAR process defined by object of class 'gmvar'.

Usage

simulateGMVAR(gmvar, nsimu, init_values = NULL, ntimes = 1)

Arguments

gmvar

object of class 'gmvar', generated by function fitGMVAR() or GMVAR().

nsimu

number of observations to be simulated.

init_values

a size \((pxd)\) matrix specifying the initial values to be used in the simulation, where d is the number of time series in the system. The last row will be used as initial values for the first lag, the second last row for second lag etc. If not specified, initial values will be generated from the stationary distribution.

ntimes

how many sets of simulations should be done?

Value

Returns a list with...

$sample

a size (nsimu\( x M\)) matrix containing the simulated values.

$component

a numeric vector the containing the information from which mixture component each value is generated from.

$mixing_weights

a size (nsimu\( x M\)) matrix containing the mixing weights corresponding to the sample so that \(i\):th column is for \(i\):th mixture component.

Or if ntimes>1 returns a size (nsimu\( x d x \)ntimes) 3D array containing the samples so that the i:th sample can be obtained from [, , i].

References

• Kalliovirta L., Meitz M. and Saikkonen P. 2016. Gaussian mixture vector autoregression. Journal of Econometrics, 192, 485-498.

Examples

# NOT RUN {
# These examples use the data 'eurusd' which comes with the
# package, but in a scaled form.
data <- cbind(10*eurusd[,1], 100*eurusd[,2])
colnames(data) <- colnames(eurusd)
set.seed(1)

# GMVAR(1,2), d=2 process:
params122 <- c(0.623, -0.129, 0.959, 0.089, -0.006, 1.006, 1.746,
 0.804, 5.804, 3.245, 7.913, 0.952, -0.037, -0.019, 0.943, 6.926,
 3.982, 12.135, 0.789)
mod122 <- GMVAR(data, p=1, M=2, params=params122)
sim122 <- simulateGMVAR(mod122, nsimu=500)
plot.ts(sim122$sample)
ts.plot(sim122$mixing_weights, col=c("blue", "red"), lty=2)
plot(sim122$component, type="l")

# GMVAR(2,2), d=2 model with mean-parametrization:
params222 <- c(-11.904, 154.684, 1.314, 0.145, 0.094, 1.292, -0.389,
 -0.070, -0.109, -0.281, 0.920, -0.025, 4.839, 11.633, 124.983, 1.248,
  0.077, -0.040, 1.266, -0.272, -0.074, 0.034, -0.313, 5.855, 3.570,
  9.838, 0.740)
mod222 <- GMVAR(data, p=2, M=2, params=params222, parametrization="mean")
sim222 <- simulateGMVAR(mod222, nsimu=500)
plot.ts(sim222$sample)
ts.plot(sim222$mixing_weights, col=c("blue", "red"), lty=2)
plot(sim222$component, type="l")

# GMVAR(2,2), d=2 model with AR-parameters restricted to be
# the same for both regimes:
C_mat <- rbind(diag(2*2^2), diag(2*2^2))
params222c <- c(1.031, 2.356, 1.786, 3.000, 1.250, 0.060, 0.036,
 1.335, -0.290, -0.083, -0.047, -0.356, 0.934, -0.152, 5.201, 5.883,
 3.560, 9.799, 0.368)
mod222c <- GMVAR(data, p=2, M=2, params=params222c, constraints=C_mat)
sim222c <- simulateGMVAR(mod222c, nsimu=100,
             init_values=matrix(c(30, 30, 80, 80), nrow=2))
plot.ts(sim222c$sample)
ts.plot(sim222c$mixing_weights, col=c("blue", "red"), lty=2)
plot(sim222$component, type="l")
# }