47 research outputs found
Asymptotics of Asynchronicity
In this article we focus on estimating the quadratic covariation of
continuous semimartingales from discrete observations that take place at
asynchronous observation times. The Hayashi-Yoshida estimator serves as
synchronized realized covolatility for that we give our own distinct
illustration based on an iterative synchronization algorithm. We consider
high-frequency asymptotics and prove a feasible stable central limit theorem.
The characteristics of non-synchronous observation schemes affecting the
asymptotic variance are captured by a notion of asymptotic covariations of
times. These are precisely illuminated and explicitly deduced for the important
case of independent time-homogeneous Poisson sampling.Comment: technical report, 36 page
An estimator for the quadratic covariation of asynchronously observed Itô processes with noise: Asymptotic distribution theory
The article is devoted to the nonparametric estimation of the quadratic covariation of non-synchronously observed Itô processes in an additive microstructure noise model. In a high-frequency setting, we aim at establishing an asymptotic distribution theory for a generalized multiscale estimator including a feasible central limit theorem with optimal convergence rate on convenient regularity assumptions. The inevitably remaining impact of asynchronous deterministic sampling schemes and noise corruption on the asymptotic distribution is precisely elucidated. A case study for various important examples, several generalizations of the model and an algorithm for the implementation warrant the utility of the estimation method in applications.non-synchronous observations, microstructure noise, integrated covolatility, multiscale estimator, stable limit theorem
Asymptotics of Asynchronicity
In this article we focus on estimating the quadratic covariation of continuous semimartingales from discrete observations that take place at asynchronous observation times. The Hayashi-Yoshida estimator serves as synchronized realized covolatility for that we give our own distinct illustration based on an iterative synchronization algorithm. We consider high-frequency asymptotics and prove a feasible stable central limit theorem. The characteristics of non-synchronous observation schemes affecting the asymptotic variance are captured by a notion of asymptotic covariations of times. These are precisely illuminated and explicitly deduced for the important case of independent time-homogeneous Poisson sampling.non-synchronous observations, quadratic covariation, Hayashi-Yoshida estimator, stable limit theorem, asymptotic distribution
Common price and volatility jumps in noisy high-frequency data
We introduce a statistical test for simultaneous jumps in the price of a
financial asset and its volatility process. The proposed test is based on
high-frequency data and is robust to market microstructure frictions. For the
test, local estimators of volatility jumps at price jump arrival times are
designed using a nonparametric spectral estimator of the spot volatility
process. A simulation study and an empirical example with NASDAQ order book
data demonstrate the practicability of the proposed methods and highlight the
important role played by price volatility co-jumps