OPTIMAL SPARSE VOLATILITY MATRIX ESTIMATION FOR HIGH-DIMENSIONAL ITÔ PROCESSES WITH MEASUREMENT ERRORS

By Minjing Tao, Yazhen Wang, Harrison H. Zhou. 2013

73 citations recorded by the source corpus.

Stochastic processes are often used to model complex scientiflc problems in flelds ranging from biology and flnance to engineering and physical science. This paper investigates rate-optimal estimation of the volatility matrix of a high dimensional It^o process observed with measurement errors at discrete time points. The minimax rate of convergence is established for estimating sparse volatility matrices. By combining the multi-scale and threshold approaches we construct a volatility matrix estimator to achieve the optimal convergence rate. The minimax lower bound is derived by considering a subclass of It^o processes for which the minimax lower bound is obtained through a novel equivalent model of covariance matrix estimation for independent but non-identically distributed observations and through a delicate construction of the least favorable parameters. In addition, a simulation study was conducted to test the flnite sample performance of the optimal estimator, and the simulation results were found to support the established asymptotic theory.

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/9f39517a972ff1632daa44ec28e95cc2a7609b19

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Citations in the corpus

Using Principal Component Analysis to Estimate a High Dimensional Factor Model with High-Frequency Data (2017, background): “Dealing with an increased dimensionality without a factor structure typically requires the additional assumption that the population covariance matrix itself is sparse (see, e.g., Tao et al. (2011), Tao et al. (2013b), and Tao et al. (2013a)).”
Estimating structured high-dimensional covariance and precision matrices: Optimal rates and adaptive estimation (2016, methodology): “For example, it was used in Cai et al. (2012) for establishing the optimal rate of convergence for estimating sparse precision matrices and Tao et al. (2013) applied the technique to obtain the optimal rate for volatility matrix estimation.”