Abstract

We give a general time-varying parameter model, where the multidimensional parameter possibly includes jumps. The quantity of interest is defined as the integrated value over time of the parameter process $\Theta =T^{-1}{\int }_0^T{\theta }_t^{*}dt$. We provide a local parametric estimator (LPE) of Θ and conditions under which we can show the central limit theorem. Roughly speaking those conditions correspond to some uniform limit theory in the parametric version of the problem. The framework is restricted to the specific convergence rate n^1∕2. Several examples of LPE are studied: estimation of volatility, powers of volatility, volatility when incorporating trading information and time-varying MA(1).

摘要

我们给出了一个通用的时变参数模型，其中多维参数可能包括跳跃。感兴趣的数量定义为参数过程随时间的累计值 $\Theta ={Ť}^{-\mathrm{1个}}{\int }_0^{Ť}{\theta }_{Ť}^{*}dŤ$。我们提供Θ的局部参数估计量（LPE）和条件，在这些条件下我们可以证明中心极限定理。粗略地说，这些条件对应于问题的参数形式中的一些统一极限理论。该框架限于特定的收敛速度n ^1∕2。研究了LPE的几个示例：波动率估计，波动率幂，合并交易信息时的波动率和时变MA（1）。