Nonsynchronous covariation process and limit theorems

Hayashi, Teru; Yoshida, Nakahiro

doi:10.1016/j.spa.2010.12.005

Cited by 52 publications

(74 citation statements)

References 15 publications

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“…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

Stat Inference Stoch Process

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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.

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Section: Asymptotic Resultsmentioning

confidence: 99%

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

Li¹

2015

Stat Inference Stoch Process

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“…They proposed an alternative estimator and they investigated the asymptotic distributions. In [2], the authors complement the results in [5] by establishing a second-order asymptotic expansion for the distribution of the estimator in a fairly general setup, including random sampling schemes and (possibly random) drift terms. Several further works have been realized when data on two securities are observed non-synchronously, see also [1].…”

Section: Motivation and Contextmentioning

confidence: 92%

“…In the bivariate case, Hayashi and Yoshida [5] considered the problem of estimating the covariation of two diffusion processes under a non-synchronous sampling scheme. They proposed an alternative estimator and they investigated the asymptotic distributions.…”

Section: Motivation and Contextmentioning

confidence: 99%

Large and moderate deviations of realized covolatility

Djellout

Samoura

2014

Statistics & Probability Letters

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Abstract. In this note, we consider the large and moderate deviation principle of the estimators of the integrated covariance of two-dimensional diffusion processes when they are observed only at discrete times in a synchronous manner. The proof is extremely simple. It is essentially an application of the contraction principle for the results given in the case of the volatility [4].AMS 2000 subject classifications: 60F10, 62J05, 60J05. Motivation and contextGiven a filtred probability space (Ω, F, (F t ), P), let (X 1,t , X 2,t ) be a two dimensional diffusion process given bywhere ((B 1,t , B 2,t ), t ≥ 0) is a two-dimensional Gaussian process with independent increments, zero mean and covariance matrixIn (1.1), (u 1 , u 2 ) is a progressively measurable process (possibly unknown). In what follows, we restrict our attention to the case when σ 1 , σ 2 and ρ are deterministic functions; the functions σ i , i = 1, 2 take positive values while ρ takes values in the interval [−1, 1]. Note that the marginal processes B 1 and B 2 are Brownian motions (BM). Moreover, we can define a process B * t such that (B 1,t , B * t ) t≥0 is a two-dimensional BM and dB 2,t = ρ t dB 1,t + 1 − ρ 2 t dB * t for every t ≥ 0. In this note, the parameter of interest is the (deterministic) covariance of X 1 and X 2(1.2)In finance, X 1 , X 2 · is the integrated covariance (over [0, 1]) of the logarithmic prices X 1 and X 2 of two securities. It is an essential quantity to be measured for risk management purposes. The covariance for multiple price processes is of great interest in many financial applications. The naive estimator is the realized covariance, which is the analogue of realized variance for a single process.Typically X 1,t and X 2,t are not observed in continuous time but we have only discrete time observations. Given discrete equally spaced observation (X 1,t n k , X 2,t n k , k = 1, · · · , n) in Date: October 11, 2013.

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“…Non-synchronous covariance estimation schemes have been developed: Fourier analytic approach (Malliavin and Mancino [32], Malliavin et al [33]) and the cumulative covariance estimator (Hayashi and Yoshida [23,21,22], Mykland [40]).…”

Section: Introductionmentioning

confidence: 99%

Confidence interval for correlation estimator between latent processes

Kimura

2019

Jpn J Stat Data Sci

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Kimura and Yoshida [26] treated a model in which the finite variation part of a two-dimensional semimartingale is expressed by time-integration of latent processes. They proposed a correlation estimator between the latent processes and proved its consistency and asymptotic mixed normality. In this paper, we discuss the confidence interval of the correlation estimator to detect the correlation. We propose two types of estimators for asymptotic variance of the correlation estimator and prove their consistency in a high frequency setting. Our model includes doubly stochastic Poisson processes whose intensity processes are correlated Itô processes. We compare our estimators based on the simulation of the doubly stochastic Poisson processes.

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Nonsynchronous covariation process and limit theorems

Cited by 52 publications

References 15 publications

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

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

Large and moderate deviations of realized covolatility

Confidence interval for correlation estimator between latent processes

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