An efficient estimator is constructed for the quadratic covariation or integrated co-volatility matrix of a multivariate continuous martingale based on noisy and nonsynchronous observations under high-frequency asymptotics. Our approach relies an asymptotically equivalent continuous-time observation model where local generalised method moments in spectral domain turns out to be optimal. Asymptotic semi-parametric efficiency established Cram\'{e}r-Rao sense. Main findings are that...

We propose a new estimator for the spot covariance matrix of multi-dimensional continuous semimartingale log asset price process, which is subject to noise and nonsynchronous observations. The constructed based on local average block-wise parametric spectral estimates. latter originate from method moments (LMM), recently has been introduced by Bibinger et al.. prove consistency point-wise stable central limit theorem proposed in very general setup with stochastic volatility, leverage...

We consider the distribution of sum and maximum a collection independent exponentially distributed random variables. The focus is laid on explicit form density functions (pdf) non-i.i.d. sequences. Those are recovered in simple direct way based conditioning. A connection between pdf representation convolution characteristic function as linear combination single drawn. It demonstrated how results order statistics merge.

Abstract. We focus on estimating the integrated covariance of log‐price processes in presence market microstructure noise. construct a consistent asymptotically unbiased estimator for quadratic covariation two Itô case where high‐frequency asynchronous discrete returns under noise are observed. This is based synchronization and multi‐scale methods attains optimal rate convergence. A lower bound convergence derived from local asymptotic normality property simpler parametric model with...

ABSTRACT We propose localized spectral estimators for the quadratic covariation and spot covolatility of diffusion processes, which are observed discretely with additive observation noise. The appropriate estimation time‐varying volatilities is based on an asymptotic equivalence underlying statistical model to a white‐noise correlation volatility processes being constant over small time intervals. continuous‐time discrete‐time experiments proved by construction linear interpolation in one...

This paper proposes a new econometric approach to disentangle two distinct response patterns of the yield curve monetary policy announcements. Based on cojumps in intraday tick data short- and long-term interest rate futures, we develop day-wise test that detects occurrence significant surprise identifies market perceived source surprise. The is applied 133 announcements European Central Bank (ECB) period from 2001 2012. Our main findings indicate good predictability ECB decisions remarkably...

Abstract We consider estimation of the spot volatility in a stochastic boundary model with one-sided microstructure noise for high-frequency limit order prices. Based on discrete, noisy observations an Itô semimartingale jumps and general volatility, we present simple explicit estimator using local statistics. establish consistency stable central theorems as asymptotic properties. The analysis builds upon expansion tail probabilities statistics based generalized arcsine law. In to use...

We introduce a statistical test for simultaneous jumps in the price of financial asset and its volatility process. The proposed is based on high-frequency data robust to market microstructure frictions. For test, local estimators at jump arrival times are designed using nonparametric spectral estimator spot A simulation study an empirical example with NASDAQ order book demonstrate practicability methods highlight important role played by co-jumps.

In this work, we develop change-point methods for statistics of high-frequency data. The main interest is in the volatility an Itô semimartingale, latter being discretely observed over a fixed time horizon. We construct minimax-optimal test to discriminate continuous paths from with jumps, and it shown that can be embedded into more general theory infer smoothness volatilities. setting, prove weak convergence statistic under hypothesis extreme value distribution. Moreover, changes Hurst...

An efficient estimator is constructed for the quadratic covariation or integrated covolatility matrix of a multivariate continuous martingale based on noisy and non-synchronous observations under high-frequency asymptotics. Our approach relies an asymptotically equivalent continuous-time observation model where local generalised method moments in spectral domain turns out to be optimal. Asymptotic semiparametric efficiency established Cramer-Rao sense. Main findings are that...

Abstract We find the asymptotic distribution of multi‐dimensional multi‐scale and kernel estimators for high‐frequency financial data with microstructure. Sampling times are allowed to be asynchronous endogenous. In process, we show that classes smoothing noise perturbation asymptotically equivalent in sense having same corresponding weight functions. The theory leads stable central limit theorems feasible versions. Hence, they allow draw statistical inference a broad class multivariate...

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 give our own distinct illustration based an iterative synchronization algorithm. We consider high-frequency asymptotics and prove a feasible stable central limit theorem. characteristics non-synchronous schemes affecting asymptotic variance are...

We propose methods to infer jumps of a semi-martingale, which describes long-term price dynamics based on discrete, noisy, high-frequency observations. Different the classical model additive, centered market microstructure noise, we consider one-sided noise for order prices in limit book. develop estimate, locate and test using local statistics. provide show that can consistently estimate jumps. The main contribution is global establish asymptotic properties optimality this test. derive...

We propose a new estimator for the spot covariance matrix of multi-dimensional continuous semi-martingale log asset price process which is subject to noise and non-synchronous observations. The constructed based on local average block-wise parametric spectral estimates. latter originate from method moments (LMM) recently has been introduced by Bibinger et al. (2014). extend LMM allow autocorrelated adaptively infer autocorrelations data. prove consistency asymptotic normality proposed...

For a semi-martingale $X_{t}$, which forms stochastic boundary, rate-optimal estimator for its quadratic variation $\langle X,X\rangle_{t}$ is constructed based on observations in the vicinity of $X_{t}$. The problem embedded Poisson point process framework, reveals an interesting connection to theory Brownian excursion areas. We derive $n^{-1/3}$ as optimal convergence rate high-frequency framework with $n$ (in mean). discuss potential application estimation integrated squared volatility...

Abstract We construct estimators for the parameters of a parabolic SPDE with one spatial dimension based on discrete observations solution in time and space bounded domain. establish central limit theorems high-frequency asymptotic regime. The variances are shown to be substantially smaller compared existing estimation methods. Moreover, confidence intervals directly feasible. Our approach builds upon realized volatilities their illustration as response log-linear model explanatory variable....