Estimation of Parameters in the NLAR(<i>p</i>) Model

Zhu, Fukang; Wang, Dehui

doi:10.1111/j.1467-9892.2008.00574.x

Cited by 9 publications

(5 citation statements)

References 8 publications

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“…For the FAMVIOL data, which is underdispersed with small-count data, the EB-INAR(1) with m > 2 is also competitive. Based on the proof of the Theorem in [25], q 1t (θ 1 ) corresponds to u t and q 2t (θ 2 ) corresponds to U t in [25]. Based on the result of V 1 , W 1 in Proposition 2 and V 2 , W 2 in Proposition 3, we can obtain M = E q 11 (θ 1,0 )q 21 (θ 2,0 ) ∂ ∂θ 1…”

Section: Underdispersed Casementioning

confidence: 98%

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A New Extension of Thinning-Based Integer-Valued Autoregressive Models for Count Data

Liu

Zhu

2020

Entropy

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The thinning operators play an important role in the analysis of integer-valued autoregressive models, and the most widely used is the binomial thinning. Inspired by the theory about extended Pascal triangles, a new thinning operator named extended binomial is introduced, which is a general case of the binomial thinning. Compared to the binomial thinning operator, the extended binomial thinning operator has two parameters and is more flexible in modeling. Based on the proposed operator, a new integer-valued autoregressive model is introduced, which can accurately and flexibly capture the dispersed features of counting time series. Two-step conditional least squares (CLS) estimation is investigated for the innovation-free case and the conditional maximum likelihood estimation is also discussed. We have also obtained the asymptotic property of the two-step CLS estimator. Finally, three overdispersed or underdispersed real data sets are considered to illustrate a superior performance of the proposed model.

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Section: Underdispersed Casementioning

confidence: 98%

“…Based on the proof of the Theorem in [ 25 ],

corresponds to

and

corresponds to

in [ 25 ]. Based on the result of

in Proposition 2 and

in Proposition 3, we can obtain

.…”

Section: Proof Of Propositionmentioning

confidence: 99%

A New Extension of Thinning-Based Integer-Valued Autoregressive Models for Count Data

Liu

Zhu

2020

Entropy

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“…To conduct the randomness test for the thinning parameter ϕ t , we also need to estimate the parameter θ = (σ 2 1 , σ 2 2 ) T and establish the asymptotic behaviors of the estimators in the second step. For this purpose, we refer to Nicholls and Quinn [27] and Hwang and Basaea [31], as well as Zhu and Wang [32], and adopt the two-step least squares method that has been widely used for time series models with random coefficients. Denote…”

Section: Parameter Estimation and Asymptotic Properties Of The Estima...mentioning

confidence: 99%

Randomness Test of Thinning Parameters for the NBRCINAR(1) Process

Zhang

2024

Axioms

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Non-negative integer-valued time series are usually encountered in practice, and a variety of integer-valued autoregressive processes based on various thinning operators are commonly used to model these count data with temporal dependence. In this paper, we consider a first-order integer-valued autoregressive process constructed by the negative binomial thinning operator with random coefficients, to address the problem of constant thinning parameters which might not always accurately represent real-world settings because of numerous external and internal causes. We estimate the model parameters of interest by the two-step conditional least squares method, obtain the asymptotic behaviors of the estimators, and furthermore devise a technique to test the constancy of the thinning parameters, which is essential for determining whether or not the proposed model should consider the parameters’ randomness. The effectiveness and dependability of the suggested approach are illustrated by a series of thorough simulation studies. Finally, two real-world data analysis examples reveal that the suggested approach is very useful and flexible for applications.

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“…The CLS method consists in minimizing the following function:

CLS (Ψ^{*}) \equiv {falsefalse}_{\sum}^{t = p + 1} {(X_{t} - E (X_{t} | F_{t - 1}))}^{2} .

Since the above function does not depend on ϕ , we need an additional equation to estimate it. To do this, we consider a two‐step procedure introduced by Karlsen and Tjøstheim () and further generalized by Zhu and Wang () to the NLAR( p ) (new p ‐order Laplace autoregressive) model. Thus we take the estimator for the dispersion parameter as the argument that minimizes the function

{CLS}^{*} (ϕ) = {falsefalse}_{\sum}^{t = p + 1} {(X_{t}^{2} - \tilde{E} (X_{t}^{2} | F_{t - 1}))}^{2},

where

\overset{E}{true} ((), X_{t}^{2} false| {scriptF}_{t - 1}) = {\overset{μ}{false}}_{t} + {\overset{μ}{false}}_{t}^{2} false(1 + ϕ^{- 1} b^{''} false(ξ_{0} false) false)

and

{\overset{μ}{false}}_{t}

is the estimate of μ t based on the CLS estimators

\overset{bold-italicβ}{true}

and

\overset{bold-italicα}{true} <...>

…”

Section: Em‐based Likelihood Inferencementioning

confidence: 99%

“…Since the above function does not depend on , we need an additional equation to estimate it. To do this, we consider a two-step procedure introduced by Karlsen and Tjøstheim (1988) and further generalized by Zhu and Wang (2008) to the NLAR(p) (new p-order Laplace autoregressive) model. Thus we take the estimator for the dispersion parameter as the argument that minimizes the function…”

mentioning

confidence: 99%

Flexible and Robust Mixed Poisson INGARCH Models

Silva

Barreto‐Souza

2019

Journal Time Series Analysis

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In this article, we propose a general class of INteger‐valued Generalized AutoRegressive Conditional Heteroskedastic (INGARCH) models based on a flexible family of mixed Poisson (MP) distributions. Our proposed class of count time series models contains the negative binomial (NB) INGARCH process as particular case and open the possibility to introduce new models such as the Poisson‐inverse Gaussian (PIG) and Poisson generalized hyperbolic secant processes. In particular, the PIG INGARCH model is an interesting and robust alternative to the NB model. We explore first‐order and second‐order stationary properties of our MPINGARCH models and provide expressions for the autocorrelation function and mean and variance marginals. Conditions to ensure strict stationarity and ergodicity properties for our class of INGARCH models are established. We propose an Expectation‐Maximization algorithm to estimate the parameters and obtain the associated information matrix. Further, we discuss two additional estimation methods. Monte Carlo simulation studies are considered to evaluate the finite‐sample performance of the proposed estimators. We illustrate the flexibility and robustness of the MPINGARCH models through two real‐data applications about number of cases of Escherichia coli and Campylobacter infections. This article contains a Supporting Information.

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Estimation of Parameters in the NLAR(p) Model

Cited by 9 publications

References 8 publications

A New Extension of Thinning-Based Integer-Valued Autoregressive Models for Count Data

A New Extension of Thinning-Based Integer-Valued Autoregressive Models for Count Data

Randomness Test of Thinning Parameters for the NBRCINAR(1) Process

Flexible and Robust Mixed Poisson INGARCH Models

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