Local Parametric Estimation in High Frequency Data

TL;DR

This paper introduces a local parametric estimator for time-varying parameters in high-frequency data, accommodating jumps and providing asymptotic normality under specific conditions.

Contribution

It develops a general framework for local parametric estimation of integrated parameters in high-frequency models with time-varying and jump components.

Findings

Established a central limit theorem for the estimator.

Applied the method to volatility and trading data.

Analyzed various models including volatility and MA(1).

Abstract

In this paper, 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 $\Theta$ 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).