具有偶尔紧约束的协整
Cointegration with Occasionally Binding Constraints
AI总结：
本文在CKSVAR框架下刻画偶尔紧约束导致的线性与非线性共同随机趋势，推广Granger-Johansen表示定理，解决非线性协整VAR的长期开放问题。
摘要：
在非线性协整文献中，一个长期存在的开放问题是：一个为时间序列向量的短期和长期动态提供统一描述的（非线性）向量自回归，如何能够在这些序列共享共同非线性随机趋势这一深刻意义上产生“非线性协整”。我们在截尾且弯折的结构VAR（CKSVAR）框架下研究这一问题；该框架为受阈值型非线性影响的时间序列提供了灵活且易于处理的建模方式，这类非线性例如由偶尔紧约束引起，其中短期名义利率的零下限（ZLB）就是一个典型例子。我们完整刻画了该模型如何通过单位根以及对通常秩条件的适当推广来产生共同的线性和非线性随机趋势，首次将Granger-Johansen表示定理扩展到非线性协整情形，从而首次成功处理了上述开放问题。极限共同趋势过程包括受调节、截尾和弯折的Brown运动，这些过程此前均未在协整VAR文献中出现。我们的结果和贯穿全文的示例表明，CKSVAR能够支持远比线性VAR丰富的长期行为，其方式可能对结构参数识别特别有用。
英文摘要：
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.
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