simulate.gsmvar: Simulate method for class 'gsmvar' objects

In saviviro/gmvarkit: Estimate Gaussian and Student's t Mixture Vector Autoregressive Models

Simulate method for class 'gsmvar' objects

Description

simulate.gsmvar is a simulate method for class 'gsmvar' objects. It allows to simulate observations from a GMVAR, StMVAR, or G-StMVAR process.

Usage

## S3 method for class 'gsmvar'
simulate(
  object,
  nsim = 1,
  seed = NULL,
  ...,
  init_values = NULL,
  init_regimes = 1:sum(gsmvar$model$M),
  ntimes = 1,
  drop = TRUE,
  girf_pars = NULL
)

Arguments

object	an object of class 'gsmvar', typically created with fitGSMVAR or GSMVAR.
nsim	number of observations to be simulated.
seed	set seed for the random number generator?
...	currently not in use.
init_values	a size (pxd) matrix specifying the initial values, 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 drawn according to mixture distribution specifed by the argument init_regimes.
init_regimes	a numeric vector of length at most M and elements in 1,...,M specifying the regimes from which the initial values should be generated from. The initial values will be generated from a mixture distribution with the mixture components being the stationary distributions of the specific regimes and the (proportional) mixing weights given by the mixing weight parameters of those regimes. Note that if init_regimes=1:M, the initial values are generated from the stationary distribution of the process and if init_regimes=m, the initial value are generated from the stationary distribution of the mth regime. Ignored if the argument init_values is specified.
ntimes	how many sets of simulations should be performed?
drop	if TRUE (default) then the components of the returned list are coerced to lower dimension if ntimes==1, i.e., $sample and $mixing_weights will be matrices, and $component will be vector.
girf_pars	This argument is used internally in the estimation of generalized impulse response functions (see ?GIRF). You should ignore it (specifying something else than null to it will change how the function behaves).

Details

The argument ntimes is intended for forecasting: a GMVAR, StMVAR, or G-StMVAR process can be forecasted by simulating its possible future values. One can easily perform a large number simulations and calculate the sample quantiles from the simulated values to obtain prediction intervals (see the forecasting example).

Value

If drop==TRUE and ntimes==1 (default): $sample, $component, and $mixing_weights are matrices. Otherwise, returns a list with...

$sample

a size (nsim x d x ntimes) array containing the samples: the dimension [t, , ] is the time index, the dimension [, d, ] indicates the marginal time series, and the dimension [, , i] indicates the i:th set of simulations.

$component

a size (nsim x ntimes) matrix containing the information from which mixture component each value was generated from.

$mixing_weights

a size (nsim x M x ntimes) array containing the mixing weights corresponding to the sample: the dimension [t, , ] is the time index, the dimension [, m, ] indicates the regime, and the dimension [, , i] indicates the i:th set of simulations.

References

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

• Lütkepohl H. 2005. New Introduction to Multiple Time Series Analysis, Springer.

• McElroy T. 2017. Computation of vector ARMA autocovariances. Statistics and Probability Letters, 124, 92-96.

• Virolainen S. (forthcoming). A statistically identified structural vector autoregression with endogenously switching volatility regime. Journal of Business & Economic Statistics.

• Virolainen S. 2022. Gaussian and Student's t mixture vector autoregressive model with application to the asymmetric effects of monetary policy shocks in the Euro area. Unpublished working paper, available as arXiv:2109.13648.

See Also

fitGSMVAR, GSMVAR, diagnostic_plot, predict.gsmvar, profile_logliks, quantile_residual_tests, GIRF, GFEVD

Examples

 # GMVAR(1,2), d=2 process, initial values from the stationary
 # distribution
 params12 <- c(0.55, 0.112, 0.344, 0.055, -0.009, 0.718, 0.319, 0.005,
  0.03, 0.619, 0.173, 0.255, 0.017, -0.136, 0.858, 1.185, -0.012, 0.136,
  0.674)
 mod12 <- GSMVAR(p=1, M=2, d=2, params=params12)
 set.seed(1)
 sim12 <- simulate(mod12, nsim=500)
 plot.ts(sim12$sample)
 ts.plot(sim12$mixing_weights, col=c("blue", "red"), lty=2)
 plot(sim12$component, type="l")

 # StMVAR(2, 2), d=2 model
 params22t <- c(0.554, 0.033, 0.184, 0.005, -0.186, 0.683, 0.256, 0.031,
  0.026, 0.204, 0.583, -0.002, 0.048, 0.697, 0.154, 0.049, 0.374, 0.476,
   0.318, -0.645, -0.302, -0.222, 0.193, 0.042, -0.013, 0.048, 0.818,
    4.334, 20)
 mod22t <- GSMVAR(gdpdef, p=2, M=2, params=params22t, model="StMVAR")
 sim22t <- simulate(mod22t, nsim=100)
 plot.ts(sim22t$mixing_weights)

 ## FORECASTING EXAMPLE ##
 # Forecast 5-steps-ahead, 500 sets of simulations with initial
 # values from the data:
 # GMVAR(2,2), d=2 model
 params22 <- c(0.36, 0.121, 0.223, 0.059, -0.151, 0.395, 0.406, -0.005,
  0.083, 0.299, 0.215, 0.002, 0.03, 0.484, 0.072, 0.218, 0.02, -0.119,
   0.722, 0.093, 0.032, 0.044, 0.191, 1.101, -0.004, 0.105, 0.58)
 mod22 <- GSMVAR(gdpdef, p=2, M=2, params=params22)
 sim22 <- simulate(mod22, nsim=5, ntimes=500)

 # Point forecast + 95% prediction intervals:
 apply(sim22$sample, MARGIN=1:2, FUN=quantile, probs=c(0.025, 0.5, 0.972))

 # Similar forecast for the mixing weights:
 apply(sim22$mixing_weights, MARGIN=1:2, FUN=quantile,
       probs=c(0.025, 0.5, 0.972))

saviviro/gmvarkit documentation built on March 8, 2024, 4:15 a.m.