uGMAR (version 3.0.1)

simulateGSMAR: Simulate values from GMAR, StMAR or G-StMAR process

Description

simulateGSMAR simulates values from the specified GMAR, StMAR or G-StMAR process.

Usage

simulateGSMAR(gsmar, nsimu, initvalues, ntimes = 1)

Arguments

gsmar

object of class 'gsmar', generated by function fitGSMAR() or GSMAR().

nsimu

a positive integer specifying how many values will be simulated.

initvalues

a numeric vector with length >=p specifying the initial values for the simulation. The last element will be used as the initial value for the first lag, the second last element will be initial value for the second lag, etc. If not specified, initial values will be simulated from the process's stationary distribution.

ntimes

a positive integer specifying how many sets of simulations should be performed. If larger than one then only the samples are returned. Uses the same initial values for each set. Default is one.

Value

Returns a list with...

$sample

a numeric vector containing the simulated values.

$component

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

$mixingWeights

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

Or if ntimes>1 returns a matrix containing the samples so that the i:th sample can be obtained at i:th column.

References

• Galbraith, R., Galbraith, J. 1974. On the inverses of some patterned matrices arising in the theory of stationary time series. Journal of Applied Probability 11, 63-71.

• Kalliovirta L., Meitz M. and Saikkonen P. 2015. Gaussian Mixture Autoregressive model for univariate time series. Journal of Time Series Analysis, 36, 247-266.

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

• Meitz M., Preve D., Saikkonen P. 2018. A mixture autoregressive model based on Student's t-distribution. arXiv:1805.04010 [econ.EM].

• There are currently no published references for G-StMAR model, but it's a straightforward generalization with theoretical properties similar to GMAR and StMAR models.

Examples

# NOT RUN {
 
# }
# NOT RUN {
 # GMAR model
 params13 <- c(1.4, 0.88, 0.26, 2.46, 0.82, 0.74, 5.0, 0.68, 5.2, 0.72, 0.2)
 gmar13 <- GSMAR(p=1, M=3, params=params13, model="GMAR")
 sim13 <- simulateGSMAR(gmar13, nsimu=500)
 ts.plot(sim13$sample)
 ts.plot(sim13$component)
 ts.plot(sim13$mixingWeights, col=rainbow(3), lty=2)

 # Restricted GMAR model
 params12r <- c(1.4, 1.8, 0.88, 0.29, 3.18, 0.84)
 gmar12r <- GSMAR(p=1, M=2, params=params12r, model="GMAR",
 restricted=TRUE)
 sim12r <- simulateGSMAR(gmar12r, nsimu=500)
 ts.plot(sim12r$sample)
 ts.plot(sim12r$component)
 ts.plot(sim12r$mixingWeights, col=rainbow(3), lty=2)

 # G-StMAR model, with initial values
 params12gs <- c(1.38, 0.88, 0.27, 3.8, 0.74, 3.15, 0.8, 3.6)
 gstmar12 <- GSMAR(p=1, M=c(1, 1), params=params12gs,
 model="G-StMAR")
 sim12gs <- simulateGSMAR(gstmar12, nsimu=500, initvalues=5:6)
 ts.plot(sim12gs$sample)
 ts.plot(sim12gs$component)
 ts.plot(sim12gs$mixingWeights, col=rainbow(3), lty=2)

 # Such StMAR(3,2) that the AR coefficients are restricted to be
 # the same for both regimes and that the second AR coefficients are
 # constrained to zero.
 params32trc <- c(2.2, 1.8, 0.88, -0.03, 2.4, 0.27, 0.40, 3.9, 1000)
 stmar32rc <- GSMAR(data=VIX, p=3, M=2, params=params32trc, model="StMAR",
  restricted=TRUE, constraints=matrix(c(1, 0, 0, 0, 0, 1), ncol=2))
 sim32trc <- simulateGSMAR(stmar32rc, nsimu=500)
 ts.plot(sim32trc$sample)
 ts.plot(sim32trc$component)
 ts.plot(sim32trc$mixingWeights, col=rainbow(3), lty=2)

 # Mixture version of Heterogenuous Autoregressive (HAR) model (without data)
 paramsHAR <- c(1, 0.1, 0.2, 0.3, 1, 1, 0.15, 0.25, 0.35, 1, 0.55)
 r1 = c(1, rep(0, 21)); r2 = c(rep(0.2, 5), rep(0, 17)); r3 = rep(1/22, 22)
 R0 = cbind(r1, r2, r3)
 mixhar <- GSMAR(p=22, M=2, params=paramsHAR, model="GMAR", constraints=list(R0, R0))
 simhar <- simulateGSMAR(mixhar, nsimu=1000)
 ts.plot(simhar$sample)
 ts.plot(simhar$component)
 ts.plot(simhar$mixingWeights, col=rainbow(3), lty=2)
# }