Research output: Working paper › Research
Edgeworth expansion for the pre-averaging estimator. / Podolskij, Mark; Veliyev, Bezirgen; Yoshida, Nakahiro.
Aarhus : Institut for Økonomi, Aarhus Universitet, 2015.Research output: Working paper › Research
}
TY - UNPB
T1 - Edgeworth expansion for the pre-averaging estimator
AU - Podolskij, Mark
AU - Veliyev, Bezirgen
AU - Yoshida, Nakahiro
PY - 2015/12/15
Y1 - 2015/12/15
N2 - 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.
AB - 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.
KW - diffusion processes, Edgeworth expansion, high frequency observations, quadratic variation, pre-averaging
M3 - Working paper
T3 - CREATES Research Papers
BT - Edgeworth expansion for the pre-averaging estimator
PB - Institut for Økonomi, Aarhus Universitet
CY - Aarhus
ER -