WEAK CONVERGENCE TO STOCHASTIC INTEGRALS UNDER PRIMITIVE CONDITIONS IN NONLINEAR ECONOMETRIC MODELS
提出了随机积分弱收敛的新条件，允许创新项具有长记忆、因果过程和近邻依赖，适用于TAR、双线性等非线性计量经济模型。
Limit theory with stochastic integrals plays a major role in time series econometrics. In earlier contributions on weak convergence to stochastic integrals, the literature commonly uses martingale and semi-martingale structures. Liang, Phillips, Wang, and Wang (2016) (see also Wang (2015), Chap. 4.5) currently extended weak convergence to stochastic integrals by allowing for a linear process or a α -mixing sequence in innovations. While these martingale, linear process and α -mixing structures have wide relevance, they are not sufficiently general to cover many econometric applications that have endogeneity and nonlinearity. This paper provides new conditions for weak convergence to stochastic integrals. Our frameworks allow for long memory processes, causal processes, and near-epoch dependence in innovations, which have applications in a wide range of econometric areas such as TAR, bilinear, and other nonlinear models.