Edgeworth expansion for the pre-averaging estimator

2015/12/15 by Mark Podolskij, Podolskij, Mark, Bezirgen Veliyev +3
Economics, Econometrics and Finance · Mathematics · #60F05 #62H12 #62M09 #FOS: Economics and business #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Statistical Finance (q-fin.ST) #Statistical Methods and Inference #Statistics Theory (math.ST) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1512.04716

openalex publication_date 2015/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the Edgeworth expansion for a pre-averaging estimator of quadratic variation in the framework of continuous diffusion models observed with noise. More specifically, we obtain a second order expansion for the joint density of the estimators of quadratic variation and its asymptotic variance. Our approach is based on martingale embedding, Malliavin calculus and stable central limit theorems for continuous diffusions. Moreover, we derive the density expansion for the studentized statistic, which might be applied to construct asymptotic confidence regions.

Citations

• Asymptotic expansion for the quadratic form of the diffusion process

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