uGMAR (version 3.1.0)

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

Description

simulateGSMAR simulates values from the specified GMAR, StMAR or G-StMAR process. Can be used for forecasting future values of the process.

Usage

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

Arguments

gsmar

object of class 'gsmar' created with the 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.

drop

if TRUE (default) then the components of the returned list are coerced to the lowest possible dimension, i.e, for ntimes=1, $sample and $component will be vectors and $mixing_weights will be matrix.

Value

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

$sample

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

$component

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

$mixing_weights

a size (nsimu\(xMx\)ntimes) array containing the mixing weights corresponding to the sample: the dimension [i, , ] is the time index, the dimension [, i, ] indicates the regime, and the dimension [, , i] indicates the i:th set of simulations.

Details

The argument ntimes is intended for forecasting: a GSMAR process can be forecasted by simulating it's 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).

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.

• 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 the G-StMAR model, but it's a straightforward generalization with theoretical properties similar to the GMAR and StMAR models.

See Also

fitGSMAR, GSMAR, predict.gsmar, add_data, condMoments, mixingWeights

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$mixing_weights, col=rainbow(3), lty=2)

 # FORECASTING EXAMPLE:
 # Restricted GMAR model, 10000 sets of simulations with initial values 6 and 6.2.
 params22r <- c(1.4, 1.8, 0.8, -0.1, 0.29, 3.18, 0.84)
 gmar22r <- GSMAR(p=2, M=2, params=params22r, model="GMAR",
  restricted=TRUE)
 sim22r <- simulateGSMAR(gmar22r, nsimu=5, initval=c(6, 6.2), ntimes=10000)
 apply(sim22r$sample, 1, median) # Point forecast
 apply(sim22r$sample, 1, quantile, probs=c(0.025, 0.975)) # 95% interval
 apply(sim22r$mixing_weights, MARGIN=1:2, FUN=median) # mix.weight point forecast
 apply(sim22r$mixing_weights, MARGIN=1:2, FUN=quantile,
  probs=c(0.025, 0.975)) # mix.weight 95% intervals

 # 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$mixing_weights, 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$mixing_weights, col=rainbow(3), lty=2)
# }