Fast Convergence Rates in Estimating Large Volatility Matrices Using High-Frequency Financial Data

Tao, Minjing; Wang, Yazhen; Chen, Xiaohong

doi:10.1017/s0266466612000746

Cited by 48 publications

(53 citation statements)

References 21 publications

(31 reference statements)

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Several issues arise for the estimation of Σ x (t): 1. asynchronous observations of different assets; 2. microstructure noise; 3. the number of assets can be larger than the sample size. In this paper, we adopt the threshold Multi-Scale Realized Volatility Matrix estimator (threshold MSRVM) proposed by Tao et al (2013), denoted byΣ x (t), t = 1, · · · , T . The threshold MSRVM estimator has many attractive properties, for instance, it is consistent for the highdimensional integrated co-volatility matrix with the optimal convergence rate.…”

Section: Realized Covariance Matrix Estimatormentioning

confidence: 99%

“…We firstly conduct data cleaning with the procedures introduced in Brownlees and Gallo (2006) and Barndorff-Nielsen et al (2009). The steps are the following: Then, we construct the threshold MSRVM estimator based on the cleaned tick-by-tick data following the steps in Tao et al (2013). We set the threshold to be 5% of the largest of the absolute value of entries in the matrix.…”

Section: Data Descriptionmentioning

confidence: 99%

“…Tao et al (2011) propose the threshold averaging realized volatility matrix (TARVM) estimator which is of twoscale and uses the previous-tick method and the threshold technique in constructing realized volatility matrices. Then, inspired by Zhang (2006) and Fan and Wang (2007), Tao et al (2013) propose the threshold multi-scale realized volatility matrix (TMSRVM) estimator. The TARVM and TMSRVM estimators are shown to be consistent for the integrated covariance matrix when the dimension of the realized covariance matrix, the sample size of intraday points and the length of sampling days go to infinity.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Forecasting high-dimensional realized volatility matrices using a factor model

Shen

Yao

2018

Quantitative Finance

View full text Add to dashboard Cite

Modeling and forecasting covariance matrices of asset returns play a crucial role in finance.The availability of high frequency intraday data enables the modeling of the realized covariance matrix directly. However, most models in the literature suffer from the curse of dimensionality. To solve the problem, we propose a factor model with a diagonal CAW model for the factor realized covariance matrices. Asymptotic theory is derived for the estimated parameters. In an extensive empirical analysis, we find that the number of parameters can be reduced significantly. Furthermore, the proposed model maintains a comparable performance with a benchmark vector autoregressive model.

show abstract

Section: Realized Covariance Matrix Estimatormentioning

confidence: 99%

Section: Data Descriptionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Forecasting high-dimensional realized volatility matrices using a factor model

Shen

Yao

2018

Quantitative Finance

View full text Add to dashboard Cite

show abstract

“…When there are a large number of assets in financial practices such as asset pricing, portfolio allocation, and risk management, the volatility estimators designed for estimating a small integrated volatility matrix perform very poorly, and in fact, they are inconsistent when both the number of assets and sample size go to infinity [27]. For the case of a large number of assets, we need to impose some sparse structure on the integrated volatility matrix and employ regularization such as thresholding to obtain consistent estimators of the large volatility matrix [23,24,25]. In particular, Tao et al [23,24] investigated convergence rates of multi-scale realized volatility matrix estimator in the asymptotic framework that allows both the number of assets and sample size to go to infinity, and showed that the estimator achieves optimal convergence rate with respect to the sample size.…”

Section: Introductionmentioning

confidence: 99%

“…For the case of a large number of assets, we need to impose some sparse structure on the integrated volatility matrix and employ regularization such as thresholding to obtain consistent estimators of the large volatility matrix [23,24,25]. In particular, Tao et al [23,24] investigated convergence rates of multi-scale realized volatility matrix estimator in the asymptotic framework that allows both the number of assets and sample size to go to infinity, and showed that the estimator achieves optimal convergence rate with respect to the sample size. This paper considers the kernel realized volatility (KRV) [4,5], the pre-averaging realized volatility (PRV) [13,18], and the multi-scale realized volatility (MSRV) [23,30] based on generalized sampling time scheme.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic theory for large volatility matrix estimation based on high-frequency financial data

Kim

Wang

Zou

2016

Stochastic Processes and their Applications

Self Cite

View full text Add to dashboard Cite

In financial practices and research studies, we often encounter a large number of assets. The availability of high-frequency financial data makes it possible to estimate the large volatility matrix of these assets. Existing volatility matrix estimators such as kernel realized volatility and pre-averaging realized volatility perform poorly when the number of assets is very large, and in fact they are inconsistent when the number of assets and sample size go to infinity. In this paper, we introduce threshold rules to regularize kernel realized volatility, pre-averaging realized volatility, and multi-scale realized volatility. We establish asymptotic theory for these threshold estimators in the framework that allows the number of assets and sample size to go to infinity. Their convergence rates are derived under sparsity on the large integrated volatility matrix. In particular we have shown that the threshold kernel realized volatility and threshold pre-averaging realized volatility can achieve the optimal rate with respect to the sample size through proper bias corrections, but the bias adjustments causes the estimators to lose positive semi-definiteness; on the other hand, in order to be positive semi-definite, the threshold kernel realized volatility and threshold pre-averaging realized volatility have slower convergence rates with respect to the sample size. A simulation study is conducted to check the finite sample performances of the proposed threshold estimators with over hundred assets.H is a bandwidth parameter, and k(·) is a kernel function satisfying Assumption 2 and the following further assumption.Similar to the KRVM estimator, KRVPM estimator Γ KRVPM relies on jittering parameter J, bandwidth parameter H and kernel function k(·). As we will study in Section 4, theoretically J and H are selected to be of orders n 1/5 and n 3/5 , respectively, 6 Remark 3. Kernel realized volatility estimators Γ KRVM in Definition 2 and Γ KRVPM in Definition 3 have almost identical expressions, but their asymptotic behaviors are very different [4,5]. For example, when p is fixed and n goes to infinity, Γ KRVM has convergence rate n −1/4 , while Γ KRVPM can only achieve convergence rate n −1/5 . The slower convergence rate for Γ KRVPM

show abstract

Volatility analysis in high‐frequency financial data

Wang

Zou

2014

WIREs Computational Stats

Self Cite

View full text Add to dashboard Cite

In this paper we provide a detailed review of univariate and multivariate volatility analysis within the framework of high-frequency financial data setting. The field of volatility modeling and analysis for high-frequency financial data has experienced a rapid development over the past decade. High-frequency financial data pose tremendous challenges on volatility modeling and analysis, such as microstructure noise, non-synchronization, irregularly spaced times between observations, nonstationarity, and jumps. We present models for asset prices and high-frequency financial data. We discuss common volatility estimators such as realized volatility, two-time scale and multi-scale realized volatility estimators, realized kernel volatility estimator and pre-averaging volatility estimator in the univariate setting. For estimating co-volatility, we illustrate data synchronization methods including previous tick, refresh time, and generalized sampling time and present two-time scale and multi-scale realized volatility matrix estimators, realized kernel volatility estimator, and the quasi-maximum likelihood method built on the synchronized data. We also feature pre-averaging volatility and Hayashi-Yoshida estimators which are based on inexplicit data synchronization. We provide detailed formulation and properties for each estimator or method and point out their relationships and differences. Given the recent interests in big data and high-dimensional statistics, large volatility matrix inference approaches are highlighted in the end.

show abstract

Fast Convergence Rates in Estimating Large Volatility Matrices Using High-Frequency Financial Data

Cited by 48 publications

References 21 publications

Forecasting high-dimensional realized volatility matrices using a factor model

Forecasting high-dimensional realized volatility matrices using a factor model

Asymptotic theory for large volatility matrix estimation based on high-frequency financial data

Volatility analysis in high‐frequency financial data

Contact Info

Product

Resources

About