Related papers: Operator Analysis of MACD
In the paper, we introduce a new measure of correlation between possibly non-stationary series. As the measure is based on the detrending moving-average cross-correlation analysis (DMCA), we label it as the DMCA coefficient…
In today's financial markets, quantitative trading has become an essential trading method, with the MACD indicator widely employed in quantitative trading strategies. This paper begins by screening and cleaning the dataset, establishing a…
Representations of AC power systems by frequency dependent impedance equivalents is an emerging technique in the dynamic analysis of power systems including power electronic converters. The technique has been applied for decades in DC-power…
Video Anomaly Detection (VAD) is essential for computer vision research. Existing VAD methods utilize either reconstruction-based or prediction-based frameworks. The former excels at detecting irregular patterns or structures, whereas the…
The standardized mean difference (SMD) is a widely used measure of effect size, particularly common in psychology, clinical trials, and meta-analysis involving continuous outcomes. Traditionally, under the equal variance assumption, the SMD…
The Maxwell operator in a 3D cylinder is considered. The coefficients are assumed to be scalar functions depending on the longitudinal variable only. Such operator is represented as a sum of countable set of matrix differential operators of…
We consider the well-studied problem of decomposing a vector time series signal into components with different characteristics, such as smooth, periodic, nonnegative, or sparse. We describe a simple and general framework in which the…
The use of moving averages is pervasive in macroeconomic monitoring, particularly for tracking noisy series such as inflation. The choice of the look-back window is crucial. Too long of a moving average is not timely enough when faced with…
IEEE 802.11ad specifies a hybrid medium access control (MAC) protocol consisting of contention as well as noncontention-based channel access mechanisms. Further, it also employs directional antennas to compensate for the high freespace path…
As a first step to deriving effective dynamics and ray optics, we prove that the perturbed periodic Maxwell operator in d = 3 can be seen as a pseudodifferential operator. This necessitates a better understanding of the periodic Maxwell…
In science and engineering, intelligent processing of complex signals such as images, sound or language is often performed by a parameterized hierarchy of nonlinear processing layers, sometimes biologically inspired. Hierarchical systems…
Dynamic mode decomposition (DMD) provides a principled approach to extract physically interpretable spatial modes from time-resolved flow field data, along with a linear model for how the amplitudes of these modes evolve in time. Recently,…
Functional time series have become an integral part of both functional data and time series analysis. Important contributions to methodology, theory and application for the prediction of future trajectories and the estimation of functional…
This paper introduces an algorithmic approach to the analysis of bifurcation of limit cycles from the centers of nonlinear continuous differential systems via the averaging method. We develop three algorithms to implement the averaging…
Dynamic Mode Decomposition (DMD) is a data-driven modal decomposition technique that extracts coherent spatio-temporal structures from high-dimensional time-series data. By decomposing the dynamics into a set of modes, each associated with…
We develop a novel EDMD-type algorithm that captures the spectrum of the Koopman operator defined on a reproducing kernel Hilbert space of analytic functions. This method, which we call analytic EDMD, relies on an orthogonal projection on…
This article provides an overview of some of the mathematical principles of Automatic Differentiation (AD). In particular, we summarise different descriptions of the Forward Mode of AD, like the matrix-vector product based approach, the…
The convergence of a new general variable metric algorithm based on compositions of averaged operators is established. Applications to monotone operator splitting are presented.
Detrended fluctuation analysis (DFA) and detrended moving average (DMA) are two scaling analysis methods designed to quantify correlations in noisy non-stationary signals. We systematically study the performance of different variants of the…
We study the correspondence between almost periodic difference operators and algebraic curves (spectral surfaces). An especial role plays the parametrization of the spectral curves in terms of, so called, branching divisors. The…