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  • Jiangyan Peng (a1) and Qiying Wang (a2)

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.

Corresponding author
*Address corresponding to Qiying Wang, School of Mathematics and Statistics, The University of Sydney, NSW 2006, Australia; e-mail:
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The authors thank Professor Peter Phillips, Professor Saikkonen and two anonymous referees for their very helpful comments on the original version. This work was completed when Jiangyan Peng visited the University of Sydney with financial support from the China Scholarship Council (CSC). Peng thanks the University of Sydney for providing a friendly research environment. Peng also acknowledges research support from the National Natural Science Foundation of China (project no: 71501025), Applied Basic Project of Sichuan Province (grant number: 2016JY0257), and the China Postdoctoral Science Foundation (grant number: 2015M572467). Wang acknowledges research support from the Australian Research Council.

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Econometric Theory
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