Related papers: Jump activity estimation for pure-jump semimarting…
We propose a nonparametric estimator of the jump activity index $\beta$ of a pure-jump semimartingale $X$ driven by a $\beta$-stable process when the underlying observations are coming from a high-frequency setting at irregular times. The…
We propose new nonparametric estimators of the integrated volatility of an It\^{o} semimartingale observed at discrete times on a fixed time interval with mesh of the observation grid shrinking to zero. The proposed estimators achieve the…
In this paper we present the asymptotic analysis of the realised quadratic variation for multivariate symmetric $\beta$-stable L\'evy processes, $\beta \in (0,2)$, and certain pure jump semimartingales. The main focus is on derivation of…
This paper derives the asymptotic behavior of realized power variation of pure-jump It\^{o} semimartingales as the sampling frequency within a fixed interval increases to infinity. We prove convergence in probability and an associated…
The jump behavior of an infinitely active It\^o semimartingale can be conveniently characterized by a jump activity index of Blumenthal-Getoor type, typically assumed to be constant in time. We study Markovian semimartingales with a…
Statistical inference for stochastic processes based on high-frequency observations has been an active research area for more than two decades. One of the most well-known and widely studied problems has been the estimation of the quadratic…
In applications the properties of a stochastic feature often change gradually rather than abruptly, that is: after a constant phase for some time they slowly start to vary. In this paper we discuss statistical inference for the detection…
In quantitative finance, we often model asset prices as semimartingales, with drift, diffusion and jump components. The jump activity index measures the strength of the jumps at high frequencies, and is of interest both in model selection…
We consider specification and inference for the stochastic scale of discretely-observed pure-jump semimartingales with locally stable L\'{e}vy densities in the setting where both the time span of the data set increases, and the mesh of the…
This paper introduces test and estimation procedures for abrupt and gradual changes in the entire jump behaviour of a discretely observed Ito semimartingale. In contrast to existing work we analyse jumps of arbitrary size which are not…
We propose methods to infer jumps of a semi-martingale, which describes long-term price dynamics, based on discrete, noisy, high-frequency observations. Different to the classical model of additive, centered market microstructure noise, we…
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…
Statistical inference for stochastic processes based on high-frequency observations has been an active research area for more than a decade. One of the most well-known and widely studied problems is that of estimation of the quadratic…
This paper presents a central limit theorem for a pre-averaged version of the realized covariance estimator for the quadratic covariation of a discretely observed semimartingale with noise. The semimartingale possibly has jumps, while the…
We consider estimation of the quadratic (co)variation of a semimartingale from discrete observations which are irregularly spaced under high-frequency asymptotics. In the univariate setting, results by Jacod (2008) are generalized to the…
The optimal rate of convergence of estimators of the integrated volatility, for a discontinuous It\^{o} semimartingale sampled at regularly spaced times and over a fixed time interval, has been a long-standing problem, at least when the…
We consider estimation of a step function $f$ from noisy observations of a deconvolution $\phi*f$, where $\phi$ is some bounded $L_1$-function. We use a penalized least squares estimator to reconstruct the signal $f$ from the observations,…
We provide a comprehensive analysis of spot volatility inference in pure-jump semimartingales under two asymptotic settings: fixed-$k$, where each local window uses a fixed number of observations, and large-$k$, where this number grows with…
We propose a new estimator for the integrated covariance of two Ito semimartingales observed at a high-frequency. This new estimator, which we call the pre-averaged truncated Hayashi-Yoshida estimator, enables us to separate the sum of the…
We develop an adaptive jump test for discretely observed high-frequency semimartingales by combining the A"it-Sahalia--Jacod ratio statistic (A"it-Sahalia and Jacod, 2009) and the Lee--Mykland extreme-return statistic (Lee and Mykland,…