ptsr.sim {PTSR}

Function to simulate a PTSR model

Description

Function to simulate a PTSR model

Usage

ptsr.sim(n = 1, burn = 0, xreg = NULL, xregar = TRUE, varphi = 1,
  alpha = 0, beta = NULL, phi = NULL, theta = NULL,
  seed = stats::runif(1, 1000, 10000), rdist = r.gamma, link1 = "log",
  link2 = "identity", g1 = NULL, g1.inv = NULL, g2 = NULL)

Arguments

n

a strictly positive integer. The sample size of yt (after burn-in). Default is 1.

burn

a non-negative integer. length of "burn-in" period. Default is 0.

xreg

optionally, a vector or matrix of external regressors. For simulation purposes, the length of xreg must be n+burn. Default is NULL.

xregar

logical, if FALSE, the regressors are not included in the AR component of the model. Default is TRUE.

varphi

non-negative parameter. Default is 1.

alpha

a numeric value corresponding to the intercept. Default is 0.

beta

optionally, a vector of coefficients corresponding to the regressors in xreg. Default is NULL.

phi

optionally, for the simulation function this must be a vector of size p, corresponding to the autoregressive coefficients (including the ones that are zero), where p is the AR order. Default is NULL.

theta

optionally, for the simulation function this must be a vector of size q, corresponding to the moving average coefficients (including the ones that are zero), where q is the MA order. Default is NULL. that g_2(y_t) = 0, for t < 1.

seed

optionally, an integer which gives the value of the fixed seed to be used by the random number generator. If missing, a random integer is chosen uniformly from 1,000 to 10,000.

rdist

function, the random number generator to be used

link1

character indicating which link must be used for \mu_t. See ptsr.link for available links. Default is ‘log’.

link2

character indicating which link must be used for y_t in the AR recursion. See ptsr.link for available links. Default is ‘identity’.

g1

optionally, a link function to be used for \mu_t. Default is NULL, so that it is calculated internally, using link1.

g1.inv

optionally, a the inverse link function to be used for \eta_t. It must the the ivnerse of g1. Default is NULL, so that it is calculated internally, using link1.

g2

optionally, a link function to be used for y_t. Default is NULL, so that it is calculated internally, using link2.

Details

The function ptsr.sim generates a random sample from a positive time series regression model, with a given distribution.

Value

Returns a list with the following components

• yt: the simulated time series

• mut: the conditional mean

• etat: the linear predictor g(\mu_t)

• error: the error term.

Examples

#-------------------------------------------------------------------
# Generating a sample of a Gamma-ARMA(1,1) model with no regressors
#-------------------------------------------------------------------

simu = ptsr.sim(n = 300, burn = 50,
                varphi = 20, alpha = 0,
                phi = 0.35, theta = 0.2,
                seed = 1234, rdist = r.gamma,
                link1 = "log", link2 = "log")

names(simu)
plot.ts(simu$yt)
lines(simu$mut, col= "red")