Related papers: Long Memory in Nonlinear Processes

Typical neural networks with external memory do not effectively separate capacity for episodic and working memory as is required for reasoning in humans. Applying knowledge gained from psychological studies, we designed a new model called…

Linear Response theory aims to predict how added forcing alters the statistical properties of an unforced system. These kinds of questions have been studied predominantly for autonomous dynamical systems, yet many systems in the physical,…

Advection-dominated dynamical systems, characterized by partial differential equations, are found in applications ranging from weather forecasting to engineering design where accuracy and robustness are crucial. There has been significant…

Numerical modeling of different structural materials that have highly nonlinear behaviors has always been a challenging problem in engineering disciplines. Experimental data is commonly used to characterize this behavior. This study aims to…

Multivariate processes with long-range dependent properties are found in a large number of applications including finance, geophysics and neuroscience. For real data applications, the correlation between time series is crucial. Usual…

Regression models are used in a wide range of applications providing a powerful scientific tool for researchers from different fields. Linear, or simple parametric, models are often not sufficient to describe complex relationships between…

We consider the general problem of modeling temporal data with long-range dependencies, wherein new observations are fully or partially predictable based on temporally-distant, past observations. A sufficiently powerful temporal model…

Typical methods for supervised sequence modeling are built upon the recurrent neural networks to capture temporal dependencies. One potential limitation of these methods is that they only model explicitly information interactions between…

In regression analysis, associations between continuous predictors and the outcome are often assumed to be linear. However, modeling the associations as non-linear can improve model fit. Many flexible modeling techniques, like (fractional)…

We introduce a class of quantum non-Markovian processes -- dubbed process trees -- that exhibit polynomially decaying temporal correlations and memory distributed across time scales. This class of processes is described by a tensor network…

Moving average models, linear or nonlinear, are characterized by their short memory. This paper shows that, in the presence of feedback in the dynamics, the above characteristic can disappear.

There has been an increasing interest from the scientific community in using likelihood-free inference (LFI) to determine which parameters of a given simulator model could best describe a set of experimental data. Despite exciting recent…

In this paper, we study nonparametric models allowing for locally stationary regressors and a regression function that changes smoothly over time. These models are a natural extension of time series models with time-varying coefficients. We…

The object of this paper is to study the asymptotic dependence structure of the linear time series models with infinitely divisible innovations by the use of their characteristic functions. Autoregressive moving-average (ARMA) models and…

Deep learning is playing an increasingly important role in time series analysis. We focused on time series forecasting using attention free mechanism, a more efficient framework, and proposed a new architecture for time series prediction…

This paper introduces a semiparametric regression estimator of the memory parameter for long-memory time series process. It is based on the regression in a neighborhood of the zero-frequency of the periodogram averaged over epochs. The…

We consider the residual empirical process in random design regression with long memory errors. We establish its limiting behaviour, showing that its rates of convergence are different from the rates of convergence for to the empirical…

Repeated measures analyses require proper choice of the correlation model to ensure accurate inference and optimal efficiency. The linear exponent autoregressive (LEAR) correlation model provides a flexible two-parameter correlation…

Long and short memory in economic processes is usually described by the so-called discrete fractional differencing and fractional integration. We prove that the discrete fractional differencing and integration are the Grunwald-Letnikov…

Nonlinear stochastic modeling is useful for describing complex engineering systems. Meanwhile, neuromorphic (brain-inspired) computing paradigms are developing to tackle tasks that are challenging and resource intensive on digital…