Cointegration with Occasionally Binding Constraints
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偶尔约束生效条件下的协整
- 研究问题
- 具有阈值非线性与偶尔生效约束的向量自回归，如何产生共享的非线性随机趋势，并统一描述短期和长期动态？
- 方法与思路
- 作者在删失与折 kink 结构 VAR 框架中，结合单位根与广义秩条件刻画共同趋势，并推导相应的极限过程。
- 材料陈述的贡献
- 摘要称其将 Granger–Johansen 表示定理扩展至非线性协整，得到调节、删失及折 kink 布朗运动等共同趋势极限。
- 阅读关注点
- 应核对广义秩条件与单位根的具体定义、不同约束机制对应的趋势过程，以及这些长期性质如何帮助识别结构参数。
- 阅读边界
- 这是 arXiv 预印本，同行评审与期刊接收未经核实；摘要未列出完整定理条件，首次扩展与完整刻画的主张仍需全文核对。
原文摘要
In the literature on nonlinear cointegration, a long-standing open problem relates to how a (nonlinear) vector autoregression, which provides a unified description of the short- and long-run dynamics of a vector of time series, can generate 'nonlinear cointegration' in the profound sense of those series sharing common nonlinear stochastic trends. We consider this problem in the setting of the censored and kinked structural VAR (CKSVAR), which provides a flexible yet tractable framework within which to model time series that are subject to threshold-type nonlinearities, such as those arising due to occasionally binding constraints, of which the zero lower bound (ZLB) on short-term nominal interest rates provides a leading example. We provide a complete characterisation of how common linear and nonlinear stochastic trends may be generated in this model, via unit roots and appropriate generalisations of the usual rank conditions, providing the first extension to date of the Granger-Johansen representation theorem to a nonlinearly cointegrated setting, and thereby giving the first successful treatment of the open problem. The limiting common trend processes include regulated, censored and kinked Brownian motions, none of which have previously appeared in the literature on cointegrated VARs. Our results and running examples illustrate that the CKSVAR is capable of supporting a far richer variety of long-run behaviour than is a linear VAR, in ways that may be particularly useful for the identification of structural parameters.