generate_data: generate_data

In hlennon/copulaIVTS: Dependence modelling of a digitised Gaussian ARMA(p,q) copula model for Integer-Valued Time Series

Description

generates data from the Gaussian copula model with Negative Binomial or Poisson marginals of length n

Usage

generate_data(n, a, b, marginal_dist, marginal_parameters)

Arguments

n	length of times series
a	autoregressive parameters
b	moving average parameters
marginal_dist	"poisson" or "nbinom" or "zeroinf_poisson" or "zeroinf_nbinom"
marginal_parameters	If negbin then c(nb.s, nb.p), If poisson then lambda

Details

Simulates 1 time series from the GCNB or GCP model

Value

An integer-valued time series of length n

Note

Marginals fixed to be Poisson, nb, zero_inf_poisson or zero_inf_negbin at present. The example below has ARMA(2,2) dependence structure, NB(p,s) marginal structure which is coupled together using a Gaussian copula Note:

"nbinom" uses p and s representation. "zeroinf_nbinom" uses negbinomial() which uses the alternate parametrization via mean mu and an index parameter k An alternative parametrization (often used in ecology) is by the mean mu, and size, the dispersion parameter, where prob = size/(size+mu). The variance is mu + mu^2/size in this parametrization.

Author(s)

Hannah Lennon <[e-mail]>

References

Schmidt (2007)

Examples

library("VGAM")
generate_data(4, 0.7, -0.5, "poisson", 3)
generate_data(4, 0.7, -0.5, "nbinom",  c(3, 0.3))
generate_data(4, 0.7, -0.5, "zeroinf_poisson",  3)
generate_data(4, 0.7, -0.5, "zeroinf_nbinom",  c(3, 0.3))


tabulate(generate_data(40, 0.7, -0.5, "nbinom",  c(3, 0.5)) $x);
tabulate(generate_data(4, 0.7, -0.5, "zeroinf_nbinom",  c(3, 0.5)) $x)


set.seed(12)
data        <- generate_data(10000, c(0.2, 0.3), c(-0.1, 0.5), "nbinom",  c(5, 0.5))
ins.data21  <- data$x
ins.data21y <- data$y
hist(ins.data21)

## Code currentlt is defined as:
function (n, a, b, marginal_dist, marginal_parameters){

            if(marginal_dist=="poisson"){        lambda  <- marginal_parameters[1]}
            if(marginal_dist=="zeroinf_poisson"){lambda  <- marginal_parameters[1]}
            if(marginal_dist=="nbinom"){          nb.s   <- marginal_parameters[1]
                                              nb.p   <- marginal_parameters[2]}
            if(marginal_dist=="zeroinf_nbinom"){  nb.s   <- marginal_parameters[1]
                                                  nb.p   <- marginal_parameters[2]}


            ar.sigma <- arma_cov(a, b, 0)
            ar.sigma <- sqrt(1/ar.sigma)

            if(a[1]==0){  y <- arima.sim(list(ma = b), n, sd = ar.sigma)}
            else if(b[1]==0){  y <- arima.sim(list(ar = a), n, sd = ar.sigma)}
            else{ y <- arima.sim(list(ar = a, ma = b), n, sd = ar.sigma)}

            if(marginal_dist=="poisson")  x <- qpois(pnorm(y), lambda)
            if(marginal_dist=="nbinom")   x <- qnbinom(pnorm(y), size = nb.s, prob = nb.p)
            if(marginal_dist=="zeroinf_poisson") {
                        library(VGAM)
                        x <- qzipois(pnorm(y), lambda, pstr0 = 0)
            }
            if(marginal_dist=="zeroinf_nbinom") {
                        library(VGAM)
                        x <- qzinegbin(pnorm(y), size=nb.s, prob=nb.p, pstr0 = 0)
            }

            list(x = x, y = y)
}

hlennon/copulaIVTS documentation built on Dec. 20, 2021, 4:45 p.m.