Related papers: Long Memory in Nonlinear Processes

Considering the difficulty of financial time series forecasting in financial aid, much of the current research focuses on leveraging big data analytics in financial services. One modern approach is to utilize "predictive analysis",…

Stationary and ergodic time series can be constructed using an s-vine decomposition based on sets of bivariate copula functions. The extension of such processes to infinite copula sequences is considered and shown to yield a rich class of…

This article is a short review of the recent results on properties of nonlinear fractional maps which are maps with power- or asymptotically power-law memory. These maps demonstrate the new type of attractors - cascade of bifurcations type…

Memory is fundamental to large language model (LLM)-based agents, but existing surveys emphasize application-level use (e.g., personalized dialogue), while overlooking the atomic operations governing memory dynamics. This work categorizes…

The recurrent neural network and its variants have shown great success in processing sequences in recent years. However, this deep neural network has not aroused much attention in anomaly detection through predictively process monitoring.…

We propose a setup for fractionally cointegrated time series which is formulated in terms of latent integrated and short-memory components. It accommodates nonstationary processes with different fractional orders and cointegration of…

Current large language models (LLMs) generally lack an effective runtime memory mechanism,making it difficult to adapt to dynamic and personalized interaction requirements. To address this issue, this paper proposes a novel neural memory…

Regression methods for interval-valued data have been increasingly studied in recent years. As most of the existing works focus on linear models, it is important to note that many problems in practice are nonlinear in nature and therefore…

In this work we introduce the class of beta autoregressive fractionally integrated moving average models for continuous random variables taking values in the continuous unit interval $(0,1)$. The proposed model accommodates a set of…

Various methods using machine and deep learning have been proposed to tackle different tasks in predictive process monitoring, forecasting for an ongoing case e.g. the most likely next event or suffix, its remaining time, or an…

We propose a simple model of recognition, short-term memory, long-term memory and learning.

The space time autoregressive model has been widely applied in science, in areas such as economics, public finance, political science, agricultural economics, environmental studies and transportation analyses. The classical space time…

We make an observation that facilitates exact likelihood-based inference for the parameters of the popular ARFIMA model without requiring stationarity by allowing the upper bound $\bar{d}$ for the memory parameter $d$ to exceed $0.5$:…

We predict asset returns and measure risk premia using a prominent technique from artificial intelligence -- deep sequence modeling. Because asset returns often exhibit sequential dependence that may not be effectively captured by…

Large and moderate deviation probabilities play an important role in many applied areas, such as insurance and risk analysis. This paper studies the exact moderate and large deviation asymptotics in non-logarithmic form for linear processes…

Machine learning models exhibit two seemingly contradictory phenomena: training data memorization, and various forms of forgetting. In memorization, models overfit specific training examples and become susceptible to privacy attacks. In…

We predict the emergence of extreme events in a parametrically driven nonlinear dynamical system using three Deep Learning models, namely Multi-Layer Perceptron, Convolutional Neural Network and Long Short-Term Memory. The Deep Learning…

Regression models are popular tools in empirical sciences to infer the influence of a set of variables onto a dependent variable given an experimental dataset. In neuroscience and cognitive psychology, Generalized Linear Models (GLMs)…

For the challenging task of modeling multivariate time series, we propose a new class of models that use dependent Mat\'ern processes to capture the underlying structure of data, explain their interdependencies, and predict their unknown…

Accurate time series prediction is challenging due to the inherent nonlinearity and sensitivity to initial conditions. We propose a novel approach that enhances neural network predictions through differential learning, which involves…