Inference for Volatility Functionals of Multivariate It\^o Semimartingales Observed with Jump and Noise

Richard Y. Chen

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arXiv · 1810.04725

Inference for Volatility Functionals of Multivariate It\^o Semimartingales Observed with Jump and Noise

Richard Y. Chen

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Abstract

This paper presents the nonparametric inference for nonlinear volatility functionals of general multivariate It\^o semimartingales, in high-frequency and noisy setting. Pre-averaging and truncation enable simultaneous handling of noise and jumps. Second-order expansion reveals explicit biases and a pathway to bias correction. Estimators based on this framework achieve the optimal convergence rate. A class of stable central limit theorems are attained with estimable asymptotic covariance matrices. This paper form a basis for infill asymptotic results of, for example, the realized Laplace transform, the realized principal component analysis, the continuous-time linear regression, and the generalized method of integrated moments, hence helps to extend the application scopes to more frequently sampled noisy data.

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BibTeX RIS

Richard Y. Chen. 2018-10-10. Inference for Volatility Functionals of Multivariate It\^o Semimartingales Observed with Jump and Noise. https://arxiv.org/abs/1810.04725

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