Related papers: Statistical Properties of Microstructure Noise
We find the asymptotic distribution of the multi-dimensional multi-scale and kernel estimators for high-frequency financial data with microstructure. Sampling times are allowed to be asynchronous and endogenous. In the process, we show that…
When the number of subjects, $n$, is large, paired comparisons are often sparse. Here, we study statistical inference in a class of paired comparison models parameterized by a set of merit parameters, under an Erd\"{o}s--R\'{e}nyi…
One form of big data are signals - time series of consecutive values. In physical experiments, billions of values can now be measured within a second. Signals of heart and brain in intensive care, as well as seismic waves, are measured with…
We investigate the impact of noise on a two-dimensional simple paradigmatic piecewise-smooth dynamical system. For that purpose we consider the motion of a particle subjected to dry friction and coloured noise. The finite correlation time…
We introduce and validate a machine learning-assisted protocol to classify time and space correlations of classical noise acting on a quantum system, using two interacting qubits as probe. We consider different classes of noise, according…
Accurate state estimation requires careful consideration of uncertainty surrounding the process and measurement models; these characteristics are usually not well-known and need an experienced designer to select the covariance matrices. An…
We introduce a new stochastic model for the variations of asset prices at the tick-by-tick level in dimension 1 (for a single asset) and 2 (for a pair of assets). The construction is based on marked point processes and relies on linear self…
This article studies estimation of a stationary autocovariance structure in the presence of an unknown number of mean shifts. Here, a Yule-Walker moment estimator for the autoregressive parameters in a dependent time series contaminated by…
In this paper, we investigate the influence of noise giving an estimate of the gradient having a acute angle with the original. Noise amplitude has a relative model. The work offers both theoretical calculations and theorems, as well as…
Self-organizing neural networks are used to analyze uncorrelated white noises of different distribution types (normal, triangular, and uniform). The artificially generated noises are analyzed by clustering the measured time signal sequence…
This paper presents some limit theorems for certain functionals of moving averages of semimartingales plus noise which are observed at high frequency. Our method generalizes the pre-averaging approach (see [Bernoulli 15 (2009) 634--658,…
1/f noise is very common but is difficult to handle in a metrological way. After having recalled the main characteristics of stongly correlated noise, this paper will determine relationships giving confidence intervals over the arithmetic…
We study an extended system that without noise shows a spatially homogeneous state, but when submitted to an adequate multiplicative noise, some "noise-induced patterns" arise. The stochastic resonance between these structures is…
We provide transition rates for Markov counting systems subject to correlated environmental noises motivated by multi-strain disease models. Such noises induce simultaneous counts, which can help model infinitesimal count correlation…
We propose localized spectral estimators for the quadratic covariation and the spot covolatility of diffusion processes which are observed discretely with additive observation noise. The eligibility of this approach to lead to an…
In this paper, we consider an inference problem for the first order autoregressive process with non-zero mean driven by a long memory stationary Gaussian process. Suppose that the covariance function of the noise can be expressed as…
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…
This chapter considers the computational and statistical aspects of learning linear thresholds in presence of noise. When there is no noise, several algorithms exist that efficiently learn near-optimal linear thresholds using a small amount…
The effect of a small amount of noise on the standard mapping is considered. Whenever the standard mapping possesses accelerator modes (where the action increases approximately linearly with time), the diffusion coefficient contains a term…
Correlation between microstructure noise and latent financial logarithmic returns is an empirically relevant phenomenon with sound theoretical justification. With few notable exceptions, all integrated variance estimators proposed in the…