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Type: Package
Title: Simulate INAR/ZINAR(p) Models and Estimate Its Parameters
Version: 0.1.0
Maintainer: Tharso Augustus Rossiter Araújo Monteiro <tharso.augustus@ufpe.br>
Description: Simulation, exploratory data analysis and Bayesian analysis of the p-order Integer-valued Autoregressive (INAR(p)) and Zero-inflated p-order Integer-valued Autoregressive (ZINAR(p)) processes, as described in Garay et al. (2020) <doi:10.1080/00949655.2020.1754819>.
License: GPL (≥ 3.0)
Encoding: UTF-8
LazyData: true
Imports: progress, stats, utils, graphics
RoxygenNote: 7.1.1
Depends: R (≥ 2.10)
NeedsCompilation: no
Packaged: 2022-05-06 14:57:02 UTC; tharso
Author: Aldo William Medina Garay [aut], Francyelle de Lima Medina [aut], Tharso Augustus Rossiter Araújo Monteiro [aut, cre]
Repository: CRAN
Date/Publication: 2022-05-09 11:30:02 UTC

Parameter estimation for ZINARp models

Description

This function uses MCMC algorithms (Metropolis-Hastings and Gibbs Sampler) to generate a chain of INAR/ZINAR(p) parameter estimators.

Usage

estimate_zinarp(
  x,
  p,
  iter = 5000,
  thin = 2,
  burn = 0.1,
  innovation = "Poisson"
)

Arguments

x

A vector containing a discrete non-negative time series dataset.

p

The order of the INAR/ZINAR process.

iter

The number of iterations to be considered. Defaults to 5000.

thin

Lag for posterior sample. Defaults to 2.

burn

Burn-in for posterior sample. Defaults to 0.1. Must be in (0,1).

innovation

Distribution to be used for the innovation : "Poisson" or "ZIP". Defaults to Poisson.

Value

Returns a list containing a posteriori samples for the specified model parameters.

References

Garay, Aldo M., Francyelle L. Medina, Celso RB Cabral, and Tsung-I. Lin. "Bayesian analysis of the p-order integer-valued AR process with zero-inflated Poisson innovations." Journal of Statistical Computation and Simulation 90, no. 11 (2020): 1943-1964.

Garay, Aldo M., Francyelle L. Medina, Isaac Jales CS, and Patrice Bertail. "First-Order Integer Valued AR Processes with Zero-Inflated Innovations." In Workshop on Nonstationary Systems and Their Applications, pp. 19-40. Springer, Cham, 2021.

Examples

test <- simul_zinarp(alpha = 0.1, lambda = 1, n = 100)
e.test <- estimate_zinarp(x = test, p = 1, iter = 800, innovation= "Poisson")
alpha_hat <- mean(e.test$alpha)
lambda_hat <- mean(e.test$lambda)

data(slesions)
e.slesions <- estimate_zinarp(slesions$y, p = 1, iter = 800, innovation = 'ZIP')
alpha_hat_slesions <- mean(e.slesions$alpha)
lambda_hat_slesions <- mean(e.slesions$lambda)
rho_hat_slesions <- mean(e.slesions$rho)

EXPLORATORY DATA ANALYSIS FOR ZINAR(p) PROCESSES

Description

This function generates a graph for exploring ZINAR(p) processes.

Usage

explore_zinarp(x)

Arguments

x

A vector containing a discrete non-negative time series data set.

Value

Plot time series graph, relative frequency bar plot, autocorrelation function graph and partial autocorrelation function graph on a common plot.


Sample Generator for ZINAR(p)

Description

This function generates a realization of a ZINAR(p) process.

Usage

simul_zinarp(n, alpha, lambda, pii = 0)

Arguments

n

The length of the simulated chain.

alpha

The p-dimensional vector (in which p is the process order) of alpha values, the probabilities of an element remaining in the process.All alpha elements must be in [0,1] and their sum must be smaller than 1.

lambda

The Poisson rate parameter. Must be greater than zero.

pii

The probability of a structural zero (i.e., ignoring the Poisson distribution) under ZIP innovation sequences. Defaults to 0, following a standard Poisson.

Value

Returns a numeric vector representing a realization of an INAR/ZINAR(p) process.

References

Garay, Aldo M., Francyelle L. Medina, Celso RB Cabral, and Tsung-I. Lin. "Bayesian analysis of the p-order integer-valued AR process with zero-inflated Poisson innovations." Journal of Statistical Computation and Simulation 90, no. 11 (2020): 1943-1964.

Garay, 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.


Skin lesions dataset

Description

Monthly number of skin lesions-related submissions to animal health laboratories from a region in New Zealand, obtained from 2003 to 2009.

Usage

slesions

Format

An object of class data.frame with 84 rows and 1 columns.

References

Jazi, Mansour Aghababaei, Geoff Jones, and Chin‐Diew Lai. "First‐order integer valued AR processes with zero inflated Poisson innovations." Journal of Time Series Analysis 33.6 (2012): 954-963.

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
Health stats visible at Monitor.