Linear GARCH(1,1) and threshold GARCH(1,1) processes are established as regularly varying, meaning their heavy tails are Pareto like, under conditions that allow the innovations from the, respective, processes to be skewed. Skewness is considered a stylized fact for many financial returns...

Simple, multi-step estimators are developed for the popular GARCH(1,1) model, where these estimators are either available entirely in closed form or dependent upon a preliminary estimate from, for example, quasi-maximum likelihood. Identification sources to asymmetry in the model's innovations,...

Contained herein are detailed proofs of all the Lemmas that support the main Theorems discussed in the paper, "Simple Estimators for GARCH models."Original paper can be found at: "https://ssrn.com/abstract=2897867" https://ssrn.com/abstract=2897867

Closed-form estimators are developed for the popular GARCH(1,1) and threshold GARCH(1,1) models, with select results extending to the general GARCH(p, q) model. Identification sources to asymmetry, either in the distribution of rescaled errors or in the conditional variance function. Given...

Strong consistency and weak distributional convergence to highly non-Gaussian limits are established for closed-form, two stage least squares (TSLS) estimators for a class of ARCH(p) models. Conditions for these results include (relatively) mild moment existence criteria that are supported...

Simple, multi-step estimators are developed for the popular GARCH(1,1) model, where these estimators are either available entirely in closed form or dependent upon a preliminary estimate from, for example, quasi-maximum likelihood. Identification sources to asymmetry in the model's innovations,...

I propose closed-form estimators for the GARCH(1,1) model that are based on second-order covariances. The ability to obtain closed-form estimates derives from skewness in the sequence being modeled, which permits separate identification and estimation of the ARCH and GARCH effects. I show these...

This paper provides detailed proofs of all Lemmas contained in “Closed-Form Estimation of Finite-Order ARCH Models: Asymptotic Theory and Finite-Sample Performance.” Specifically, regular variation of ARCH(1) and threshold ARCH(1) processes is established when the, respective, model's...