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 |
Y |
A non-negative integer; the initial value of the process. |
p2 |
A numeric value between |
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
Examples
X = zi_inar_process(70, 2, c(0.1,0.1), Y = 1, p2 = 0.2, lamb = 0.7)
plot(X, type="l")