Testing For Common Features

This paper introduces a class of statistical tests for the hypothesis that some feature of a data set is common to several variables. A feature is detected in a single series by a hypothesis test where the null is that it is absent, and the alternative is that it is present. Examples are serial correlation, trends, seasonality, heteroskedasticity, ARCH, excess kurtosis and many others. A feature is common to a multivariate data set if a linear combination of the series no longer has the feature. A test for common features can be based on the minimized value of the feature test over all linear combinations of the data. A bound on the distribution for such a test is developed in the paper. For many important cases, an exact asymptotic critical value can be obtained which is simply a test of overidentifying restrictions in an instrumental variable regression.