Estimating ARCH Models when the Coefficients are Allowed to be Equal to Zero

In order to be consistent with volatility processes, the autoregressiveconditional heteroskedastic (ARCH) models are constrained to havenon-negative coefficients. The estimators incorporating these constraints possessnon standard asymptotic distributions when the true parameter has zerocoefficients. This situation, where the parameter is on the boundary of theparameter space, must be considered to derive the critical values of tests thatone or several ARCH coefficients are equal to zero. In this paper we comparethe asymptotic theoretical properties, as well as the finite sample behavior, ofthe main estimation methods in this framework.