Further Results on Pseudo‐Maximum Likelihood Estimation and Testing in the Constant Elasticity of Variance Continuous Time Model

Abstract

Constant elasticity volatility processes have been shown to be useful, for example, to encompass a number of existing models that have closed‐form likelihood functions. In this article, we extend the existing literature in two directions: first we find explicit closed form solutions of the pseudo maximum likelihood estimators (MLEs) by discretizing the diffusion function and we provide their asymptotic theory in the context of the constant elasticity of variance (CEV) model characterized by a general CEV parameter ρ ≥ 0. Second we obtain bias expansions for those pseudo MLEs also in terms of ρ ≥ 0. We provide a general framework since only the cases with ρ = 0 and ρ = 0.5 have been considered in the literature so far. When the time series is not positive almost surely, we need to impose the restriction that ρ is a non‐negative integer.