Related papers: Application of p-adic analysis to time series
Time series analysis finds wide applications in fields such as weather forecasting, anomaly detection, and behavior recognition. Previous methods attempted to model temporal variations directly using 1D time series. However, this has been…
Data series generated by complex systems exhibit fluctuations on many time scales and/or broad distributions of the values. In both equilibrium and non-equilibrium situations, the natural fluctuations are often found to follow a scaling…
p-Adic wavelet transform is considered as a possible tool for the description of hierarchic quantum systems
This paper proposes Fourier-based and wavelet-based techniques for analyzing periodic financial time series. Conventional models such as the periodic autoregressive conditional heteroscedastic (PGARCH) and periodic autoregressive…
New orthonormal basis of eigenfunctions for the Vladimirov operator of p-adic fractional derivation is constructed. The map of p-adic numbers onto real numbers (p-adic change of variables) is considered. This map (for p=2) provides an…
An approach is presented for making predictions about functional time series. The method is applied to data coming from periodically correlated processes and electricity demand, obtaining accurate point forecasts and narrow prediction bands…
We present a method for time series analysis of both, scalar and nonscalar time-delay systems. If the dynamics of the system investigated is governed by a time-delay induced instability, the method allows to determine the delay time. In a…
This paper develops a threshold model with a time-varying threshold, represented using a wavelet series expansion. The model adequately captures irregular and abrupt variations, as well as smooth changes in the threshold parameter, allowing…
We study correlations of hydrodynamic fluctuations in shear flow analytically and also by dissipative particle dynamics~(DPD) simulations. The hydrodynamic equations are linearized around the macroscopic velocity field and then solved by a…
The study of topology is strictly speaking, a topic in pure mathematics. However in only a few years, Topological Data Analysis (TDA), which refers to methods of utilizing topological features in data (such as connected components, tunnels,…
In this article we study the Cauchy problem for a new class of parabolic-type pseudodifferential equations with variable coefficients for which the fundamental solutions are transition density functions of Markov processes in the four…
A methodology for high dimensional causal inference in a time series context is introduced. It is assumed that there is a monotonic transformation of the data such that the dynamics of the transformed variables are described by a Gaussian…
We conduct an empirical study using the quantile-based correlation function to uncover the temporal dependencies in financial time series. The study uses intraday data for the S\&P 500 stocks from the New York Stock Exchange. After…
Functional data analysis is ubiquitous in most areas of sciences and engineering. Several paradigms are proposed to deal with the dimensionality problem which is inherent to this type of data. Sparseness, penalization, thresholding, among…
Time series data analysis is a critical component in various domains such as finance, healthcare, and meteorology. Despite the progress in deep learning for time series analysis, there remains a challenge in addressing the non-stationary…
The Fourier phase information play a key role for the quantified description of nonlinear data. We present a novel tool for time series analysis that identifies nonlinearities by sensitively detecting correlations among the Fourier phases.…
The general scheme for the treatment of relaxation processes and temporal autocorrelations of dynamical variables for many particle systems is presented in framework of the recurrence relations approach. The time autocorrelation functions…
The paper develops a calculus for a class of real-valued functions having a quadratic variation. The main result is a solution of the representation problem for a class of evolutions having a quadratic variation. The result is applied to…
We propose a new approach for properly analyzing stochastic time series by mapping the dynamics of time series fluctuations onto a suitable nonequilibrium surface-growth problem. In this framework, the fluctuation sampling time interval…
The concept of distance covariance/correlation was introduced recently to characterize dependence among vectors of random variables. We review some statistical aspects of distance covariance/correlation function and we demonstrate its…