# Vast volatility matrix estimation for high-frequency financial data - Mathematics > Statistics Theory

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Abstract: High-frequency data observed on the prices of financial assets are commonlymodeled by diffusion processes with micro-structure noise, and realizedvolatility-based methods are often used to estimate integrated volatility. Forproblems involving a large number of assets, the estimation objects we face arevolatility matrices of large size. The existing volatility estimators work wellfor a small number of assets but perform poorly when the number of assets isvery large. In fact, they are inconsistent when both the number, $p$, of theassets and the average sample size, $n$, of the price data on the $p$ assets goto infinity. This paper proposes a new type of estimators for the integratedvolatility matrix and establishes asymptotic theory for the proposed estimatorsin the framework that allows both $n$ and $p$ to approach to infinity. Thetheory shows that the proposed estimators achieve high convergence rates undera sparsity assumption on the integrated volatility matrix. The numericalstudies demonstrate that the proposed estimators perform well for large $p$ andcomplex price and volatility models. The proposed method is applied to realhigh-frequency financial data.

Author: ** Yazhen Wang, Jian Zou**

Source: https://arxiv.org/