论文标题
具有高频数据的扩散模型的基于预测的估计
Prediction-based estimation for diffusion models with high-frequency data
论文作者
论文摘要
本文使用基于预测的估计函数获得参数推断的渐近结果，当数据是具有无限时间范围扩散过程的高频观察结果时。具体而言，数据是在$ n $等距时间点$δ_ni $的扩散过程的观察，而渐近方案为$Δ_n\ to 0 $ to $ to $和$nδ_n\ to \ infty $。对于有用的基于预测的估计功能的有用且可拖动的类别，在扩散过程和估计函数的标准弱规则条件下证明了一致的估计器的存在。估计器的渐近正态性是在额外的速率条件下建立的$nδ_n^3 \至0 $。基于预测的估计函数是近似Martingale的估计功能，其功能比以前所研究的范围较小，并且需要新的非标准渐近理论。提出了一种用于计算估计量渐近方差的蒙特卡洛方法。
This paper obtains asymptotic results for parametric inference using prediction-based estimating functions when the data are high frequency observations of a diffusion process with an infinite time horizon. Specifically, the data are observations of a diffusion process at $n$ equidistant time points $Δ_n i$, and the asymptotic scenario is $Δ_n \to 0$ and $nΔ_n \to \infty$. For a useful and tractable classes of prediction-based estimating functions, existence of a consistent estimator is proved under standard weak regularity conditions on the diffusion process and the estimating function. Asymptotic normality of the estimator is established under the additional rate condition $nΔ_n^3 \to 0$. The prediction-based estimating functions are approximate martingale estimating functions to a smaller order than what has previously been studied, and new non-standard asymptotic theory is needed. A Monte Carlo method for calculating the asymptotic variance of the estimators is proposed.
