We propose a new concept of modulated bipower variation for diffusion models with microstructure noise. show that this method provides simple estimates such important quantities as integrated volatility or quarticity. Under mild conditions the consistency is proven. further assumptions we prove stable convergence our optimal rate $n^{−1/4}$. Moreover, construct which are robust to finite activity jumps.

Abstract This article contributes to the theory for preaveraging estimators of daily quadratic variation asset prices and provides novel empirical evidence. We develop asymptotic in case autocorrelated microstructure noise propose an explicit test serial dependence. Moreover, we extend on processes involving jumps. discuss several jump-robust measures derive feasible central limit theorems general variation. Using transaction data different stocks traded at New York Stock Exchange, analyze...

This paper presents some limit theorems for certain functionals of moving averages semimartingales plus noise which are observed at high frequency. Our method generalizes the pre-averaging approach (see [Bernoulli 15 (2009) 634–658, Stochastic Process. Appl. 119 2249–2276]) and provides consistent estimates various characteristics general semimartingales. Furthermore, we prove associated multidimensional (stable) central theorems. As expected, find with a convergence rate n−1/4, if n is...

This paper presents a short survey on limit theorems for certain functionals of semimartingales that are observed at high frequency. Our aim is to explain the main ideas theory broader audience. We introduce concept stable convergence, which crucial our purpose. show some laws large numbers (for continuous and discontinuous case) most interesting from practical point view, demonstrate associated central theorems. Moreover, we state simple sketch proofs give examples.

In this paper we study the asymptotic behaviour of power and multipower variations processes $Y$:\[Y_t=\int_{-\in fty}^tg(t-s)\sigma_sW(\mathrm{d}s)+Z_t,\] where $g:(0,\infty)\rightarrow\mathbb{R}$ is deterministic, $\sigma >0$ a random process, $W$ stochastic Wiener measure $Z$ process in nature drift term. Processes type serve, particular, to model data velocity increments fluid turbulence regime with spot intermittency $\sigma$. The purpose determine probabilistic limit (multi)power $Y$...

Statistical inference for stochastic processes has advanced significantly due to applications in diverse fields, but challenges remain high-dimensional settings where parameters are allowed grow with the sample size. This paper analyzes a d-dimensional ergodic diffusion process under sparsity constraints, focusing on adaptive Lasso estimator, which improves variable selection and bias over standard Lasso. We derive conditions achieves support recovery property asymptotic normality drift...

In this paper, we present a test for the maximal rank of matrix-valued volatility process in continuous Itô semimartingale framework. Our idea is based upon random perturbation original high frequency observations an semimartingale, which opens way testing. We develop complete limit theory statistic and apply it to various null alternative hypotheses. Finally, demonstrate homoscedasticity process.

Dans cet article, nous étudions le problème d'estimation semi-paramétrique pour une classe d'équations différentielles stochastiques de type McKean–Vlasov. Notre but est d'estimer coefficient dérive d'une EDS MV à partir d'observations du système particules associé. Nous proposons méthode et obtenons les vitesses convergence estimateurs correspondants. démontrons également que sont quasi-optimales au sens minimax.

Abstract. Properties of a specification test for the parametric form variance function in diffusion processes are discussed. The is based on estimation certain integrals volatility function. If does not depend variable x it known that corresponding statistics have an asymptotic normal distribution. However, most models mathematical finance use which depends state . In this paper we prove general case, where σ also estimates converge stably law to random variables with non‐standard limit...