Related papers: A Comparison of High-Frequency Cross-Correlation M…
The simplicity of a question such as wondering if correlations characterize or not a certain system collides with the experimental difficulty of accessing such information. Here we present a low demanding experimental approach which refers…
Frequency-filtered photon correlations have been proven to be extremely useful in grasping how the detection process alters photon statistics. Harnessing the spectral correlations also permits refinement of the emission and unraveling of…
We present a method that allows to distinguish between nearly periodic and strictly periodic time series. To this purpose, we employ a conservative criterion for periodicity, namely that the time series can be interpolated by a periodic…
This paper considers the problem of testing temporal homogeneity of $p$-dimensional population mean vectors from the repeated measurements of $n$ subjects over $T$ times. To cope with the challenges brought by high-dimensional longitudinal…
It is demonstrated how to generate time series with tailored nonlinearities by inducing well- defined constraints on the Fourier phases. Correlations between the phase information of adjacent phases and (static and dynamic) measures of…
Interferometric measurements of high-harmonics induced by multiple laser fields in an emerging field of research that promises optimized yield of harmonics, and time and space-resolved nonlinear spectroscopy. Most of the measurements have…
Ramsey interferometry is a widely used tool for precisely measuring transition frequencies between two energy levels of a quantum system, with applications in time-keeping, precision spectroscopy, quantum optics, and quantum information.…
We analyze the spectral properties of correlation matrices between distinct statistical systems. Such matrices are intrinsically non symmetric, and lend themselves to extend the spectral analyses usually performed on standard Pearson…
The phasing problem of heterodyne-detected nonlinear spectroscopy states that the relative time delay between the exciting pulses and a local oscillator must be known with subcycle precision to separate absorptive and dispersive…
We present a theorem concerning the invariance of cross-correlation peak positions, which provides a foundation for a new method for time difference estimation that is potentially faster than the conventional fast Fourier transform (FFT)…
Besides the classical distinction of correlation and dependence, many dependence measures bear further pitfalls in their application and interpretation. The aim of this paper is to raise and recall awareness of some of these limitations by…
Commonalities and differences in correlation analysis in terms of phase space, conditioning and uncorrelatedness are discussed. The Poisson process is not generally appropriate as reference distribution for normalisation and cumulants, so…
Interferometric photon-correlation measurements, which correspond to the second-order intensity cross-correlations between the two output ports of an unbalanced Michelson interferometer, are sensitive to both amplitude and phase…
We develop a new tool, the time inhomogeneous Poisson equation in the whole space and with a terminal condition at infinity, to study the asymptotic behavior of the non-autonomous multi-scale stochastic system with irregular coefficients,…
Temporal disaggregation is a method commonly used in official statistics to enable high-frequency estimates of key economic indicators, such as GDP. Traditionally, such methods have relied on only a couple of high-frequency indicator series…
A frequency counter measures the input frequency $\bar{\nu}$ averaged over a suitable time $\tau$, versus the reference clock. High resolution is achieved by interpolating the clock signal. Further increased resolution is obtained by…
Interferometric methods, renowned for their reliability and precision, play a vital role in phase imaging. Interferometry typically requires high coherence and stability between the measured and the reference beam. The presence of rapid…
The presence of significant cross-correlations between the synchronous time evolution of a pair of equity returns is a well-known empirical fact. The Pearson correlation is commonly used to indicate the level of similarity in the price…
Correlation coefficient is usually used to measure the correlation degree between two time signals. However, its performance will drop or even fail if the signals are noised. Based on the time-frequency phase spectrum (TFPS) provided by…
Here we propose a method, based on detrended covariance which we call detrended cross-correlation analysis (DXA), to investigate power-law cross-correlations between different simultaneously-recorded time series in the presence of…