Estimation of the Intercept Parameter in Integrated Galton–Watson Processes
针对积分Galton-Watson过程，提出一种新的加权最小二乘估计量，在过程为瞬态或零常返时均一致，解决了现有估计量依赖未知截距参数的问题。
ABSTRACT We study the estimation of the intercept parameter in an integrated Galton–Watson process, an important building block for many count‐valued time series models. In this unit root setting, the ordinary least squares estimator is known to be inconsistent, whereas the existing weighted least squares (WLS) estimator is consistent only in the case where the process is transient, a condition that depends on the unknown intercept parameter. We propose an alternative WLS estimator based on the new weight function of , and show that it is consistent regardless of whether the process is transient or null recurrent, with a common convergence rate of .