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Context: Several approaches to estimate frequency, phase and amplitude errors in time series analyses were reported in the literature, but they are either time consuming to compute, grossly overestimating the error, or are based on empirically determined criteria. Aims: A simple, but realistic estimate of the frequency uncertainty in time series analyses. Methods: Synthetic data sets with mono- and multi-periodic harmonic signals and with randomly distributed amplitude, frequency and phase were generated and white noise added. We tried to recover the input parameters with classical Fourier techniques and investigated the error as a function of the relative level of noise, signal and frequency difference. Results: We present simple formulas for the upper limit of the amplitude, frequency and phase uncertainties in time-series analyses. We also demonstrate the possibility to detect frequencies which are separated by less than the classical frequency resolution and that the realistic frequency error is at least 4 times smaller than the classical frequency resolution.
The unshielded nature of gravity means that stellar systems are inherently inhomogeneous. As a result, stars do not move in straight lines. This obvious fact severely complicates the kinetic theory of stellar systems because position and velocity tur
Financial time-series analysis and forecasting have been extensively studied over the past decades, yet still remain as a very challenging research topic. Since the financial market is inherently noisy and stochastic, a majority of financial time-ser
Based on law of large numbers and central limit theorem under nonlinear expectation, we introduce a new method of using G-normal distribution to measure financial risks. Applying max-mean estimators and small windows method, we establish autoregressi
Data discretization, also known as binning, is a frequently used technique in computer science, statistics, and their applications to biological data analysis. We present a new method for the discretization of real-valued data into a finite number of
The absolute frequency of the $^{87}{rm Sr}$ lattice clock transition was evaluated with an uncertainty of $1.1times 10^{-15}$ using a frequency link to the international atomic time (TAI). The frequency uncertainty of a hydrogen maser used as a tran