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PreprintCC BY 4.0arXiv

Consistent intercept estimation and inference for unit-root INAR(2) processes

  • Yang Lu
  • Márton Ispány
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Abstract

\citet{barczy2014asymptotic} showed that the ordinary least-squares (OLS) estimator of the innovation mean is inconsistent for a unit-root INAR(2) process. We construct a consistent intercept estimator using inverse-time weighted least squares (WLS) and derive its mixed-rate asymptotics: the intercept estimator is asymptotically normal at rate √(log n), with a Gaussian limit independent of the autoregressive limits, while the autoregressive estimators retain their OLS rates. We develop an OLS unit-root test calibrated with WLS nuisance estimates. Under the maintained unit root, residual-score Gaussian intervals for the innovation mean and long-run drift remain asymptotically valid after test nonrejection. Simulations show that WLS reduces root mean squared error for both quantities relative to OLS, with further gains from imposing the unit root. An application to two Canadian flood inventories shows that conclusions about persistence depend on the inventory and weighting offset.

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Cite

BibTeXRIS
BibTeX
@misc{lu2026consistent,
  title = {{Consistent intercept estimation and inference for unit-root INAR(2) processes}},
  author = {Yang Lu and Márton Ispány},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.23339},
  eprint = {2609.23339},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.23339},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Consistent intercept estimation and inference for unit-root INAR(2) processes
AU  - Yang Lu
AU  - Márton Ispány
PY  - 2026
DA  - 2026/10/07
PB  - arXiv
DO  - 10.48550/arxiv.2609.23339
UR  - https://arxiv.org/abs/2609.23339
AB  - \citet{barczy2014asymptotic} showed that the ordinary least-squares (OLS) estimator of the innovation mean is inconsistent for a unit-root INAR(2) process. We construct a consistent intercept estimator using inverse-time weighted least squares (WLS) and derive its mixed-rate asymptotics: the intercept estimator is asymptotically normal at rate √(log n), with a Gaussian limit independent of the autoregressive limits, while the autoregressive estimators retain their OLS rates. We develop an OLS unit-root test calibrated with WLS nuisance estimates. Under the maintained unit root, residual-score Gaussian intervals for the innovation mean and long-run drift remain asymptotically valid after test nonrejection. Simulations show that WLS reduces root mean squared error for both quantities relative to OLS, with further gains from imposing the unit root. An application to two Canadian flood inventories shows that conclusions about persistence depend on the inventory and weighting offset.
ER  -