SimulateDMQ {DMQ}

Simulate from the DMQ model

Description

Approximate simulation from the DMQ model. Allows to simulate quantiles and observations.

Usage

SimulateDMQ(iT, vQ_0, vTau, iTau_star, vPn, ScalingType = "InvSqrt", fSim = NULL)

Arguments

iT

Number of observations to simulate.

vQ_0

numeric vector of limiting quantiles.

vTau

numeric vector of length Jx1 containing probability levels at which quantiles are estimated.

iTau_star

Integer indicating the position in vTau where the reference quantile is placed. For instance, if vTau = seq(0.01, 0.99, 0.01) then iTau_star = 50 means that the median is used as the reference quantile.

vPn

numeric named vector of length 4x1 with starting values for the optimizer. For example vPn = c("phi" = 0.9, "gamma" = 0.05, "alpha" = 0.01, "beta" = 0.7).

ScalingType

character Indicating the scaling mechanism for the conditional quasi score. Possible choices are "Identity", "Inv","InvSqrt". When ScalingType = "InvSqrt" quasi scores are scaled by their standard deviation. When ScalingType = "Inv" quasi scores are scaled by their variance. When ScalingType = "Identity" quasi scores are not scaled. Default value ScalingType = "InvSqrt".

fSim

function to simulate from the discretized distribution implied by the simulated quantiles. By default fSim = NULL meaning that an internal simulation scheme is employed. See details.

Details

Given a set of simulated quantiles a Uniform variable drawn. The discretized quantile function is linearly interpoled at the simulated Uniform draw to obtain an observations. When the Uniform draw is outside the range spanned by vTau a Gaussian quantile function is used. The mean and variance of the Gaussian quantile distribution are set to those implied by the simulated quantiles using the same scheme of MomentsDMQ.

Value

A list with two elements:

vY

A numeric vector of T simulated observations.

mQ

A numeric TxJ matrix of simulated quantiles.

Author(s)

Leopoldo Catania

Examples

set.seed(123)

# Simulate 500 observations from the DMQ model.

# Use the percentiles
vTau = seq(0.01, 0.99, 0.01)

# Median as reference quantile
iTau_star = 50

# Standard Gaussian limiting distribution
vQ_0 = qnorm(vTau)

# vector of parameters
vPn = c("phi" = 0.95, "gamma" = 0.10, "alpha" = 0.01, "beta" = 0.7)

lSim = SimulateDMQ(iT = 500, vQ_0, vTau, iTau_star, vPn)

plot.ts(lSim$vY)
plot.ts(lSim$mQ, plot.type = "single")