Inference on Common Trends in a Cointegrated Nonlinear SVAR
针对两区制分段仿射SVAR模型，提出一种改进的多元方差比检验，用于推断共同随机趋势的数量，该检验对已知形式的非线性协整具有稳健性。
ABSTRACT We consider the problem of performing inference on the number of common stochastic trends when data is generated by a cointegrated CKSVAR (a two‐regime, piecewise affine SVAR; Mavroeidis, 2021), using a modified version of the Breitung (2002) multivariate variance ratio test that is robust to the presence of nonlinear cointegration (of a known form). To derive the asymptotics of our test statistic, we prove a fundamental LLN‐type result for a class of stable but nonstationary autoregressive processes, using a novel dual linear process approximation. We show that our modified test yields correct inferences regarding the number of common trends in such a system, whereas the unmodified test tends to infer a higher number of common trends than are actually present, when cointegrating relations are nonlinear.