Residual-Based Inference on Moment Hypotheses, With an Application to Testing for Constant Correlation

The paper proposes a test for constant correlations allowing for breaks at unknown times in the marginal means and variances. Theoretically and in an application to US and German stock returns, we find that not accounting for changes in the marginal moments has severe consequences. This is because incorrect standardization of the series transfers to the sample correlations onto which the tests are built. Correcting for variance breaks at unknown time will have an asymptotic effect. To discuss adjustments, we tackle the issue more generally by considering partial-sums based inference on moment properties of unobserved processes which is conducted on the basis of estimated counterparts obtained in a preliminary step. The paper gives a characterization of the conditions under which the effect of filtering does not vanish asymptotically. The analysis extends to models with breaks in parameters at estimated time