Limit theorems for the pre-averaged Hayashi–Yoshida estimator with random sampling

Self Cite

We establish a central limit theorem for a class of pre-averaging covariance estimators in a general endogenous time setting. In particular, we show that the time endogeneity has no impact on the asymptotic distribution if certain functionals of observation times are asymptotically well-defined. This contrasts with the case of the realized volatility in a pure diffusion setting. We also discuss an optimal choice of the weight function in the pre-averaging.

“…; see Koike (2014) for details. See also Section 6.3 of Bibinger (2012) where other advantages of such a procedure are discussed for the case of the subsampling approach.…”

Section: The Settingmentioning

confidence: 99%

Time endogeneity and an optimal weight function in pre-averaging covariance estimation

Koike

2016

Self Cite

“…Without presence of the multiple observations, the limit theorems of the covariation estimator under non-synchronous observations and random sampling have been deduced by Hayashi and Yoshida (2011) without microstructure noise and by Koike (2014) with presence of microstructure noise.…”

Section: Asymptotic Resultsmentioning

confidence: 99%

Estimating integrated co-volatility with partially miss-ordered high frequency data

Li¹

2015

The covariation of short-time period returns between securities plays an important role in many area of finance. Under the wide availability of high frequency financial data, realized covariation, as an ex-post measure of the covariation, can accurately estimate the quadratic covariation. However, the realized covariation fails to work when the multiple records appear. In this paper, we propose an estimator of integrated covariation, which is robust to the high frequency data containing multiple records. Consistency of the estimator and central limit theorem have been established. Moreover, several extensions which make the estimator available to different types of high frequency data are also considered. Simulation study confirms the performance of the estimator.

“…However, it is unclear whether the same approach works or not in our non-semimartingale case. For the properties of the pre-averaged Hayashi-Yoshida estimator, see Koike (2014Koike ( , 2016b and references therein.…”

Section: 2mentioning

confidence: 99%

Estimation of the lead–lag parameter between two stochastic processes driven by fractional Brownian motions

Chiba

2019

In this paper, we consider the problem of estimating the lead-lag parameter between two stochastic processes driven by fractional Brownian motions (fBMs) of the Hurst parameter greater than 1/2. First we propose a lead-lag model between two stochastic processes involving fBMs, and then construct a consistent estimator of the lead-lag parameter with possible convergence rate. Our estimator has the following two features. Firstly, we can construct the lead-lag estimator without using the Hurst parameters of the underlying fBMs. Secondly, our estimator can deal with some non-synchronous and irregular observations. We explicitly calculate possible convergence rate when the observation times are (1) synchronous and equidistant, and (2) given by the Poisson sampling scheme. We also present numerical simulations of our results using the R package YUIMA.2010 Mathematics Subject Classification. 62M09 and 60G22.