Related papers: Detecting long and short memory via spectral metho…
In this article, we aim to further clarify certain subtle aspects of processes that exhibit long memory in the second-order sense. We construct a long-memory stochastic sequence, in the sense that the series of absolute autocovariances…
In many mechanical, electrical, and general physical systems evolving over time or space, spectral analysis methods as Fast Fourier Transform (FFT), Short Term Fourier Transform (STFT), Power Spectrum Density (PSD) plays a very important…
Modern high-frequency trading (HFT) environments are characterized by sudden price spikes that present both risk and opportunity, but conventional financial models often fail to capture the required fine temporal structure. Spiking Neural…
Topological Data Analysis (TDA) is increasingly crucial in investigating the shape of complex data structures across scientific fields, particularly in neuroscience and finance. This study delves into persistent homology, a TDA component…
A simple model of an irreversible process is introduced. The equation of iterations in the model includes a noise generation term. We study the properties of the system when the noise generation term is a stochastic process (e.g. a random…
With the advance of modern technology, more and more data are being recorded continuously during a time interval or intermittently at several discrete time points. They are both examples of "functional data", which have become a prevailing…
We propose a model of fractal point process driven by the nonlinear stochastic differential equation. The model is adjusted to the empirical data of trading activity in financial markets. This reproduces the probability distribution…
Spiking Neural Networks (SNNs) are emerging as a promising alternative to Artificial Neural Networks (ANNs) due to their inherent energy efficiency. Owing to the inherent sparsity in spike generation within SNNs, the in-depth analysis and…
Here, we present a new method to evaluate the expectation value of the power spectrum of a time series. A statistical approach is adopted to define the method. After its demonstration, it is validated showing that it leads to the known…
Signal decomposition and multiscale signal analysis provide many useful tools for time-frequency analysis. We proposed a random feature method for analyzing time-series data by constructing a sparse approximation to the spectrogram. The…
Real time sensor based applications in pervasive computing require edge deployable models to ensure low latency privacy and efficient interaction. A prime example is sensor based human activity recognition where models must balance accuracy…
From natural language processing to vision, Scaled Dot Product Attention (SDPA) is the backbone of most modern deep learning applications. Unfortunately, its memory and computational requirements can be prohibitive in low-resource settings.…
Power spectrum estimation is an important tool in many applications, such as the whitening of noise. The popular multitaper method enjoys significant success, but fails for short signals with few samples. We propose a statistical model…
Understanding and predicting the electric consumption patterns in the short-, mid- and long-term, at the distribution and transmission level, is a fundamental asset for smart grids infrastructure planning, dynamic network reconfiguration,…
This article studies the financial time series data processing for machine learning. It introduces the most frequent scaling methods, then compares the resulting stationarity and preservation of useful information for trend forecasting. It…
We perform an analysis of fractal properties of the positive and the negative changes of the German DAX30 index separately using Multifractal Detrended Fluctuation Analysis (MFDFA). By calculating the singularity spectra $f(\alpha)$ we show…
Change detection has been a hotspot in remote sensing technology for a long time. With the increasing availability of multi-temporal remote sensing images, numerous change detection algorithms have been proposed. Among these methods, image…
The estimation of power spectra from LDA data provides signal processing challenges for fluid dynamicists for several reasons: acquisition is dictated by randomly arriving particles, the registered particle velocities tend to be biased…
A stochastic analysis of financial data is presented. In particular we investigate how the statistics of log returns change with different time delays $\tau$. The scale dependent behaviour of financial data can be divided into two regions.…
Spectral networks derived from multivariate time series data arise in many domains, from brain science to Earth science. Often, it is of interest to study how these networks change under different conditions. For instance, to better…