Distribution-free specification tests of conditional models |
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Authors: | Miguel A Delgado Winfried Stute |
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Institution: | 1. Departamento de Economía, Universidad Carlos III de Madrid, C./ Madrid 126-128, Getafe 28903, Madrid, Spain;2. Mathematical Institute, University of Giessen, Arndtstr. 2, Germany |
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Abstract: | This article proposes a class of asymptotically distribution-free specification tests for parametric conditional distributions. These tests are based on a martingale transform of a proper sequential empirical process of conditionally transformed data. Standard continuous functionals of this martingale provide omnibus tests while linear combinations of the orthogonal components in its spectral representation form a basis for directional tests. Finally, Neyman-type smooth tests, a compromise between directional and omnibus tests, are discussed. As a special example we study in detail the construction of directional tests for the null hypothesis of conditional normality versus heteroskedastic contiguous alternatives. A small Monte Carlo study shows that our tests attain the nominal level already for small sample sizes. |
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Keywords: | Conditional models Martingale transformation Sequential empirical process Specification tests |
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