The paper introduces the concept of fault diagnosis using an observer bank of autoregressive time series models. The concept was applied experimentally to diagnose a number of induced faults in a rolling element bearing using the measured time series vibration signal. Three distinct techniques of autoregressive modeling were compared for their performance and reliability under conditions of var...

This paper proposes an easy test for independence between two stationary autoregressive fractionally integrated moving average (ARFIMA) processes via AR approximations. We prove that an ARFIMA (p, d, q) process, φ(L)(1 − L)yt = θ(L)et, d ∈ (0, 0.5), where et is a white noise, can be approximated well by an autoregressive (AR) model and establish the theoretical foundation of Haugh’s (1976) stat...

In the study of complex physical and biological systems represented by multivariate stochastic processes, an issue of great relevance is the description of the system dynamics spanning multiple temporal scales. While methods to assess the dynamic complexity of individual processes at different time scales are well established, multiscale analysis of directed interactions has never been formaliz...

A time series is a realization or sample function from a certain stochastic process. The main goals of the analysis of time series are forecasting, modeling and characterizing. Conventional time series models i.e. autoregressive (AR), moving average (MA), hybrid AR and MA (ARMA) models, assume that the time series is stationary. The other methods to model time series are soft computing techniqu...

In what concerns extreme values modeling, heavy tailed autoregressive processes defined with the minimum or maximum operator have proved to be good alternatives to classical linear ARMA with heavy tailed marginals (Davis and Resnick [8], Ferreira and Canto e Castro [13]). In this paper we present a complete characterization of the tail behavior of the autoregressive Pareto process known as Yeh–...

The concept of the autoregressive (AR) sieve bootstrap is investigated for the case of spatial processes in Z. This procedure fits AR models of increasing order to the given data and, via resampling of the residuals, generates bootstrap replicates of the sample. The paper explores the range of validity of this resampling procedure and provides a general check criterion which allows to decide wh...

Electroencephalography is an essential clinical tool for the evaluation and treatment of neurophysiologic disorders related to epilepsy. Careful analyses of the electroencephalograph (EEG) records can provide valuable insight and improved understanding of the mechanisms causing epileptic disorders. The detection of epileptiform discharges in the EEG is an important element in the diagnosis of e...

MOTIVATION Molecular dynamics (MD) simulations have dramatically improved the atomistic understanding of protein motions, energetics and function. These growing datasets have necessitated a corresponding emphasis on trajectory analysis methods for characterizing simulation data, particularly since functional protein motions and transitions are often rare and/or intricate events. Observing that ...

This paper deals with autoregressive (AR) models of singular spectra, whose corresponding transfer function matrices can be expressed in a stable AR matrix fraction description [Formula: see text] with [Formula: see text] a tall constant matrix of full column rank and with the determinantal zeros of [Formula: see text] all stable, i.e. in [Formula: see text]. To obtain a parsimonious AR model, ...