Efficient Sampling for Realized Variance Estimation in Time-Changed Diffusion Models

TL;DR

This paper compares different intrinsic time sampling methods for realized variance estimation, demonstrating that hitting time sampling is optimal under low noise, while realized business time excels with higher noise, supported by theory, simulations, and stock data.

Contribution

It introduces and analyzes the efficiency of hitting time and realized business time sampling schemes within a flexible diffusion-jump model for realized variance estimation.

Findings

Hitting time sampling is most efficient at low noise levels.

Realized business time sampling outperforms at higher noise levels.

Empirical application shows improved forecast accuracy using intrinsic sampling schemes.

Abstract

This paper analyzes the benefits of sampling intraday returns in intrinsic time for the realized variance (RV) estimator. We theoretically show in finite samples that depending on the permitted sampling information, the RV estimator is most efficient under either hitting time sampling that samples whenever the price changes by a pre-determined threshold, or under the new concept of realized business time that samples according to a combination of observed trades and estimated tick variance. The analysis builds on the assumption that asset prices follow a diffusion that is time-changed with a jump process that separately models the transaction times. This provides a flexible model that allows for leverage specifications and Hawkes-type jump processes and separately captures the empirically varying trading intensity and tick variance processes, which are particularly relevant for disentangling the driving forces of the sampling schemes. Extensive simulations confirm our theoretical results and show that for low levels of noise, hitting time sampling remains superior while for increasing noise levels, realized business time becomes the empirically most efficient sampling scheme. An application to stock data provides empirical evidence for the benefits of using these intrinsic sampling schemes to construct more efficient RV estimators as well as for an improved forecast performance.