Testing strategies for model specification
The paper discusses the main types of test procedures in the econometric analysis of time series. Special emphasis focusses on the opportunity to uphold the Neyman-Pearson theory in the case of repeated testing on the same set of sample data. The test procedures employed in the paper are the Wald-, Lagrange multiplier-, and the likelihood-ratio test. All these procedures are asymptotically equivalent but may differ for finite samples. Using these test procedures, the authors prove that for the case where a sequence of superposed alternatives is tested by marginal tests, the various test statistics are asymptotically independent under a common null hypothesis. It is further shown how independence of test statistics allows for the control of the overall type I error. By distinguishing constructive hypotheses and auxiliary hypotheses a clear separation between specification tests and misspecification tests can be made. Specification tests are concerned with the determination of the order of dynamics and with the discrimination between system dynamics and error dynamics, whereas misspecification tests deal with problems like nonconstant parameters, heteroscedasticity, serially correlated errors, and nonnormality of disturbances. The paper discusses the problems associated with testing for several (mis-) specification tests jointly or sequentially, and suggests an overall testing strategy.
scientific article; zbMATH DE number 3980334
scientific article