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<p>An alternative dependent counting (ADC) nonnegative integer-valued autoregressive (INAR) process of the higher-order is introduced for modeling the count time series. The condition for the strictly stationarity (with the second moment) and ergodicity is given by embedding the proposed ADCINAR process into a random coefficient INAR process of the higher-order. Then, the estimation of parameters is discussed in details. The easiest methods are the conditional least squares (CLS) method and the Yule–Walker method by which only the INAR parameter and the innovation mean are estimable. For estimating the new parameter as well as the innovation variance, the two-step CLS (2CLS) method is separately applied on the basis of the estimated squared residuals, by plugging a suitable estimator for the parameter in the conditional mean function. To avoid unnecessary (unconditional) higher moments conditions that ensure desirable properties of the CLS/2CLS estimators, the Gaussian quasi maximum likelihood (QML) method is employed, together with its asymptotic properties under mild conditions. Some non-standard testing problems are mentioned for the proposed ADCINAR process. Monte Carlo simulations are carried out to assess the performance of the Gaussian QML estimator. Also, practical effectiveness of the proposed higher-order ADCINAR process over the widely used higher-order INAR process is illustrated by two real-world examples.</p>

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Parameter estimation of pth-order ADCINAR process

  • 期刊论文

  • 发表日期：

    2026年5月29日

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  • Xiaoqiang Zeng,
  • Yoshihide Kakizawa

摘要

An alternative dependent counting (ADC) nonnegative integer-valued autoregressive (INAR) process of the higher-order is introduced for modeling the count time series. The condition for the strictly stationarity (with the second moment) and ergodicity is given by embedding the proposed ADCINAR process into a random coefficient INAR process of the higher-order. Then, the estimation of parameters is discussed in details. The easiest methods are the conditional least squares (CLS) method and the Yule–Walker method by which only the INAR parameter and the innovation mean are estimable. For estimating the new parameter as well as the innovation variance, the two-step CLS (2CLS) method is separately applied on the basis of the estimated squared residuals, by plugging a suitable estimator for the parameter in the conditional mean function. To avoid unnecessary (unconditional) higher moments conditions that ensure desirable properties of the CLS/2CLS estimators, the Gaussian quasi maximum likelihood (QML) method is employed, together with its asymptotic properties under mild conditions. Some non-standard testing problems are mentioned for the proposed ADCINAR process. Monte Carlo simulations are carried out to assess the performance of the Gaussian QML estimator. Also, practical effectiveness of the proposed higher-order ADCINAR process over the widely used higher-order INAR process is illustrated by two real-world examples.