zi_inar_process {boodd}R Documentation

Generate a ZI-INAR Process

Description

Simulates a zero-inflated Poisson distributed (ZI)-INAR(p) process.

Usage

zi_inar_process(n, p, alpha, Y = 1, p2, lamb)

Arguments

n

A positive integer; the length of the simulated process.

p

A positive integer; the order of the simulated process.

alpha

A numeric vector whose components belong to the interval (0,1); parameters of the thinning operator (see details below).

Y

A non-negative integer; the initial value of the process.

p2

A numeric value between 0 and 1; parameter of the Bernoulli distribution (see details below).

lamb

A positive numeric value; parameter of the Poisson distribution (see details below).

Details

The ZI-INAR process is defined by the equation

Y_t=\sum_{i=1}^p \alpha_i\circ Y_{t-i} +V_t, \qquad t\in \mathbb{Z},

where the so called thinning operator is defined as

\alpha\circ Y=\sum_{i=1}^Y Z_i,

where \{Z_i\}_{i\in \mathcal{Z}} is an i.i.d. sequence of random variables with Bernoulli distribution with parameter \alpha with \alpha_i\in[0,1] for i\in 1,\dots,p and independent of Y. Additionally, \{V_t\}_{t\in \mathcal{Z}} is an i.i.d. non-negative and integer valued sequence of random variables.

Let V be a non-negative discrete random variable with parameters p2 and \lambda. We said that V follows a zero-inflated distribution and we denote it by V\sim ZI(p2,\lambda), if it can be expressed as

V=BU,\qquad \text{with }\qquad B \perp U,

where B has Bernoulli distribution with mean 1-p2, for p2\in[0,1) and U is a non-negative discrete valued random variable with finite variance and parameter vector \lambda. We consider the zero-inflated Poisson distribution (ZI-INAR(p))), when U has Poisson distribution with mean \lambda.

Value

A numeric vector of length n.

References

Bertail, P. and Dudek, A. (2025). Bootstrap for Dependent Data, with an R package (by Bernard Desgraupes and Karolina Marek) - submitted.

Bertail, P., Medina-Garay, A., De Lima-Medina, F. and Jales, I. (2024). A maximum likelihood and regenerative bootstrap approach for estimation and forecasting of inar (p) processes with zero-inated innovations. Statistics, 58, 336-363.

See Also

regenboot, genETARCH, genMM1.

Examples

X = zi_inar_process(70, 2, c(0.1,0.1), Y = 1, p2 = 0.2, lamb = 0.7)
plot(X, type="l")

[Package boodd version 0.1 Index]