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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…

Statistics Theory · Mathematics 2017-04-14 Michael Hoffmann , Mathias Vetter , Holger Dette

This paper proposes a novel test for simultaneous jumps in a bivariate It\^o semimartingale when observation times are asynchronous and irregular. Inference is built on a realized correlation coefficient for the jumps of the two processes…

Statistics Theory · Mathematics 2016-06-24 Ole Martin , Mathias Vetter

In this paper we present some new limit theorems for power variation of $k$th order increments of stationary increments L\'evy driven moving averages. In this infill sampling setting, the asymptotic theory gives very surprising results,…

Probability · Mathematics 2015-06-23 Andreas Basse-O'Connor , Raphaël Lachièze-Rey , Mark Podolskij

In this paper, we first investigate the estimation of the empirical joint Laplace transform of volatilities of two semi-martingales within a fixed time interval [0, T] by using overlapped increments of high-frequency data. The proposed…

Statistics Theory · Mathematics 2025-03-05 XinWei Feng , Yu Jiang , Zhi Liu , Zhe Meng

We study the asymptotic behaviour of modified weighted power variations of the Hermite process of arbitrary order. By selecting suitable "good" increments and exploiting their decomposition into dominant independent components, we establish…

Statistics Theory · Mathematics 2026-01-06 Antoine Ayache , laurent Loosveldt , Ciprian Tudor

A well-known It\^o formula for finite dimensional processes, given in terms of stochastic integrals with respect to Wiener processes and Poisson random measures, is revisited and is revised. The revised formula, which corresponds to the…

Probability · Mathematics 2020-07-30 István Gyöngy , Sizhou Wu

In this paper we present some new limit theorems for power variation of $k$th order increments of stationary increments L\'evy driven moving averages. In the infill asymptotic setting, where the sampling frequency converges to zero while…

Probability · Mathematics 2016-03-25 Andreas Basse-O'Connor , Raphaël Lachièze-Rey , Mark Podolskij

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…

Statistics Theory · Mathematics 2013-05-15 Markus Bibinger , Mathias Vetter

In this paper, we consider a framework adapting the notion of cointegration when two asset prices are generated by a driftless It\^{o}-semimartingale featuring jumps with infinite activity, observed regularly and synchronously at high…

Statistical Finance · Quantitative Finance 2021-03-24 Simon Clinet , Yoann Potiron

For a semimartingale with jumps, we propose a new estimation method for integrated volatility, i.e., the quadratic variation of the continuous martingale part, based on the global jump filter proposed by Inatsugu and Yoshida [8]. To decide…

Statistics Theory · Mathematics 2021-02-16 Haruhiko Inatsugu , Nakahiro Yoshida

We consider the moderate deviations behaviors for two (co-) volatility estima-tors: generalised bipower variation, Hayashi-Yoshida estimator. The results are obtained by using a new result about the moderate deviations principle for…

Probability · Mathematics 2017-02-06 Hacène Djellout , Arnaud Guillin , Hui Jiang , Yacouba Samoura

In this paper, we develop necessary and sufficient conditions for the validity of a martingale approximation for the partial sums of a stationary process in terms of the maximum of consecutive errors. Such an approximation is useful for…

Probability · Mathematics 2011-02-11 Mikhail Gordin , Magda Peligrad

We study the asymptotics of lattice power variations of two-parameter ambit fields driven by white noise. Our first result is a law of large numbers for power variations. Under a constraint on the memory of the ambit field, normalized power…

Probability · Mathematics 2014-08-20 Mikko S. Pakkanen

This work is concerned with tests on structural breaks in the spot volatility process of a general It\^o semimartingale based on discrete observations contaminated with i.i.d. microstructure noise. We construct a consistent test building up…

Statistics Theory · Mathematics 2018-09-25 Markus Bibinger , Mehmet Madensoy

We prove that typical (in the model-free finance setting) price paths with jumps may be uniformly approximated with accuracy $c>0$ by paths whose total variation is of order $1/c.$ A more precise result is obtained for semimartingales with…

Probability · Mathematics 2017-06-26 Rafał M. Łochowski

In this paper we consider two semimartingales driven by diffusions and jumps. We allow both for finite activity and for infinite activity jump components. Given discrete observations we disentangle the {\it integrated covariation} (the…

Probability · Mathematics 2008-12-10 Fabio Gobbi , Cecilia Mancini

In this paper, we consider a diffusion process with jumps whose drift and jump coefficient depend on an unknown parameter. We then give a self-contained proof of the local asymptotic mixed normality (LAMN) property when the process is…

Probability · Mathematics 2016-11-26 Ngoc Khue Tran , Eulalia Nualart

We consider noisy non-synchronous discrete observations of a continuous semimartingale with random volatility. Functional stable central limit theorems are established under high-frequency asymptotics in three setups: one-dimensional for…

Statistics Theory · Mathematics 2015-07-28 Randolf Altmeyer , Markus Bibinger

We consider a process $X_t$, which is observed on a finite time interval $[0,T]$, at discrete times $0,\Delta_n,2\Delta_n,\ldots.$ This process is an It\^{o} semimartingale with stochastic volatility $\sigma_t^2$. Assuming that $X$ has…

Statistical Finance · Quantitative Finance 2010-10-26 Jean Jacod , Viktor Todorov

This paper is concerned with tests for changes in the jump behaviour of a time-continuous process. Based on results on weak convergence of a sequential empirical tail integral process, asymptotics of certain tests statistics for breaks in…

Methodology · Statistics 2014-12-18 Axel Bücher , Michael Hoffmann , Mathias Vetter , Holger Dette