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We establish the asymptotic validity of frequency-domain inference for stationary multivariate Hawkes processes under mild conditions, bridging the gap between theory and application. By developing upper-bounds on the reduced cumulant…
In this paper we study the asymptotic theory for spectral analysis of stationary random fields, including linear and nonlinear fields. Asymptotic properties of Fourier coefficients and periodograms, including limiting distributions of…
The estimation of local characteristics of Ito semimartingales has received a great deal of attention in both academia and industry over the past decades. In various papers limit theorems were derived for functionals of increments and…
We consider discrete-time observations of a continuous martingale under measurement error. This serves as a fundamental model for high-frequency data in finance, where an efficient price process is observed under microstructure noise. It is…
In this article, we consider flexible seasonal time series models which consist of a common trend function over periods and additive individual trend (seasonal effect) functions. The consistency and asymptotic normality of the local linear…
When the study variable is functional and storage capacities are limited or transmission costs are high, selecting with survey sampling techniques a small fraction of the observations is an interesting alternative to signal compression…
The linear fractional stable motion generalizes two prominent classes of stochastic processes, namely stable L\'evy processes, and fractional Brownian motion. For this reason it may be regarded as a basic building block for continuous time…
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 of an It\^o semimartingale with jumps and general…
We provide a nonparametric method for the computation of instantaneous multivariate volatility for continuous semi-martingales, which is based on Fourier analysis. The co-volatility is reconstructed as a stochastic function of time by…
The semivarying coefficient models are widely used in the application of finance, economics, medical science and many other areas. The functional coefficients are commonly estimated by local smoothing methods, e.g. local linear estimator.…
We consider the problem of estimating stochastic volatility for a class of second-order parabolic stochastic PDEs. Assuming that the solution is observed at a high temporal frequency, we use limit theorems for multipower variations and…
The paper establishes the central limit theorems and proposes how to perform valid inference in factor models. We consider a setting where many counties/regions/assets are observed for many time periods, and when estimation of a global…
The typical central limit theorems in high-frequency asymptotics for semimartingales are results on stable convergence to a mixed normal limit with an unknown conditional variance. Estimating this conditional variance usually is a hard…
We establish central and non-central limit theorems for sequences of functionals of the Gaussian output of an infinitely-wide random neural network on the d-dimensional sphere . We show that the asymptotic behaviour of these functionals as…
We consider the estimation of two-sample integral functionals, of the type that occur naturally, for example, when the object of interest is a divergence between unknown probability densities. Our first main result is that, in wide…
We establish a general criterion for the positivity of the variance of a chaotic component of local functionals of stationary vector-valued Gaussian fields. This criterion is formulated in terms of the spectral properties of the covariance…
This paper proposes feasible asymptotically efficient estimators for a certain class of Gaussian noises with self-similar and stationary properties, which includes the fractional Gaussian noise, under high frequency observations. In this…
The basic model for high-frequency data in finance is considered, where an efficient price process is observed under microstructure noise. It is shown that this nonparametric model is in Le Cam's sense asymptotically equivalent to a…
The article is devoted to the nonparametric estimation of the quadratic covariation of non-synchronously observed It\^o processes in an additive microstructure noise model. In a high-frequency setting, we aim at establishing an asymptotic…
Parametric estimation for diffusion processes is considered for high frequency observations over a fixed time interval. The processes solve stochastic differential equations with an unknown parameter in the diffusion coefficient. We find…