VAST VOLATILITY MATRIX ESTIMATION FOR HIGH-FREQUENCY FINANCIAL DATA

By Yazhen Wang, Jian Zou. 2010

142 citations recorded by the source corpus.

High-frequency data observed on the prices of financial assets are commonly modeled by diffusion processes with micro-structure noise, and realized volatility-based methods are often used to estimate integrated volatility. For problems involving a large number of assets, the estimation objects we face are volatility matrices of large size. The existing volatility estimators work well for a small number of assets but perform poorly when the number of assets is very large. In fact, they are inconsistent when both the number, p, of the assets and the average sample size, n, of the price data on the p assets go to infinity. This paper proposes a new type of estimators for the integrated volatility matrix and establishes asymptotic theory for the proposed estimators in the framework that allows both n and p to approach to infinity. The theory shows that the proposed estimators achieve high convergence rates under a sparsity assumption on the integrated volatility matrix. The numerical studies demonstrate that the proposed estimators perform well for large p and complex price and volatility models. The proposed method is applied to real high-frequency financial data.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/e334597246b911f4fcfc5b6aa6f1cf96d7fc717d

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Citations in the corpus

On the estimation of integrated covariance matrices of high dimensional diffusion processes (2010, methodology): “See, for example, Wang and Zou (2010); Tao et al. (2011) who made use of data over long time horizons by proposing a method incorporating low-frequency dynamics; and Fan, Li and Yu (2011) who studied the estimation of ICV matrices for portfolio allocation under gross exposure constraint.”
On the number of common factors with high‐frequency data (2017, methodology): “These are commonly used in the literature (see, e.g., Wang & Zou, 2010; Jing et al., 2012a,b; Jacod & Podolskij, 2013; Jacod & Rosenbaum, 2013).”
FAST CONVERGENCE RATES IN ESTIMATING LARGE VOLATILITY MATRICES USING HIGH-FREQUENCY FINANCIAL DATA (2013, methodology): “However, when estimating volatility matrices of a large number of assets, Wang and Zou (2010) and Tao, Wang, Yao, and Zou (2011) show that the existing volatility matrix estimators have poor performance and in fact are inconsistent when both the number of assets and the sample sizes go to infinity.”
OPTIMAL SPARSE VOLATILITY MATRIX ESTIMATION FOR HIGH-DIMENSIONAL ITÔ PROCESSES WITH MEASUREMENT ERRORS (2013, methodology): “…inequality is due to the fact that the sparsity of Γ implies which are the respective bounds on the number of those entries on each row with absolute values larger than or equal to ̟ and the sum of those absolute entries on each row with magnitudes less than ̟ ; see Lemma 1 in Wang and Zou (2010).”
Econometric Analysis of Vast Covariance Matrices Using Composite Realized Kernels and Their Application to Portfolio Choice (2016, methodology): “This correspond to a multivariate version of the univariate estimator advocated by Zhang, Mykland, and Aı̈t-Sahalia (2005) and Bandi and Russell (2008), but modified to take into account the refresh time sampling scheme.”
A blocking and regularization approach to high dimensional realized covariance estimation (2012, unknown): “tion technique for high dimensional realized covariance matrices (see also Onatski (2009), Wang and Zou (2009) , and”
High‐dimensional covariance matrix estimation (2019, background): “See for instance Wang and Zou (2010), Dao et al. (2017) and Fan and Kim (2017) and the references therein.”
Adaptive Thresholding for Sparse Covariance Matrix Estimation (2011, unknown): “Wang and Zou (2010) considered estimation of volatility matrices based on high-frequency financial data.”
Incorporating Global Industrial Classification Standard Into Portfolio Allocation: A Simple Factor-Based Large Covariance Matrix Estimator With High-Frequency Data (2016, unknown): “…our estimator under the operator norm is different but comparable to the large literature of the precision matrix estimation, see, for example, Bickel and Levina (2008b), Yuan (2010), Cai, Liu, and Luo (2011), and Fan, Liao, and Mincheva (2011), under different structural and sparsity assumptions.”
Modeling and Forecasting Large Realized Covariance Matrices and Portfolio Choice (2017, unknown): “Several other papers have dealt with the estimation of vast covariance matrices, e.g. Bickel and Levina (2008), Levina et al. (2008), Fan et al. (2008), Wang and Zou (2010), Fan et al. (2011), Fan et al. (2012), Fan et al. (2012), Hautsch et al. (2012), Fan et al. (2013).”
Testing stationarity of functional time series (2014, background): “Extensive research has focused on scalar or vector summary statistics derived from intraday data, including realized volatility and noise variance estimation, see Barndorff- Nielsen and Shephard (2004) and Wang and Zou (2010), among many others.”
Do High-Frequency Data Improve High-Dimensional Portfolio Allocations? (2013, background): “Further possibilities to regularize the covariance matrix are, for instance, thresholding techniques (Wang and Zou, 2010).”