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.

中文翻译：

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方差连续时间模型的恒定弹性中的伪最大似然估计和检验的进一步结果

恒定弹性波动率过程已被证明是有用的，例如，包含许多具有封闭形式似然函数的现有模型。在本文中，我们将现有文献扩展到两个方向：首先，我们通过离散化扩散函数找到伪最大似然估计量 (MLE) 的显式封闭形式解，并在恒定方差弹性的背景下提供它们的渐近理论（ CEV) 模型，其特征在于通用 CEV 参数 ρ ≥ 0。其次，我们也根据 ρ ≥ 0 获得了这些伪 MLE 的偏差扩展。我们提供了一个通用框架，因为仅考虑了 ρ = 0 和 ρ = 0.5 的情况在迄今为止的文献中。当时间序列几乎肯定不是正数时，我们需要施加限制，即 ρ 是一个非负整数。