SPECIFICATION TESTING DRIVEN BY ORTHOGONAL SERIES FOR NONLINEAR COINTEGRATION WITH ENDOGENEITY
针对含内生性和非平稳性的双变量非线性协整时间序列模型，提出了两种基于正交序列的简单新检验方法，填补了回归函数可积情形下的检验空白，并通过模拟验证了其良好的有限样本性能。
This paper proposes two simple and new specification tests based on the use of an orthogonal series for a considerable class of bivariate nonlinearly cointegrated time series models with endogeneity and nonstationarity. The first test is proposed for the case where the regression function is integrable, which fills a gap in the literature, and the second test, which nests the first one, deals with regression functions in a quite large function space that is sufficient for both theoretical and practical use. As a starting point of our asymptotic theory, the first test is studied initially and then the theory is extended to the second test. Endogeneity in two general forms is allowed in the models to be tested. The finite sample performance of the tests is examined through several simulated examples. Our experience generally shows that the proposed tests are easily implementable and also have stable sizes and good power properties even when the ‘distance’ between the null hypothesis and a sequence of local alternatives is asymptotically negligible.