Search results for "Autoregressive model"
showing 10 items of 120 documents
Surrogate Data Analysis for Assessing the Significance of the Coherence Function
2004
In cardiovascular variability analysis, the significance of the coupling between two time series is commonly assessed by setting a threshold level in the coherence function. While traditionally used statistical tests consider only the parameters of the adopted estimator, the required zero-coherence level may be affected by some features of the observed series. In this study, three procedures, based on the generation of surrogate series sharing given properties with the original but being structurally uncoupled, were considered: independent identically distributed (IID), Fourier transform (FT), and autoregressive (AR). IID surrogates maintained the distribution of the original series, while …
Inclusion of Instantaneous Influences in the Spectral Decomposition of Causality: Application to the Control Mechanisms of Heart Rate Variability
2021
Heart rate variability is the result of several physiological regulation mechanisms, including cardiovascular and cardiorespiratory interactions. Since instantaneous influences occurring within the same cardiac beat are commonplace in this regulation, their inclusion is mandatory to get a realistic model of physiological causal interactions. Here we exploit a recently proposed framework for the spectral decomposition of causal influences between autoregressive processes [2] and generalize it by introducing instantaneous couplings in the vector autoregressive model (VAR). We show the effectiveness of the proposed approach on a toy model, and on real data consisting of heart period (RR), syst…
Model-Based Transfer Entropy Analysis of Brain-Body Interactions with Penalized regression techniques
2020
The human body can be seen as a functional network depicting the dynamical interactions between different organ systems. This exchange of information is often evaluated with information-theoretic approaches which comprise the use of vector autoregressive (VAR) and state space (SS) models, normally identified with the Ordinary Least Squares (OLS). However, the number of time series to be included in the model is strictly related to the length of data recorded thus limiting the use of the classical approach. In this work, a new method based on penalized regressions, the so-called LASSO, was compared with OLS on physiological time-series extracted from 18 subjects during different stress condi…
Data-based modeling of vehicle collisions by nonlinear autoregressive model and feedforward neural network
2013
Vehicle crash test is the most direct and common method to assess vehicle crashworthiness. Visual inspection and obtained measurements, such as car acceleration, are used, e.g. to examine impact severity of an occupant or to assess overall car safety. However, those experiments are complex, time-consuming, and expensive. We propose a method to reproduce car kinematics during a collision using nonlinear autoregressive (NAR) model which parameters are estimated by the use of feedforward neural network. NAR model presented in this study is derived from the more general one - nonlinear autoregressive with moving average (NARMA). Suitability of autoregressive systems for data-based modeling was …
Online topology estimation for vector autoregressive processes in data networks
2017
An important problem in data sciences pertains to inferring causal interactions among a collection of time series. Upon modeling these as a vector autoregressive (VAR) process, this paper deals with estimating the model parameters to identify the underlying causality graph. To exploit the sparse connectivity of causality graphs, the proposed estimators minimize a group-Lasso regularized functional. To cope with real-time applications, big data setups, and possibly time-varying topologies, two online algorithms are presented to recover the sparse coefficients when observations are received sequentially. The proposed algorithms are inspired by the classic recursive least squares (RLS) algorit…
Experimental approach for testing the uncoupling between cardiovascular variability series
2002
In cardiovascular variability analysis, the significance of the coupling between two series is commonly assessed by defining a zero level on the magnitude-squared coherence (MSC). Although the use of the conventional value of 0.5 does not consider the dependence of MSC estimates on the analysis parameters, a theoretical threshold Tt is available only for the weighted covariance (WC) estimator. In this study, an experimental threshold for zero coherence Te was derived by a statistical test from the sampling distribution of MSC estimated on completely uncoupled time series. MSC was estimated by the WC method (Parzen window, spectral bandwidth B = 0.015, 0.02, 0.025, 0.03 Hz) and by the parame…
Using Temporal Texture for Content-Based Video Retrieval
2000
Textures evolving over time are called temporal textures and are very common in everyday life. Examples are the smoke flowing or the wavy water of a river. The idea explored in this paper is that image features based on temporal texture could allow a better performance of current content-based video retrieval systems that are mainly based on static characteristics of representative frames, like color and texture. To this aim we analyze the spatio-temporal nature of texture and its application in content-based access to video databases. In particular, we represent temporal texture using the spatio-temporal autoregressive (STAR) model and a variation of self-organizing maps (SOM) where each n…
A Novel Time Series Kernel for Sequences Generated by LTI Systems
2017
The recent introduction of Hankelets to describe time series relies on the assumption that the time series has been generated by a vector autoregressive model (VAR) of order p. The success of Hankelet-based time series representations prevalently in nearest neighbor classifiers poses questions about if and how this representation can be used in kernel machines without the usual adoption of mid-level representations (such as codebook-based representations). It is also of interest to investigate how this representation relates to probabilistic approaches for time series modeling, and which characteristics of the VAR model a Hankelet can capture. This paper aims at filling these gaps by: deriv…
Dynamic network identification from non-stationary vector autoregressive time series
2018
Learning the dynamics of complex systems features a large number of applications in data science. Graph-based modeling and inference underpins the most prominent family of approaches to learn complex dynamics due to their ability to capture the intrinsic sparsity of direct interactions in such systems. They also provide the user with interpretable graphs that unveil behavioral patterns and changes. To cope with the time-varying nature of interactions, this paper develops an estimation criterion and a solver to learn the parameters of a time-varying vector autoregressive model supported on a network of time series. The notion of local breakpoint is proposed to accommodate changes at individu…
Online Topology Identification from Vector Autoregressive Time Series
2019
Causality graphs are routinely estimated in social sciences, natural sciences, and engineering due to their capacity to efficiently represent the spatiotemporal structure of multivariate data sets in a format amenable for human interpretation, forecasting, and anomaly detection. A popular approach to mathematically formalize causality is based on vector autoregressive (VAR) models and constitutes an alternative to the well-known, yet usually intractable, Granger causality. Relying on such a VAR causality notion, this paper develops two algorithms with complementary benefits to track time-varying causality graphs in an online fashion. Their constant complexity per update also renders these a…