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Further Results on Pseudo‐Maximum Likelihood Estimation and Testing in the Constant Elasticity of Variance Continuous Time Model
Author(s) -
Iglesias Emma M.,
Phillips Garry D. A.
Publication year - 2020
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/jtsa.12499
Subject(s) - mathematics , estimator , elasticity (physics) , constant elasticity of variance model , maximum likelihood , constant (computer programming) , variance (accounting) , likelihood function , context (archaeology) , econometrics , discretization , statistics , volatility (finance) , mathematical analysis , stochastic volatility , computer science , paleontology , materials science , accounting , business , composite material , sabr volatility model , biology , programming language
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.