Specification Tests for GARCH Processes with Nuisance Parameters on the Boundary

This article develops tests for the correct specification of conditional variance function in GARCH models when true parameter may lie on boundary space. The test statistics considered are Kolmogorov-Smirnov and Cramér-von Mises type, based empirical processes marked by centered squared residuals. limiting distributions depend unknown nuisance parameters a nontrivial way, making difficult to implement. We therefore introduce novel bootstrap procedure which is shown be asymptotically valid under general conditions, irrespective presence boundary. proposed approach shrinking estimates used generate sample toward space at proper rate. It simple implement fast applications, as associated have closed form expressions. Although designed data generating process with fixed (i.e., independent size n), we also discuss how obtain inference sequences DGPs approaching n−1/2 A simulation study demonstrates that new tests: (i) excellent finite behavior terms rejection probabilities null well alternative; (ii) provide useful complement existing procedures Ljung-Box type approaches. Two examples illustrate implementation applications.