Partially Hidden Markov Chain Multivariate Linear Autoregressive model: inference and forecasting—application to machine health prognostics

Even in sustained vowels, the durations of successive glottal cycles are not identical. They fluctuate quasi-randomly around an average. This phenomenon is known as jitter. Correlation analysis has shown that perturbations of neighboring glottal cycles are interdependent, i.e. they are not purely random. The non-random component of jitter can be modeled by means of a linear autoregressive time series model which absorbs correlations between fluctuations of adjacent cycles and leaves a purely random component. The problem is that nonlinear relations may be missed by correlation analysis or linear autoregressive modeling. Nonlinear relations could be the signature of chaotic vibratory patterns which some authors expect for some pathological conditions of the vocal folds. We therefore decided to search inside whitened jitter time series (i.e. time series from which any linear correlations had been removed) for nonlinear or other anomalous dependencies between neighboring cycles. The results showed the following. Of the 265 time series, 231 appeared to have been correctly represented by linear autoregressive models. For 29 series out of the 34 remaining, deviations from pure randomness could be traced to isolated anomalous glottal cycles which statistical time series models had not taken into account. Finally, five signals, produced by three speakers, were detected which displayed relations between neighboring cycles which could not be traced either to linear correlations or to isolated glitches.

Networks are ubiquitous throughout biology, spanning the entire range from molecules to food webs and global environmental systems. Yet, despite substantial efforts by the scientific community, the inference of these networks from data still presents a problem that is unsolved in general. One frequent strategy of addressing the structure of networks is the assumption that the interactions among molecular or organismal populations are static and correlative. While often successful, these static methods are no panacea. They usually ignore the asymmetry of relationships between two species and inferences become more challenging if the network nodes represent dynamically changing quantities. Overcoming these challenges, two very different network inference approaches have been proposed in the literature: Lotka-Volterra (LV) models and Multivariate Autoregressive (MAR) models. These models are computational frameworks with different mathematical structures which, nevertheless, have both been proposed for the same purpose of inferring the interactions within coexisting population networks from observed time-series data. Here, we assess these dynamic network inference methods for the first time in a side-by-side comparison, using both synthetically generated and ecological datasets. Multivariate Autoregressive and Lotka-Volterra models are mathematically equivalent at the steady state, but the results of our comparison suggest that Lotka-Volterra models are generally superior in capturing the dynamics of networks with non-linear dynamics, whereas Multivariate Autoregressive models are better suited for analyses of networks of populations with process noise and close-to linear behavior. To the best of our knowledge, this is the first study comparing LV and MAR approaches. Both frameworks are valuable tools that address slightly different aspects of dynamic networks.

BackgroundReliable evaluations of state-level policies are essential for identifying effective policies and informing policymakers’ decisions. State-level policy evaluations commonly use a difference-in-differences (DID) study design; yet within this framework, statistical model specification varies notably across studies. More guidance is needed about which set of statistical models perform best when estimating how state-level policies affect outcomes.MethodsMotivated by applied state-level opioid policy evaluations, we implemented an extensive simulation study to compare the statistical performance of multiple variations of the two-way fixed effect models traditionally used for DID under a range of simulation conditions. We also explored the performance of autoregressive (AR) and GEE models. We simulated policy effects on annual state-level opioid mortality rates and assessed statistical performance using various metrics, including directional bias, magnitude bias, and root mean squared error. We also reported Type I error rates and the rate of correctly rejecting the null hypothesis (e.g., power), given the prevalence of frequentist null hypothesis significance testing in the applied literature.ResultsMost linear models resulted in minimal bias. However, non-linear models and population-weighted versions of classic linear two-way fixed effect and linear GEE models yielded considerable bias (60 to 160%). Further, root mean square error was minimized by linear AR models when we examined crude mortality rates and by negative binomial models when we examined raw death counts. In the context of frequentist hypothesis testing, many models yielded high Type I error rates and very low rates of correctly rejecting the null hypothesis (< 10%), raising concerns of spurious conclusions about policy effectiveness in the opioid literature. When considering performance across models, the linear AR models were optimal in terms of directional bias, root mean squared error, Type I error, and correct rejection rates.ConclusionsThe findings highlight notable limitations of commonly used statistical models for DID designs, which are widely used in opioid policy studies and in state policy evaluations more broadly. In contrast, the optimal model we identified--the AR model--is rarely used in state policy evaluation. We urge applied researchers to move beyond the classic DID paradigm and adopt use of AR models.

The aim of this study was to compare the small sample (N = 1, 3, 5, 10, 15) performance of a Bayesian multivariate vector autoregressive (BVAR-SEM) time series model relative to frequentist power and parameter estimation bias. A multivariate autoregressive model was developed based on correlated autoregressive time series vectors of varying lengths (T = 25, 50, 75, 100, 125) using Statistical Analysis System (SAS) version 9.2. Autoregressive components for the 5 series vectors included coefficients of .80, .70, .65, .50 and .40. Error variance components included values of .20, .20, .10, .15, and .15, with cross-lagged coefficients of .10, .10, .15, .10, and .10. A Monte Carlo study revealed that in comparison to frequentist methods, the Bayesian approach provided increased sensitivity for hypothesis testing and detecting Type I error.

This study compares the efficiency of a non-linear model called artificial neural network with linear autoregressive and random walk models in the one-step-ahead prediction of daily Indian rupee/US dollar exchange rate. We find that neural network and linear autoregressive models outperform random walk model in in-sample and out-of-sample forecasts. The in-sample forecasting of neural network is found to be better than that of linear autoregressive model. As far as out-of-sample forecasting is concerned, the results are mixed and we do not find a "winner" model between neural network and linear autoregressive model. However, neural network is able to improve upon the linear autoregressive model in terms of sign predictions. In addition to this, we also find that the number of input nodes has greater impact on neural network's performance than the number of hidden nodes.

A turbidity time series, recorded every 15 min in a first‐order Scottish stream for more than a year, along with two covariates (stage height and rainfall), is considered. Turbidity time series have complex dynamics because they are nonlinear, nonnormal, nonstationary, with a long memory, and present missing values. Given these issues the turbidity process is analyzed by Markov switching autoregressive models under the Bayesian paradigm. Since the multimodality of the posterior density novel evolutionary Monte Carlo (EMC) algorithms incorporating a few original features are developed to better traverse the posterior surface and escape from local basins of attraction. This because a population of chains are processed in parallel exchanging information one another and with different temperatures attached to each chain. These advanced EMC algorithms allow performing both Bayesian inference and model choice. Hence, it is possible to efficiently fit the actual data, reconstruct the sequence of hidden states, restore the missing values, and classify the observations into a few regimes, providing new insight on turbidity dynamics. A comparison with different nonlinear time series models is also proposed. Finally, a simulation study on the selection of the tuning factors of the EMC algorithm is presented.

Stochastic dual dynamic programming (SDDP) is a popular method for hydro-thermal planning and recently has been applied to energy optimization problems in smart grids involving wind energy resources. In this method, there is a need for incorporating dynamic models in order to take into account time correlations of uncertainties. The models used should posses certain linearity properties to conserve the convexity of the optimization problem to be solved. This is crucial for the convergence of the SDDP algorithm. In the past, especially in hydro-thermal planning, linear autoregressive (AR) models were usually used for this purpose. However, they can produce negative values which is not realistic and can lead to difficulties in SDDP computations. As a remedy, one can employ additive or multiplicative AR models which are capable of producing nonnegative time series. Despite of this fact, the works using such models in SDDP based wind energy applications are very rare and model estimation methods were not elaborated. Moreover, their accuracy in representing real wind uncertainty was not studied well. Motivated with these facts, in the present study, modeling of wind speed distribution by such AR models is investigated. The parameters of the models were estimated by solving constrained least squares optimization problems. In order to asses the accuracy of corresponding distributions, a nonparametric method for computing the K-L divergence between probability density functions was utilized. Finally, the models were compared in terms of accuracy of their distributions and features of their parameter estimation algorithms.

Non-probabilistic forecasting methods are commonly used in various scientific fields. Fuzzy-time-series methods are well-known non-probabilistic and nonlinear forecasting methods. Although these methods can produce accurate forecasts, linear autoregressive models can produce forecasts that are more accurate than those produced by fuzzy-time-series methods for some real-world time series. It is well known that hybrid forecasting methods are useful techniques for forecasting time series and that they have the capabilities of their components. In this study, a new hybrid forecasting method is proposed. The components of the new hybrid method are a high-order fuzzy-time-series forecasting model and autoregressive model. The new hybrid forecasting method has a network structure and is called a fuzzy-time-series network (FTS-N). The fuzzy c-means method is used for the fuzzification of time series in FTS-N, which is trained by particle swarm optimization. Istanbul Stock Exchange daily data sets from 2009 to 2013 and the Taiwan Stock Exchange Capitalization Weighted Stock Index data sets from 1999 to 2004 were used to evaluate the performance of FTS-N. The applications reveal that FTS-N produces more accurate forecasts for the 11 real-world time-series data sets.

Impulse response function based on multivariate AR model can differentiate focal hemisphere in temporal lobe epilepsy

Event Abstract Back to Event Characterizing fetal sympatho-vagal balance through multivariate time-varying autoregressive modeling of magnetocardiographic data D. Gutiérrez1*, F M García-Guevara1, I Kiefer2, R. Draganova2 and H Preissl2 1 Centro de Investigación y de Estudios Avanzados, Mexico 2 MEG-Center, Germany We propose a method to analyze fetal beat-to-beat heart rate variability (HRV) obtained from magnetocardiographic (MCG) measurements at different times of gestation using a multivariate time-varying autoregressive (MTVAR) model. Our approach is based on treating a group of HRV signals from a single fetus and measured at different gestational periods as a dynamical system, from which we obtain a suitable MTVAR model. This kind of autoregressive model has been previously found useful to study the dynamics of multichannel data associated to brain activity. Then, changes in the values of the coefficients of the MTVAR model obtained from the HRV signals can be associated to changes in fetal sympatho-vagal balance. Therefore, in this paper we propose to characterize the variations in the sympatho-vagal balance at specific gestational period by comparing the dynamics of the MTVAR coefficients to the SDNN/RMSSD ratio, which is known to be a potential marker for sympatho-vagal balance. Furthermore, an overall behavior of the sympatho-vagal balance during the gestation (or at least over the weeks when measurements were acquired) could be estimated from the average values of the MTVAR coefficients by comparing them to the tendencies obtained through the classical analysis of the different frequency bands in the HRV signal. In order to demonstrate the applicability of the proposed modeling approach, real magnetocardiographic data from healthy fetuses is analyzed. Preliminary results show that the MTVAR model is able to mimic the sympatho-vagal development reported in the literature, and the results also show consistency independently of the number of gestational periods used in the analysis. Conference: Biomag 2010 - 17th International Conference on Biomagnetism , Dubrovnik, Croatia, 28 Mar - 1 Apr, 2010. Presentation Type: Poster Presentation Topic: Fetal and neonatal biomagnetism Citation: Gutiérrez D, García-Guevara F, Kiefer I, Draganova R and Preissl H (2010). Characterizing fetal sympatho-vagal balance through multivariate time-varying autoregressive modeling of magnetocardiographic data. Front. Neurosci. Conference Abstract: Biomag 2010 - 17th International Conference on Biomagnetism . doi: 10.3389/conf.fnins.2010.06.00135 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 25 Mar 2010; Published Online: 25 Mar 2010. * Correspondence: D. Gutiérrez, Centro de Investigación y de Estudios Avanzados, Apodaca, Mexico, dgtz@ieee.org Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers D. Gutiérrez F M García-Guevara I Kiefer R. Draganova H Preissl Google D. Gutiérrez F M García-Guevara I Kiefer R. Draganova H Preissl Google Scholar D. Gutiérrez F M García-Guevara I Kiefer R. Draganova H Preissl PubMed D. Gutiérrez F M García-Guevara I Kiefer R. Draganova H Preissl Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

Time series modeling of surface EMG based hand manipulation identification via expectation maximization algorithm

The Partial Directed Coherence (PDC) and its generalized formulation (gPDC) are popular tools for investigating, in the frequency domain, the concept of Granger causality among multivariate (MV) time series. PDC and gPDC are formalized in terms of the coefficients of an MV autoregressive (MVAR) model which describes only the lagged effects among the time series and forsakes instantaneous effects. However, instantaneous effects are known to affect linear parametric modeling, and are likely to occur in experimental time series. In this study, we investigate the impact on the assessment of frequency domain causality of excluding instantaneous effects from the model underlying PDC evaluation. Moreover, we propose the utilization of an extended MVAR model including both instantaneous and lagged effects. This model is used to assess PDC either in accordance with the definition of Granger causality when considering only lagged effects (iPDC), or with an extended form of causality, when we consider both instantaneous and lagged effects (ePDC). The approach is first evaluated on three theoretical examples of MVAR processes, which show that the presence of instantaneous correlations may produce misleading profiles of PDC and gPDC, while ePDC and iPDC derived from the extended model provide here a correct interpretation of extended and lagged causality. It is then applied to representative examples of cardiorespiratory and EEG MV time series. They suggest that ePDC and iPDC are better interpretable than PDC and gPDC in terms of the known cardiovascular and neural physiologies.

This article introduces autoregressive (AR) linear models to psychology students and researchers through a step-by-step approach using SPSS and R. Despite their relevance, AR models remain underutilized in behavioral sciences, possibly due to conceptual challenges and difficulties interpreting autocorrelation and seasonality. Our aim is to simplify their implementation by presenting time series models as special cases of linear regression, using accessible language and practical examples. The article illustrates AR estimation using real data, incorporating lagged values as predictors of the dependent variable. Residual diagnostics, a frequently overlooked aspect in applied research, receive special attention, including figures and statistical tests. As Kmenta (1971) demonstrated, serially correlated residuals can lead to artificially low p values for the parameter estimates, potentially resulting in explanatory variables being deemed significant when they truly are not. To promote understanding, we offer intuitive visualizations and clear decision rules for model building, lag selection, and seasonality detection. We compare polynomial and AR models using the confounding test. The data set and annotated R and SPSS scripts are included to support replication and help readers learn basic syntax. We also discuss conceptual and practical limitations of moving average, integration (I), and exponential smoothing models, emphasizing the practical advantages of AR-only models in psychological contexts. Throughout, we stress the importance of aligning statistical models with theoretical assumptions and the temporal structure of data. By combining step-by-step explanations, visual guidance, and real-data applications, this tutorial provides a practical foundation for incorporating AR models into applied psychological research. (PsycInfo Database Record (c) 2025 APA, all rights reserved).

L'obiettivo del lavoro e la ricerca di nessi causativi tra sequenze di dati idrologici (piezometrie e precipitazioni) mediante modelli lineari di tipo autoregressivo e a media mobile (ARMA). Tali dati derivano da un pozzo e da una stazione meteorologica situati nella Provincia di Cremona, e sono relativi al periodo Gennaio 1951-Dicembre 1998.Nel modello proposto, la sequenza pluviometrica e l'ingresso di un sistema dinamico lineare a tempo discreto, mentre la sequenza piezometrica e la sua uscita: il valore corrente di piezometria e cosi determinato dalla combinazione lineare di piezometrie e pluviometrie passate.Dopo una fase preliminare di analisi statistica delle sequenze (nei domini di tempo e frequenza), il modello ARMA e stato utilizzato dapprima per ricostruire le sequenze piezometriche disponibili e identificare i parametri della combinazione lineare, e poi per operare la previsione delle piezometrie: calcolando il residuo di previsione (tramite il confronto di piezometria predetta e misurata), e caratterizzandolo statisticamente si e valutata la capacita predittiva del modello.I risultati hanno mostrato che il predittore costruito presenta un errore quadratico di predizione relativamente piccolo. Nonostante cio, dall'analisi del residuo emerge che il predittore costruito non riesce a descrivere in maniera accurata tutte le proprieta del processo piezometrico. Questo puo essere dovuto al fatto che la grandezza impiegata come ingresso del sistema dinamico (precipitazione) non e l'unica voce che concorre al bilancio idrogeologico.

This project assessed the use of multivariate auto-regressive (MAR) models to create forecasts of continuous vital signs in hospitalized patients. A total of 20 hours continuous (1/60Hz) heart rate and respiration rate from eight postoperative patients, where used to fit a centered MAR model for forecasting in windows of 15 minutes. The model was fitted using Markov Chain Monte Carlo sampling, and the model was evaluated on data from five additional patients. The results demonstrate an average RMSE in the forecast window of 11.4 (SD: 7.30) beats per minute for heart rate and 3.3 (SD:1.3) breaths per minute for respiration rate. These results indicate potential for forecasting vital signs in a clinical setting.