Adaptive inference for a semiparametric generalized autoregressive conditional heteroskedasticity model

This paper considers a semiparametric generalized autoregressive conditional heteroskedasticity (S-GARCH) model. For this model, we first estimate the time-varying long run component for unconditional variance by the kernel estimator, and then estimate the non-time-varying parameters in GARCH-type short run component by the quasi maximum likelihood estimator (QMLE). We show that the QMLE is asymptotically normal with the parametric convergence rate. Next, we construct a Lagrange multiplier test for linear parameter constraint and a portmanteau test for model checking, and obtain their asymptotic null distributions. Our entire statistical inference procedure works for the non-stationary data with two important features: first, our QMLE and two tests are adaptive to the unknown form of the long run component; second, our QMLE and two tests share the same efficiency and testing power as those in variance targeting method when the S-GARCH model is stationary. (C) 2020 Elsevier B.V. All rights reserved.

Automated summary

This paper proposes a S-GARCH model and estimation methods for both long run and short run variance components, as well as hypothesis testing approaches. The results show that the proposed methods have good efficiency and testing power when the S-GARCH model is stationary.