发表机构
Concordia University; University of Debrecen（康科迪亚大学; 德布勒森大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对单位根INAR(2)过程OLS截距估计不一致的问题，提出逆时间加权最小二乘估计量，实现一致估计与推断，并通过模拟和加拿大洪水数据验证其有效性。
AI 中文摘要
Barczy等（2014）证明了对于单位根INAR(2)过程，创新均值的普通最小二乘（OLS）估计量是不一致的。我们利用逆时间加权最小二乘（WLS）构造了一致的截距估计量，并推导出其混合速率渐近性质：截距估计量以$\sqrt{\log n}$的速率渐近正态，其高斯极限独立于自回归极限，而自回归估计量保持其OLS速率。我们开发了一个用WLS干扰估计校准的OLS单位根检验。在维持单位根的假设下，当检验未拒绝时，基于残差得分的创新均值和长期漂移的高斯区间仍渐近有效。模拟表明，相对于OLS，WLS降低了两个量的均方根误差，且施加单位根可进一步改进。对两个加拿大洪水清单的应用表明，关于持续性的结论取决于清单和加权偏移。
英文摘要
\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 $\sqrt{\log n}$, 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.
