Specification Testing in Structural Nonparametric Cointegration

This paper proposes two simple and new specification tests based on the use of an orthogonal series for a considerable class of cointegrated time series models with endogeneity and nonstationarity. The paper then establishes an asymptotic theory for each of the proposed tests. The first test is initially proposed for the case where the regression function involved is integrable, which fills a gap in the literature, and the second test is an extended version of the first test for covering a class of non-integrable functions. Endogeneity in two general forms is allowed in the models to be tested. A potential global departure in the alternative hypothesis, which is being overlooked by the literature, is investigated. The finite sample performance of the proposed tests is examined through using several simulated examples. Meanwhile, the second test is naturally applicable to the case where there is a type of endogeneity inherited in the relationship between the United States aggregate consumers' consumption expenditure and disposable income over the period of 1960-2009. 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