Estimation of integrated quadratic covariation with endogenous sampling times

Potiron, Yoann; Mykland, Per A.

doi:10.1016/j.jeconom.2016.10.004

Cited by 18 publications

(29 citation statements)

References 39 publications

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“…Subsequently, we believe that many other examples can be solved using the framework of our paper, which is simple and natural. This was successfully done in our related papers Potiron and Mykland (2017) and Clinet and Potiron (2018a). In those instances, the regular conditional distribution trick significantly simplified the work of the proofs.…”

Section: Resultsmentioning

confidence: 86%

“…[13] Clinet, S. and Y. Potiron (2017). Estimation for high-frequency data under parametric market microstructure noise.…”

Section: Resultsmentioning

confidence: 99%

“…Two further examples include our own recent work. Potiron and Mykland (2017) introduced a bias-corrected Hayashi-Yoshida estimator (Hayashi and Yoshida (2005)) of the high-frequency covariance and showed the corresponding CLT under endogenous and asynchronous observations. To model duration data, Clinet and Potiron (2018a) built a time-varying Hawkes self-exciting process, derived the bias-corrected MLE and showed the CLT of the corresponding LPE.…”

Section: Further Examplesmentioning

confidence: 99%

“…The type of endogeneity is such that there is no asymptotic bias in the related central limit theorem. Finally, the model allows for endogenous observation times in the general multidimensional HBT model introduced in Potiron and Mykland (2017). In that case, the central limit theorem features an asymptotic bias.…”

Section: Non Regular Observation Timesmentioning

confidence: 99%

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Local Parametric Estimation in High Frequency Data

Potiron

Mykland

2019

Journal of Business & Economic Statistics

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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 Θ = T −1 T 0 θ * t dt. We provide a local parametric estimator (LPE) of Θ 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). Keywords: integrated volatility; market microstructure noise; powers of volatility; quasi maximum likelihood estimator * We are indebted to Simon Clinet, Takaki Hayashi, Dacheng Xiu, participants of the seminars in Berlin and Tokyo and conferences in Osaka, Toyama, the SoFie annual meeting in Hong Kong, the PIMS meeting in Edmonton for valuable comments, which helped in improving the quality of the paper.We assume that we observe the d-dimensional vectors Z 0,n , · · · , Z Nn,n , where N n can be random, the observation times satisfy τ 0,n := 0 < τ 1,n < · · · < τ Nn,n ≤ T . The observations and the observation times are both related to the latent parameter θ * t . As an example, the observations can satisfy Z τ i,n ,n = X τ i,n + i,n , where X t = σ t dW t stands for the efficient price, W t is a standard Brownian motion, i,n corresponds to the market microstructure noise (which will be restricted to be of order i,n = O p (1/ √ n) due to the limitation of the technology developed in Section 3), is independent and identically distributed (IID) and independent from X t , and the latent parameter is equal to the volatility, i.e. θ * t = σ 2 t . We assume that the parameter process θ * t takes values in K, a (not necessarily compact) subset of R p . We do not assume any independence between θ * t and the other quantities driving the observations, such as the Brownian motion of the efficient price process. In particular, there can be leverage effect (see e.g. Wang and Mykland (2014), Aït-Sahalia et al. (2017)). Also, the arrival times τ i,n and the parameter θ * t can be correlated, i.e. there is (some kind of) endogeneity in sampling times. AsymptoticsThere are commonly two choices of asymptotics in the literature: the high-frequency asymptotics, which makes the number of observations explode on [0, T ], and the lowfrequency asymptotics, which takes T to infinity. We choose the former one. Investigating the low-frequency implementation case is beyond the scope of this paper 1 .1 If we set down the asymptotic theory in the same way as in p.3 of Dahlhaus (1997), we conjecture that the results of this paper would stay true.

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Section: Resultsmentioning

confidence: 86%

“…[13] Clinet, S. and Y. Potiron (2017). Estimation for high-frequency data under parametric market microstructure noise.…”

Section: Resultsmentioning

confidence: 99%

Section: Further Examplesmentioning

confidence: 99%

Section: Non Regular Observation Timesmentioning

confidence: 99%

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Local Parametric Estimation in High Frequency Data

Potiron

Mykland

2019

Journal of Business & Economic Statistics

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“…As a pioneer work, [16] introduced the autoregressive conditional duration (ACD) model. Other references include and are not limited to [39], [41], as well as [4], [18], and more recently [36] and [35].…”

Section: Introductionmentioning

confidence: 99%

Statistical inference for the doubly stochastic self-exciting process

Clinet¹,

Potiron²

2018

Bernoulli

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We introduce and show the existence of a Hawkes self-exciting point process with exponentiallydecreasing kernel and where parameters are time-varying. The quantity of interest is defined as the integrated parameter T −1 T 0 θ * t dt, where θ * t is the time-varying parameter, and we consider the high-frequency asymptotics. To estimate it naïvely, we chop the data into several blocks, compute the maximum likelihood estimator (MLE) on each block, and take the average of the local estimates. The asymptotic bias explodes asymptotically, thus we provide a non-naïve estimator which is constructed as the naïve one when applying a first-order bias reduction to the local MLE. We show the associated central limit theorem. Monte Carlo simulations show the importance of the bias correction and that the method performs well in finite sample, whereas the empirical study discusses the implementation in practice and documents the stochastic behavior of the parameters.

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Estimation for high-frequency data under parametric market microstructure noise

Clinet

Potiron

2020

Ann Inst Stat Math

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Estimation of integrated quadratic covariation with endogenous sampling times

Cited by 18 publications

References 39 publications

Local Parametric Estimation in High Frequency Data

Local Parametric Estimation in High Frequency Data

Statistical inference for the doubly stochastic self-exciting process

Estimation for high-frequency data under parametric market microstructure noise

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