Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 2 of 2
Full-Text Articles in Applied Statistics
Adaptive Testing In Arch Models, Douglas G. Steigerwald, Oliver Linton
Adaptive Testing In Arch Models, Douglas G. Steigerwald, Oliver Linton
Douglas G. Steigerwald
Specification tests for conditional heteroskedasticity that are derived under the assumption that the density of the innovation is Gaussian may not be powerful in light of the recent empirical results that the density is not Gaussian. We obtain specification tests for conditional heteroskedasticity under the assumption that the innovation density is a member of a general family of densities. Our test statistics maximize asymptotic local power and weighted average power criteria for the general family of densities. We establish both first-order and second-order theory for our procedures. Simulations indicate that asymptotic power gains are achievable in finite samples.
Asymptotic Bias For Quasi-Maximum Likelihood Estimators In Models With Conditional Heteroskedasticity, Douglas G. Steigerwald, Whitney Newey
Asymptotic Bias For Quasi-Maximum Likelihood Estimators In Models With Conditional Heteroskedasticity, Douglas G. Steigerwald, Whitney Newey
Douglas G. Steigerwald
Virtually all applications of time-varying conditional variance models use a quasi-maximum likelihood estimator (QMLE). Consistency of a QMLE requires an identification condition that the quasi-log-likelihood have a unique maximum at the true conditional mean and relative scale parameters. We show that the identification condition holds for a non-Gaussian QMLE if the conditional mean is identically zero or if a symmetry condition is satisfied. Without symmetry an additional parameter, for the location of the innovation density, must be added for consistency. We calculate the efficiency loss from adding such a parameter under symmetry, when the parameter is not needed. We also …