Package 'ZINAR1'

Parameter Estimation for ZINAR(1) Models

Description

This function uses the EM algorithm to find the maximum likelihood estimates of a ZINAR(1) model.

Usage

EST_ZINAR(y,init = NULL,tol = 1e-05,iter = 1000,model,innovation,desc = FALSE)

Arguments

y	A vector containing a discrete non-negative time series dataset.
init	A vector containing the initial parameters estimates to maximize the likelihood function. If not informed, uses Yule-Walker method to calculate.
tol	Tolerance for the convergence of the algorithm. Defaults to 1e-5.
iter	Maximum number of iterations of the algorithm. Defaults to 1000.
model	Must be "zinar", if the innovation have Zero-Inflated distribution, and "inar", otherwise.
innovation	Must be "Po" if Poisson, "NB" if Negative binomial or "GI" if Gaussian inverse.
desc	TRUE to plot the exploratory graphs. Defaults to FALSE.

Value

Returns a list containing the parameters estimates and the number of interactions.

References

Aldo M.; Medina, Francyelle L.; Jales, Isaac C.; Bertail, Patrice. First-order integer valued AR processes with zero-inflated innovations. Cyclostationarity: Theory and Methods, Springer Verlag - 2021, v. 1, p. 19-40.

Examples

# Estimates the parameters of an INAR(1) and a ZINAR(1) models with Poisson innovations
# for the monthly number of drug offenses recorded from January 1990 to December 2001
# in Pittsburgh census tract 2206.

data(PghTracts)

y=ts(PghTracts$DRUGS,start=c(1990,1),end=c(2001,12),frequency=12)

Inar1 = EST_ZINAR(y, init = c(0.3,0.5,2), model = "inar", innovation = "Po",desc = TRUE)

ZIPInar1 = EST_ZINAR(y, init = c(0.3,0.5,2), model = "zinar", innovation = "Po",desc = TRUE)

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Drug Offenses

Description

Monthly number of drug offenses recorded from January 1990 to December 2001, with 144 observations, in Pittsburgh census tract 2206.

Usage

PghTracts

Format

A data frame with 144 rows and 4 columns containing the census tract and the variables YEAR,MONTH and DRUGS.

Source

Aldo M.; Medina, Francyelle L.; Jales, Isaac C.; Bertail, Patrice. First-order integer valued AR processes with zero-inflated innovations. Cyclostationarity: Theory and Methods, Springer Verlag - 2021, v. 1, p. 19-40. DOI: 10.1007/978-3-030-82110-4_2

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Simulate values for ZINAR(1)

Description

This function generates realizations of a ZINAR(1) process.

Usage

SIM_ZINAR(n, alpha, rho, th, innovation)

Arguments

n	Number of realizations of the ZINAR(1) process.
alpha	The probability of an element remaining in the process. The parameter alpha must be in [0,1].
rho	The probability of the innovation be from the state zero. The parameter rho must be in [0,1].
th	Is equal the value of the parameter lambda, if the innovations follow a Zero-Inflated Poisson (ZIP) distribution, and is a vector containing the values of the parameters (mu,phi), if the innovations follow a Zero-Inflated Negative Binomial (ZINB) or Zero-Inflated Inverse Gaussian (ZIPIG) distribution.
innovation	Must be "Po" if Poisson, "NB" if Negative binomial or "GI" if Gaussian inverse.

Value

Returns a numeric vector representing a realization of a ZINAR(1) process.

References

Aldo M.; Medina, Francyelle L.; Jales, Isaac C.; Bertail, Patrice. First-order integer valued AR processes with zero-inflated innovations. Cyclostationarity: Theory and Methods, Springer Verlag - 2021, v. 1, p. 19-40.

Examples

# Simulates values for ZIPInar1 model and estimate its parameters.

set.seed(5)

model = "zinar"
innv = "Po"
y = SIM_ZINAR(n = 500,alpha = 0.3,rho = 0.5,th = 3,innovation = innv)
ZIPInar1 = EST_ZINAR(y,model=model,innovation=innv,desc = TRUE)

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