Abstract
Abstract Much work has been done recently on analyzing ordinary least squares estimators in linear time series models when one or more of the regressors are integrated processes (that is, contain a unit root). A fairly complete asymptotic theory exists due to the work of Phillips (1986, 1987, 1988, 1991), Park and Phillips (1988, 1989), Stock (1987), Sims, Stock, and Watson (1990), Phillips and Hansen (1990), Saikkonen (1991), Stock and Watson (1993), Kitamura and Phillips (1995, 1997), and others. What has not been systematically treated is specification testing in linear models when some explanatory variables are integrated. This has not stopped researchers from applying such tests in regressions with integrated processes. For example, the book by Banerjee, Dolado, Galbraith, and Hendry (1993) contains several instances where diagnostic tests are reported after running regressions with integrated processes. The kinds of tests I have in mind are standard tests for serial correlation, tests against non-nested alternatives, and tests for endogeneity of some of the explanatory variables.
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