Designing Realised Kernels to Measure the Ex-Post Variation of Equity Prices in the Presence of Noise

Abstract

This paper shows how to use realised kernels to carry out efficient feasible inference on the ex-post variation of underlying equity prices in the presence of simple models of market frictions. The issue is subtle with only estimators which have symmetric weights delivering consistent estimators with mixed Gaussian limit theorems. The weights can be chosen to achieve the best possible rate of convergence and to have an asymptotic variance which is close to that of the maximum likelihood estimator in the parametric version of this problem. Realised kernels can also be selected to (i) be analysed using endogenously spaced data such as that in databases on transactions, (ii) allow for market frictions which are endogenous, (iii) allow for temporally dependent noise. The finite sample performance of our estimators is studied using simulation, while empirical work illustrates their use in practice.

The Testing of Causal Stock Returns-Trading Volume Dependencies with the Aid of Copulas

“…Barndorff-Nielsen et al [8,9,10] have introduced the class of realized kernel estimators. A survey of realized variance estimators can be found in Bandi and Russel [4] and McAleer and Medeiros [34].…”

Coupling High-Frequency Data with Nonlinear Models in Multiple-Step-Ahead Forecasting of Energy Markets' Volatility

“…3 Andersen and Bollerslev (1998); Andersen et al (2001Andersen et al ( , 2003; Zhang et al (2005); Bandi and Russell (2006); Hansen and Lunde (2006); Barndorff-Nielsen et al (2008). 4 Kang and Yoon (2013) recently investigate the ability of FIGARCH models to capture the volatility of energy markets.…”

“…5 We should note that the realized kernel estimator is computed without accounting for end effects, i.e., replacing the first and the last observation by local averages to eliminate the corresponding noise components (socalled "jittering"). Barndorff-Nielsen et al (2008) argue that these effects are important theoretically but are negligible practically. When studying conditional volatility, it is important to separate the contribution of the two components of the quadratic variation process, i.e., the continuous part from the jump part.…”

“…Zhang et al (2005) also provide the theory for the optimal choice of G grids, G * = cN 2/3 , where the constant c may be set to minimize the total asymptotic variance. A different approach to addressing noise developed by Barndorff-Nielsen et al (2008) is realized kernels. The realized kernel variance estimator over [t − h, t] is defined by…”

Forecasting Realized Volatility with Linear and Nonlinear Models

“…However, microstructure effects introduce a severe bias on the daily volatility estimation. Zhang, Mykland and Aït-Sahalia (2005), Bandi and Russell (2006), Hansen and Lunde (2006), and BarndorffNielsen, Hansen, Lunde, and Shephard (2008), among others, have discussed various solutions to the inconsistency problem caused.…”