Autoregressive Parameters Research Articles

Mixed-effects models for censored data with autoregressive errors

ABSTRACT Mixed-effects models, with modifications to accommodate censored observations (LMEC/NLMEC), are routinely used to analyze measurements, collected irregularly over time, which are often subject to some upper and lower detection limits. This paper presents a likelihood-based approach for fitting LMEC/NLMEC models with autoregressive of order dependence of the error term. An EM-type algorithm is developed for computing the maximum likelihood estimates, obtaining as a byproduct the standard errors of the fixed effects and the likelihood value. Moreover, the constraints on the parameter space that arise from the stationarity conditions for the autoregressive parameters in the EM algorithm are handled by a reparameterization scheme, as discussed in Lin and Lee (2007). To examine the performance of the proposed method, we present some simulation studies and analyze a real AIDS case study. The proposed algorithm and methods are implemented in the new R package ARpLMEC.

A parametrized nonlinear predictive control strategy for relaxing COVID-19 social distancing measures in Brazil

The SARS-CoV-2 virus was first registered in Brazil by the end of February 2020. Since then, the country counts over 150000 deaths due to COVID-19 and faces a profound social and economic crisis; there is also an ongoing health catastrophe, with the majority of hospital beds in many Brazilian cities currently occupied with COVID-19 patients. Thus, a Nonlinear Model Predictive Control (NMPC) scheme used to plan appropriate social distancing measures (and relaxations) in order to mitigate the effects of this pandemic is formulated in this paper. The strategy is designed upon an adapted data-driven Susceptible–Infected–Recovered–Deceased (SIRD) model, which includes time-varying auto-regressive immunological parameters. A novel identification procedure is proposed, composed of analytical regressions, Least-Squares optimization and auto-regressive model fits. The adapted SIRD model is validated with real data and able to adequately represent the contagion curves over large forecast horizons. The NMPC strategy is designed to generate piecewise constant quarantine guidelines, which can be reassessed (relaxed/strengthened) each week. Simulation results show that the proposed NMPC technique is able to mitigate the number of infections and progressively loosen social distancing measures. With respect to a “no-control” condition, the number of deaths could be reduced in up to 30% if the proposed NMPC coordinated health policy measures are enacted.

On the validity of the residual-based bootstrap for the unit root test statistic with long memory observations

Consider the AR(1) model, where is a sequence of long memory processes with possibly infinite variance. In this paper, we propose to use a residual-based m-out-of-n bootstrap procedure to approximate the distribution of a least-squares estimator for the autoregressive parameter when this parameter is equal to unity, and its asymptotic validity is also proved.

An autoregressive parametric method applied to the autowave process modelling

The authors of the paper research the topic of the autoregressive parametric spectral estimation method which is applied to oscillation (vibration). It is illustrated by the study of dynamically stable the combustion modes in a liquid-propellant engine. The scholars suppose a hypothesis that if a model parameter is selected correctly, the method offers a higher resolution. It does not require a dialogue-based weighted signal, and compensated parser/analyzer filter related to the accurate estimates of the oscillating system attributes. The survey proves that parametric spectral estimation amounts to solving an optimization problem with and seeking the autoregressive model value parameters of waveform shaping, in which the model would be as close as possible to the observed signal in reality. Based on the study, the authors design a digital model of the dynamic system that meets all the required properties.

Determination of hypertension disease using chirp z-transform and statistical features of optimal band-pass filtered short-time photoplethysmography signals

Hypertension is the condition where the normal blood pressure is high. This situation is manifested by the high pressure of the blood in the vein towards the vessel wall. Hypertension mostly affects the brain, kidneys, eyes, arteries and heart. Therefore, the diagnosis of this common disease is important. It may take days, weeks or even months for diagnosis. Often a device, called a blood pressure holter, is connected to the person for 24 or 48 h and the person’s blood pressure is recorded at certain intervals. Diagnosis can be made by the specialist physician considering these results. In recent years, various physiological measurement techniques have been used to accelerate this time-consuming diagnostic phase and intelligent models have been proposed. One of these techniques is photopletesmography (PPG). In this study, a model for the detection of hypertension disease in individuals was proposed using chirp z-transform and statistical features (total band power, autoregressive model parameters, standard deviation of signal’s derivative and zero crossing rate) of optimal band-pass filtered short-time PPG signals. The proposed method was successfully applied to 657 PPG trials, which each of them had only 2.1 s signal length and achieved a classification accuracy rate of 77.52% on the test data. The results showed that the diagnosis of hypertension can be performed effectively by chirp z-transform and statistical features and support vector machine classifier using optimal frequency range of 1.4–6 Hz.

Extrapolation of AR models using cubic splines for damage progression evaluation in composite structures

This paper presents the potentiality of the use of extrapolation of a set of Auto-Regressive (AR) models to inspect a future damage sensitive indices based on changes in one-step-ahead prediction errors. The key idea is to use multiple AR models to assess a data-driven model to represent and predict the time-series outputs of the PZT sensors receiving Lamb waves in a composite coupon. Based on some simplified assumptions, after detecting initial damage using some previous classifier, its progression evaluation by interpolating the AR parameters is proposed and examined based on cubic spline functions. After, an extrapolated AR model using this information may verify the future state and to inspect how the damage could progress. An aeronautical composite panel with bonded piezoelectric elements that act both as sensors and actuators is utilized to examine the relationship between the variation of the identified model parameters with various levels of simulated damage. The results have shown a smooth and adequate correlation between the estimates obtained by the extrapolated model and the actual progress of the damage observed. The significant advantage of the proposed procedure is implementing this task without adopting a complicated and costly mathematical-physical model.

On the asymptotic distribution of the quadratic GMM estimator of a dynamic panel data model under a unit root

This paper considers the GMM estimator, αˆ, of the autoregressive parameter in linear dynamic panel data models with fixed effects when the data-generating process has a unit root. Previous literature has established that the limit distribution of n1∕4(αˆ−1) is degenerate and nondegenerate each with probability 1/2. We sharpen this result by showing that the limit distribution of n1∕2(αˆ−1) is nondegenerate when n1∕4(αˆ−1) converges in probability to 0, and we characterize the limit distribution which is nonstandard.

Massive MIMO Channel Prediction: Kalman Filtering Vs. Machine Learning

This paper focuses on channel prediction techniques for massive multiple-input multiple-output (MIMO) systems. Previous channel predictors are based on theoretical channel models, which would be deviated from realistic channels. In this paper, we develop and compare a vector Kalman filter (VKF)-based channel predictor and a machine learning (ML)-based channel predictor using the realistic channels from the spatial channel model (SCM), which has been adopted in the 3GPP standard for years. First, we propose a low-complexity mobility estimator based on the spatial average using a large number of antennas in massive MIMO. The mobility estimate can be used to determine the complexity order of developed predictors. The VKF-based channel predictor developed in this paper exploits the autoregressive (AR) parameters estimated from the SCM channels based on the Yule-Walker equations. Then, the ML-based channel predictor using the linear minimum mean square error (LMMSE)-based noise pre-processed data is developed. Numerical results reveal that both channel predictors have substantial gain over the outdated channel in terms of the channel prediction accuracy and data rate. The ML-based predictor has larger overall computational complexity than the VKF-based predictor, but once trained, the operational complexity of ML-based predictor becomes smaller than that of VKF-based predictor.

Efficient estimation in (PINAR(1)) model: semiparametric case

The efficient estimation problem of a semi-parametric first-order periodic integer-valued autoregressive (PINAR(1)) model is considered. The unspecified distribution of the innovation process of this model is suposed to satisfy only some mild technical assumptions. We therefore provide efficient estimates for both parameters of the model, namely a periodic autoregressive parameter and a periodic probability law of the innovation non-negative integer values process which is seen as an infinite dimensional parameter. The performances of these efficient estimations are shown through intensive simulations studies and an application on real data set.

A Phase Transition for Large Values of Bifurcating Autoregressive Models

We describe the asymptotic behavior of the number $$Z_n[a_n,\infty )$$ of individuals with a large value in a stable bifurcating autoregressive process, where $$a_n\rightarrow \infty $$ . The study of the associated first moment is equivalent to the annealed large deviation problem of an autoregressive process in a random environment. The trajectorial behavior of $$Z_n[a_n,\infty )$$ is obtained by the study of the ancestral paths corresponding to the large deviation event together with the environment of the process. This study of large deviations of autoregressive processes in random environment is of independent interest and achieved first. The estimates for bifurcating autoregressive process involve then a law of large numbers for non-homogenous trees. Two regimes appear in the stable case, depending on whether one of the autoregressive parameters is greater than 1 or not. It yields different asymptotic behaviors for large local densities and maximal value of the bifurcating autoregressive process.

The factor analytical approach in near unit root interactive effects panels

In a recent study, Bai (2013) proposes a new factor analytical (FA) method for estimation of stationary dynamic panel data models with fixed effects. Our interest in this method originates with the fact it does not require explicit demeaning of the data, a practice that is known to cause problems of bias and low power in near unit root panels. The purpose is to study the properties of FA when applied to such panels when the common component admits to a interactive effects representation, which is more general than fixed effects. It is shown that the estimator of the autoregressive parameter is consistent with a well centered asymptotic normal distribution, leading to unit root tests with maximal achievable power. In fact, FA is consistent and asymptotically normal regardless of whether the data are near unit root non-stationary or stationary. It is therefore very general and hence widely applicable.

A Simple Model Correction for Modelling and Forecasting (Un)Reliable Realized Volatility

We propose a dilution bias correction approach to deal with the errors-in-variables problem observed in realized volatility (RV) measures. The absolute difference between daily and monthly RV is shown to be proportional to the relative magnitude of the measurement error. Therefore, in implementing the latter metric, and in allowing the daily auto-regressive parameter to vary as a function of the error term, the result is more responsive forecasts with greater persistence (faster mean-reversion) when the measurement error is low (high). Empirical results indicate that our models outperform some of the most popular HAR and GARCH models across various forecasting horizons.

Efficient estimation in periodic [formula omitted] model: Nonparametric innovation distributions case

The efficient estimation problem of a semi-parametric periodic integer-valued autoregressive PINARp model of arbitrary order is considered. The unspecified distribution of the innovation process of this model is supposed to satisfy only some mild technical assumptions.We therefore provide efficient estimates for both parameters of the model, namely a periodic autoregressive parameter and a periodic probability law of the innovation non-negative integer values process which is seen as an infinite dimensional parameter. The performances of these efficient estimations are shown through an intensive simulation study and an application on real data set.

Multiple change point detection and validation in autoregressive time series data

It is quite common that the structure of a time series changes abruptly. Identifying these change points and describing the model structure in the segments between these change points is of interest. In this paper, time series data is modelled assuming each segment is an autoregressive time series with possibly different autoregressive parameters. This is achieved using two main steps. The first step is to use a likelihood ratio scan based estimation technique to identify these potential change points to segment the time series. Once these potential change points are identified, modified parametric spectral discrimination tests are used to validate the proposed segments. A numerical study is conducted to demonstrate the performance of the proposed method across various scenarios and compared against other contemporary techniques.

Analysis of statistical coefficients and autoregressive parameters over intrinsic mode functions (IMFs) for epileptic seizure detection.

Epilepsy is a persistent neurological disorder impacting over 50 million people around the world. It is characterized by repeated seizures defined as brief episodes of involuntary movement that might entail the human body. Electroencephalography (EEG) signals are usually used for the detection of epileptic seizures. This paper introduces a new feature extraction method for the classification of seizure and seizure-free EEG time segments. The proposed method relies on the empirical mode decomposition (EMD), statistics and autoregressive (AR) parameters. The EMD method decomposes an EEG time segment into a finite set of intrinsic mode functions (IMFs) from which statistical coefficients and autoregressive parameters are computed. Nevertheless, the calculated features could be of high dimension as the number of IMFs increases, the Student's t-test and the Mann-Whitney U test were thus employed for features ranking in order to withdraw lower significant features. The obtained features have been used for the classification of seizure and seizure-free EEG signals by the application of a feed-forward multilayer perceptron neural network (MLPNN) classifier. Experimental results carried out on the EEG database provided by the University of Bonn, Germany, demonstrated the effectiveness of the proposed method which performance assessed by the classification accuracy (CA) is compared to other existing performances reported in the literature.

Statistical Learning of the Worst Regional Smog Extremes with Dynamic Conditional Modeling

This paper is concerned with the statistical learning of the extreme smog (PM 2.5 ) dynamics of a vast region in China. Differently from classical extreme value modeling approaches, this paper develops a dynamic model of conditional, exponentiated Weibull distribution modeling and analysis of regional smog extremes, particularly for the worst scenarios observed in each day. To gain higher modeling efficiency, weather factors will be introduced in an enhanced model. The proposed model and the enhanced model are illustrated with temporal/spatial maxima of hourly PM 2.5 observations each day from smog monitoring stations located in the Beijing–Tianjin–Hebei geographical region between 2014 and 2019. The proposed model performs more precisely on fittings compared with other previous models dealing with maxima with autoregressive parameter dynamics, and provides relatively accurate prediction as well. The findings enhance the understanding of how severe extreme smog scenarios can be and provide useful information for the central/local government to conduct coordinated PM 2.5 control and treatment. For completeness, probabilistic properties of the proposed model were investigated. Statistical estimation based on the conditional maximum likelihood principle is established. To demonstrate the estimation and inference efficiency of studies, extensive simulations were also implemented.

Multilevel Autoregressive Models when the Number of Time Points is Small

ABSTRACT The multilevel autoregressive model disentangles unobserved heterogeneity from state-dependence. Statistically, the random intercept accounts for the dependence of all measurements at different time points on an observed underlying factor, while the lagged dependent predictor allows the outcome to depend on the outcome at the previous time point. In this paper, we consider different implementations of the simplest multilevel autoregressive model, and explore how each of them deals with the endogeneity assumption and the initial conditions problem. We discuss the performance of the no centering approach, the manifest centering approach, and the latent centering approach in the setting where the number of time points is small. We find that some commonly used approaches show bias for the autoregressive parameter. When the outcome at the first time point is considered predetermined, the no centering approach assuming endogeneity performs best.

Adjusted QMLE for the spatial autoregressive parameter

One simple, and often very effective, way to attenuate the impact of nuisance parameters on maximum likelihood estimation of a parameter of interest is to recenter the profile score for that parameter. We apply this general principle to the quasi-maximum likelihood estimator (QMLE) of the autoregressive parameter λ in a spatial autoregression. The resulting estimator for λ has better finite sample properties compared to the QMLE for λ, especially in the presence of a large number of covariates. It can also solve the incidental parameter problem that arises, for example, in social interaction models with network fixed effects. However, spatial autoregressions present specific challenges for this type of adjustment, because recentering the profile score may cause the adjusted estimate to be outside the usual parameter space for λ. Conditions for this to happen are given, and implications are discussed. For inference, we propose confidence intervals based on a Lugannani–Rice approximation to the distribution of the adjusted QMLE of λ. Based on our simulations, the coverage properties of these intervals are excellent even in models with a large number of covariates.

A robust method for the identification of non-Gaussian autoregressive systems in colored Gaussian noise

This paper introduces a novel technique for parameter estimation of an autoregressive (AR) all-pole process under non-Gaussian noise environment using third order cumulants of the observed sequence. The proposed AR parameters estimation technique is based on formulating a particular structured matrix with entries of third order cumulants of the observed output sequence only. This matrix almost possesses a full rank structure. The observed sequence may be contaminated with additive Gaussian noise (white or colored), whose power spectral density is unknown. The system is driven by a zero-mean independent and identically distributed (i.i.d) non-Gaussian sequence. Simulation results confirm the good numerical conditioning of the algorithm and the improvement in performance with respect to well-known methods even when the observed signal is heavily contaminated with Gaussian noise.

Modelling Housing Rents Using Spatial Autoregressive Geographically Weighted Regression: A Case Study in Cracow, Poland

The proportion of tenants will undoubtedly rise in Poland, where at present, the ownership housing model is very dominant. As a result, the rental housing market in Poland is currently under-researched in comparison with owner-occupancy. In order to narrow this research gap, this study attempts to identify the determinants affecting rental prices in Cracow. The latter were obtained from the internet platform otodom.pl using the web scraping technique. To identify rent determinants, ordinary least squares (OLS) regression and spatial econometric methods were used. In particular, traditional spatial autoregressive model (SAR) and spatial autoregressive geographically weighted regression (GWR-SAR) were employed, which made it possible to take into account the spatial heterogeneity of the parameters of determinants and the spatially changing spatial autocorrelation of housing rents. In-depth analysis of rent determinants using the GWR-SAR model exposed the complexity of the rental market in Cracow. Estimates of the above model revealed that many local markets can be identified in Cracow, with different factors shaping housing rents. However, one can identify some determinants that are ubiquitous for almost the entire city. This concerns mainly the variables describing the area of the flat and the age of the building. Moreover, the Monte Carlo test indicated that the spatial autoregressive parameter also changes significantly over space.