This paper proposes a novel Pearson-type quasi maximum likelihood estimator (QMLE) of GARCH($p, q$) models. Unlike the existing Gaussian QMLE, Laplacian QMLE, generalized non-Gaussian QMLE, or LAD estimator, our Pearsonian QMLE (PQMLE) captures not the heavy-tailed but also the skewed...