Closed-Form Estimation of Finite-Order ARCH Models: Asymptotic Theory and Finite-Sample Performance

Prono, Todd

doi:10.17016/FEDS.2016.083r1

Working Paper

Closed-Form Estimation of Finite-Order ARCH Models: Asymptotic Theory and Finite-Sample Performance

Abstract: 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 empirically by many (high frequency) financial returns. These conditions are not shared by competing closed-form estimators like OLS. Identification of these TSLS estimators depends on asymmetry, either in the model's rescaled errors or in the conditional variance function. Monte Carlo studies reveal TSLS estimation to sizably outperform quasi maximum likelihood estimation in (relatively) small samples. This outperformance is most pronounced when returns are heavily skewed.

Keywords: ARCH; Closed form; Heavy tails; Instrumental variables; Regular variation; Two stage least squares;

JEL Classification: C13; C22; C58;

https://doi.org/10.17016/FEDS.2016.083r1