Assessment of Uncertainty in High Frequency Data: The Observed Asymptotic Variance

Mykland, Per A.; Zhang, Lan

doi:10.3982/ecta12501

Cited by 42 publications

(27 citation statements)

References 89 publications

(143 reference statements)

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“…We also contribute to the literature on Edgeworth expansions, which have been used both in parametric and, less frequently, nonparametric contexts; see, e.g., Rao (1976) andHall (1992a). Fixed-n versus asymptotic-based Studentization has also captured some recent interest in other contexts, e.g., Mykland and Zhang (2015). Finally, see Calonico et al (2016) for uniformly valid Edgeworth expansions and optimal inference.…”

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confidence: 97%

On the Effect of Bias Estimation on Coverage Accuracy in Nonparametric Inference

Calónico

Cattaneo

Farrell

2018

Journal of the American Statistical Association

302

281

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Nonparametric methods play a central role in modern empirical work. While they provide inference procedures that are more robust to parametric misspecification bias, they may be quite sensitive to tuning parameter choices. We study the effects of bias correction on confidence interval coverage in the context of kernel density and local polynomial regression estimation, and prove that bias correction can be preferred to undersmoothing for minimizing coverage error and increasing robustness to tuning parameter choice. This is achieved using a novel, yet simple, Studentization, which leads to a new way of constructing kernel-based bias-corrected confidence intervals. In addition, for practical cases, we derive coverage error optimal bandwidths and discuss easy-toimplement bandwidth selectors. For interior points, we show that the MSE-optimal bandwidth for the original point estimator (before bias correction) delivers the fastest coverage error decay rate after bias correction when second-order (equivalent) kernels are employed, but is otherwise suboptimal because it is too "large". Finally, for odddegree local polynomial regression, we show that, as with point estimation, coverage error adapts to boundary points automatically when appropriate Studentization is used; however, the MSE-optimal bandwidth for the original point estimator is suboptimal.All the results are established using valid Edgeworth expansions and illustrated with simulated data. Our findings have important consequences for empirical work as they indicate that bias-corrected confidence intervals, coupled with appropriate standard errors, have smaller coverage error and are less sensitive to tuning parameter choices in practically relevant cases where additional smoothness is available.Keywords: Edgeworth expansion, coverage error, kernel methods, local polynomial regression.to characterize leading bias terms, as is usually the case in practice where MSE-optimal bandwidth are employed, our robust bias correction approach yields higher-order improvements relative to standard undersmoothing.Our standard error formulas are based on fixed-n calculations, as opposed to asymptotics, which also turns out to be important. We show that using asymptotic variance formulas can introduce further errors in coverage probability, with particularly negative consequences at boundary points. This turns out to be at the heart of the "quite unexpected" conclusion found by Chen and Qin (2002, Abstract) that local polynomial based confidence intervals are not boundary-adaptive in coverage error: we prove that this is not the case with proper Studentization. Thus, as a by-product of our main theoretical work, we establish higher-order boundary carpentry of local polynomial based confidence intervals that use a fixed-n standard error formula, a result that is of independent (but related) interest. This paper is connected to the well-established literature on nonparametric smoothing, see for reviews. For more recent work on bias and related issues in nonparametric inference, ...

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confidence: 97%

On the Effect of Bias Estimation on Coverage Accuracy in Nonparametric Inference

Calónico

Cattaneo

Farrell

2018

Journal of the American Statistical Association

302

281

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“…Remark 2. (Estimating the asymptotic variance) If the statistician does not have a (parametric) variance estimator at hand and that her parametric estimator can be written as in Mykland and Zhang (2017), one can use the techniques of the cited paper to obtain a variance estimate. Investigating if such techniques would work in our setting is beyond the scope of this paper.…”

Section: Regular Observation Casementioning

confidence: 99%

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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“…Under some regularity conditions, according to the "integralto-spot device" in Mykland and Zhang [2016] 3 2(∆T ) 2…”

Section: Estimating Aggregated Liquidity Risk [G G]mentioning

confidence: 99%

Model-free approaches to discern non-stationary microstructure noise and time-varying liquidity in high-frequency data

Chen

Mykland

2017

Journal of Econometrics

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In this paper, we provide non-parametric statistical tools to test stationarity of microstructure noise in general hidden Itô semimartingales, and discuss how to measure liquidity risk using high-frequency financial data. In particular, we investigate the impact of non-stationary microstructure noise on some volatility estimators, and design three complementary tests by exploiting edge effects, information aggregation of local estimates and high-frequency asymptotic approximation. The asymptotic distributions of these tests are available under both stationary and non-stationary assumptions, thereby enable us to conservatively control type-I errors and meanwhile ensure the proposed tests enjoy the asymptotically optimal statistical power. Besides, it also enables us to empirically measure aggregate liquidity risks by these test statistics. As byproducts, functional dependence and endogenous microstructure noise are briefly discussed. Simulation with a realistic configuration corroborates our theoretical results, and our empirical study indicates the prevalence of non-stationary microstructure noise in New York Stock Exchange.

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Assessment of Uncertainty in High Frequency Data: The Observed Asymptotic Variance

Cited by 42 publications

References 89 publications

On the Effect of Bias Estimation on Coverage Accuracy in Nonparametric Inference

On the Effect of Bias Estimation on Coverage Accuracy in Nonparametric Inference

Local Parametric Estimation in High Frequency Data

Model-free approaches to discern non-stationary microstructure noise and time-varying liquidity in high-frequency data

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