首页/论文/0803.0392

arXiv 0803.03922008-03stat.MEstat.ML

高频数据的多尺度推断

Multiscale Inference for High-Frequency Data

Sofia Olhede, Adam Sykulski, Grigorios Pavliotis

备注：: 26 pages, 9 figures

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

摘要英文摘要相关论文

摘要：

本文提出了一种新的多尺度估计的综合波动的伊藤过程，在市场微观结构噪声（观测误差）的存在。观测过程的多尺度结构被表示为频率的频率和多尺度比的概念被引入到量化的偏差，由于观测误差的已实现的综合波动。多尺度比估计从一个单一的样本路径，并提出了一个频率的频率偏差校正程序，同时减少方差。我们扩展的方法，包括相关的观测误差，并提供隐含的时域形式的估计过程。将新方法应用于Heston模型和其他模型的综合波动率估计，仿真结果表明了新方法的有效性.

英文摘要：

This paper proposes a novel multiscale estimator for the integrated volatility of an Ito process, in the presence of market microstructure noise (observation error). The multiscale structure of the observed process is represented frequency-by-frequency and the concept of the multiscale ratio is introduced to quantify the bias in the realized integrated volatility due to the observation error. The multiscale ratio is estimated from a single sample path, and a frequency-by-frequency bias correction procedure is proposed, which simultaneously reduces variance. We extend the method to include correlated observation errors and provide the implied time domain form of the estimation procedure. The new method is implemented to estimate the integrated volatility for the Heston and other models, and the improved performance of our method over existing methods is illustrated by simulation studies.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

摘要英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Selective inference after feature selection via multiscale bootstrap

It is common to show the confidence intervals or $p$-values of selected features, or predictor variables in regression, but they often involve selection bias. The selective inference approach solves this bias by conditioning on the selection event. Most existing studies of selective inference consider a specific algorithm, such as Lasso, for feature selection, and thus they have difficulties in handling more complicated algorithms. Moreover, existing studies often consider unnecessarily restrictive events, leading to over-conditioning and lower statistical power. Our novel and widely-applicabl…

2022-06-01stat.ME

Multiscale inference for multivariate deconvolution

In this paper we provide new methodology for inference of the geometric features of a multivariate density in deconvolution. Our approach is based on multiscale tests to detect significant directional derivatives of the unknown density at arbitrary points in arbitrary directions. The multiscale method is used to identify regions of monotonicity and to construct a general procedure for the detection of modes of the multivariate density. Moreover, as an important application a significance test for the presence of a local maximum at a pre-specified point is proposed. The performance of the new m…

2016-11-16math.STstat.MEstat.TH

A central limit theorem for an omnibus embedding of multiple random graphs and implications for multiscale network inference

Performing statistical analyses on collections of graphs is of import to many disciplines, but principled, scalable methods for multi-sample graph inference are few. Here we describe an "omnibus" embedding in which multiple graphs on the same vertex set are jointly embedded into a single space with a distinct representation for each graph. We prove a central limit theorem for this embedding and demonstrate how it streamlines graph comparison, obviating the need for pairwise subspace alignments. The omnibus embedding achieves near-optimal inference accuracy when graphs arise from a common distr…

2019-06-26stat.ME

多尺度变点推断

Multiscale Change-Point Inference

针对指数族回归变点问题，提出了一种新的估计SMUCE（同时多尺度变点估计）。未知阶跃函数的估计是通过最小化α水平下多尺度检验的可接受区域上的变点数来实现的。多尺度检验统计量的渐近零分布控制了高估真实变点数K的概率。此外，我们推导出低估K的概率的指数界。通过平衡这些量，α将被选择为使得正确估计K的概率最大化。所有的结果甚至是非渐近的正常情况下。基于上述界，我们构造了未知阶跃函数及其变点的渐近诚实置信集。在同一时间，我们获得指数界估计的变点位置，例如产生的极大极小率O（1/n）的对数项。最后，SMUCE渐近地达到消失信号的最佳检测率。我们说明了如何动态规划技术可以有效地计算估计和置信区域。所提出的多尺度方法的性能说明了模拟和两个前沿的应用，从基因工程和光电子能谱。

2013-08-12math.STstat.MEstat.TH

Discrete-Time Statistical Inference for Multiscale Diffusions

We study statistical inference for small-noise-perturbed multiscale dynamical systems under the assumption that we observe a single time series from the slow process only. We construct estimators for both averaging and homogenization regimes, based on an appropriate misspecified model motivated by a second-order stochastic Taylor expansion of the slow process with respect to a function of the time-scale separation parameter. In the case of a fixed number of observations, we establish consistency, asymptotic normality, and asymptotic statistical efficiency of a minimum contrast estimator (MCE),…

2018-09-12math.PRmath.STstat.AP

基于欧拉特征包络的多尺度拓扑推断用于标记点过程

Multiscale Topological Inference for Marked Point Processes via Euler Characteristic Envelopes

本文提出一种多尺度拓扑推断框架，通过整合标记加权过滤与欧拉特征包络，用于分析标记点过程中的复杂空间结构和属性依赖关系。

2026-05-14stat.APstat.ME

更多相关论文收起更多论文

Selective inference for the problem of regions via multiscale bootstrap

A general approach to selective inference is considered for hypothesis testing of the null hypothesis represented as an arbitrary shaped region in the parameter space of multivariate normal model. This approach is useful for hierarchical clustering where confidence levels of clusters are calculated only for those appeared in the dendrogram, thus subject to heavy selection bias. Our computation is based on a raw confidence measure, called bootstrap probability, which is easily obtained by counting how many times the same cluster appears in bootstrap replicates of the dendrogram. We adjust the b…

2018-03-27math.STstat.MEstat.TH

Multiscale Bayesian State Space Model for Granger Causality Analysis of Brain Signal

Modelling time-varying and frequency-specific relationships between two brain signals is becoming an essential methodological tool to answer heoretical questions in experimental neuroscience. In this article, we propose to estimate a frequency Granger causality statistic that may vary in time in order to evaluate the functional connections between two brain regions during a task. We use for that purpose an adaptive Kalman filter type of estimator of a linear Gaussian vector autoregressive model with coefficients evolving over time. The estimation procedure is achieved through variational Bayes…

2018-04-13stat.ME

多尺度随机酶动力学模型的统计推断 via 群体混沌传播

Statistical inference for a multiscale stochastic model of enzyme kinetics via propagation of chaos

Department of Mathematics, Louisiana State University（路易斯安那州立大学数学系）；School of Mathematical Sciences, University of Nottingham（诺丁汉大学数理科学学院）

本文研究了具有跳跃的随机微分方程，用于多阶段米氏-门琴酶动力学，通过群体混沌传播建立简化模型并构造新的粒子系统进行推断。

2026-10-21math.FAmath.PRmath.ST

在 Donsker 定理的边缘：多尺度扫描统计量的渐近性质

At the edge of Donsker's Theorem: Asymptotics of multiscale scan statistics

本文提出用乘法加权替代加法惩罚，通过弱收敛论证构建可行的多尺度检验，保留最优检测性质并扩展至非平稳非线性时间序列，应用于信号发现、回归拟合优度检验、多变点检测及伊比利亚半岛停电分析。

2025-06-05math.STstat.MEstat.TH

Multiscale Causal Structure Learning

Sapienza University of Rome（罗马第一大学）；CENTAI（CENTAI研究所）

The inference of causal structures from observed data plays a key role in unveiling the underlying dynamics of the system. This paper exposes a novel method, named Multiscale-Causal Structure Learning (MS-CASTLE), to estimate the structure of linear causal relationships occurring at different time scales. Differently from existing approaches, MS-CASTLE takes explicitly into account instantaneous and lagged inter-relations between multiple time series, represented at different scales, hinging on stationary wavelet transform and non-convex optimization. MS-CASTLE incorporates, as a special case,…

2022-07-16cs.LGstat.MEstat.ML

来自Ly-alpha森林的物质场和重子声学振荡的多尺度推断

Multiscale Inference of Matter Fields and Baryon Acoustic Oscillations from the Ly-alpha Forest

提出了一种新的贝叶斯方法，用于联合重建准非线性区域的宇宙物质密度场、奇异速度场和功率谱。我们研究其适用性的Ly-alpha森林的基础上多个类星体的吸收光谱。我们解决这个问题的方法包括多尺度、非线性、两步方案，因为描述物质分布的统计依赖于尺度，在小尺度（< 0.1 h^{-1} Mpc）上是强非高斯的，在>~10 h^{-1} Mpc的尺度上是接近对数正态的。第一步是基于一个任意的非高斯单变量物质统计模型，沿z~2-3类星体的视线方向进行一维高分辨物质密度重建。第二步是基于条件PDF的吉布斯采样。物质密度场采用泊松/伽马对数正态模型在实空间中进行哈密顿采样，而红移畸变则采用线性拉格朗日微扰理论进行校正。对数正态变换变量的高斯分布（因此接近线性状态）的功率谱可以用逆伽马分布函数一致地采样。我们通过数值N体模拟测试了我们的方法，计算量足够大（> 1 h^{-3} Gpc ^3），表明线性功率谱在大于~20 h^{-1} Mpc的尺度上都能很好地恢复，即重子声学振荡（BAO）留下的特征出现的相关范围。

2012-06-27astro-ph.COmath.STstat.AP

Heterogeneous Change Point Inference

We propose HSMUCE (heterogeneous simultaneous multiscale change-point estimator) for the detection of multiple change-points of the signal in a heterogeneous gaussian regression model. A piecewise constant function is estimated by minimizing the number of change-points over the acceptance region of a multiscale test which locally adapts to changes in the variance. The multiscale test is a combination of local likelihood ratio tests which are properly calibrated by scale dependent critical values in order to keep a global nominal level alpha, even for finite samples. We show that HSMUCE control…

2016-02-05math.STstat.MEstat.TH

小波潜在位置指数随机图

Multiscale Localized Inference for Networks with a Measured Vertex Coordinate

本文提出了一种基于小波变换的指数随机图模型，用于分析多尺度网络结构的连接性偏离问题。

2026-09-16math.STstat.MEstat.TH

Multiscale Fisher's Independence Test for Multivariate Dependence

Identifying dependency in multivariate data is a common inference task that arises in numerous applications. However, existing nonparametric independence tests typically require computation that scales at least quadratically with the sample size, making it difficult to apply them to massive data. Moreover, resampling is usually necessary to evaluate the statistical significance of the resulting test statistics at finite sample sizes, further worsening the computational burden. We introduce a scalable, resampling-free approach to testing the independence between two random vectors by breaking d…

2021-07-07stat.APstat.COstat.ME