Autoregressive Coefficients Research Articles

Bayesian prior modeling in vector autoregressions via the Yule-Walker equations

In multivariate time series analysis, the Yule-Walker method refers to a system of equations relating the cross-covariances of a stationary vector autoregressive (VAR) model with the matrices of the autoregressive coefficients and the covariance matrix of the noise, both of which are unknown to be estimated. In Bayesian inference of VAR models, one of the key problems is the setting of the prior distributions on these unknown parameters. The Yule-Walker equations are used here to develop a novel prior specification that exploits the reparameterization of the unknowns in terms of the mean, the cross-covariances, and the covariance of the process. Further, the cross-covariance matrices are separated out in terms of the standard deviations and the correlations. All these new quantities are easier to handle because it is more common to have prior information on the mean and the correlation structure of a multiple time series rather than the underlying autoregressive coefficients and the white noise process. The proposed prior specification is suitable for both non informative and informative settings. Through the Yule-Walker based prior, parameter estimation and structure learning of the stationary VAR models are performed via Markov chain Monte Carlo methods. The methodology is illustrated via some synthetic data sets, a benchmark example, and an environmental time series.

Clustering and pedestrian crashes prediction modelling: Amman case

Pedestrian casualties are a severe domestic as well as international problem. This study analyses the spatial distribution of pedestrian casualties to define contributory factors and delineate the means for their prediction. Three years of crash data were collected along with other factors and analysed using kernel density estimation (KDE), spatial autocorrelation (Moran’s I), cluster K-Means, spatial regression, and general linear regressions (GLM). Kernel density estimate defines a cluster of pedestrian deaths within 1250 meters. According to Moran’s I, 17/22 attributes about casualties, road networks, demographics, and land use have positive values, indicating similar importance clustering. The spatial pattern of pedestrian casualties is random and insignificant and does not change with time. Casualties are negatively related to the surrounding attributes, indicating a tendency towards dispersion. A K-Means analysis of multiple variables revealed that when variables included in the clustering were higher, the variance explanation percentage was lower. In the multi-variable GLM assuming Poisson distribution, the road network length alone or with the house permits combined were the best predictors of casualties. Classic regressions were not significantly enhanced by spatial dimension, and none of the autoregressive coefficients were significant. The predictions from the Poisson-based GLM model are similar to the classic regressions.

A unified geographically weighted regression model

Spatial heterogeneity and spatial dependence are two cornerstones of spatial data research. It becomes more and more important to simultaneously deal with them in analyzing today’s complex spatial datasets. Along this direction, we introduce a new class of geographically weighted regression models, called unified geographically weighted regression (UGWR) models, to generalize existing geographically weighted regression models. In UGWR, the regression coefficients of all covariates can vary over the space. Moreover, the dependent variable and the disturbance are considered to be spatial autoregressive, and their spatial autoregression coefficients can also vary over the space. We propose a reconstruction parameterization approach to estimate these varying coefficients. This approach can flexibly use different bandwidths to fit various smoothness degrees of the coefficients. Based on the estimators, we also provide prediction, hypothesis testing, and model selection methods under UGWR. Simulation results indicate that the UGWR model can better fit complex datasets than existing geographically weighted regression models. An empirical study on a China’s regional GDP dataset also shows the effectiveness of the proposed methods.

APPLICATION OF PANELIZED SPLINE-SPATIAL AUTOREGRESSIVE MODEL TO HIV CASE DATA IN INDONESIA

Spatial regression analysis is a statistical method used to perform modeling by considering spatial effects. Spatial models generally use a parametric approach by assuming a linear relationship between explanatory and response variables. The nonparametric regression method is better suited for data with a nonlinear connection because it does not need linear assumptions. One of the nonparametric regression methods is penalized spline regression (P-Spline). The P-spline has a simple mathematical relationship with mixed linear model. The use of a mixed linear model allows the P-Spline to be combined with other statistical models. PS-SAR is a combination of the P-Spline and the SAR spatial model so that it can analyze spatial data with a semiparametric approach. Based on data from monitoring the development of the HIV situation in 2018, the number of HIV cases in Indonesia shows a clustered pattern that indicate spatial dependence. In addition, the relationship between the number of positive cases and the factors tends to be nonlinear. Therefore, this study aims to apply the PS-SAR model to HIV case data in Indonesia. The resulting model is evaluated based on the estimates of autoregressive spatial coefficient, MSE, MAPE, and Pseudo R2. Based on the results, the PS-SAR model has an autoregressive spatial coefficient similar to the SAR model and has smaller MSE and MAPE than the SAR model.

Seemingly Unrelated Regression Estimation for VAR Models with Explosive Roots*

AbstractFor VAR models with common explosive root, the OLS estimator of the autoregressive coefficient matrix is inconsistent (refer to Nielsen, 2009 and Phillips and Magdalinos, 2013). Although Phillips & Magdalinos (2013) proposed using the future observations as the instrumental variable for removing the endogeneity from VAR models, type I error occurs when testing for a common explosive root from the distinct explosive roots before the implementation of IV estimation. Such error creates bias and variance in the estimate and further causes incorrect inference in the structural analysis such as forecast error decomposition (FEVD). Hence, we propose using of seemingly unrelated regression (SUR) estimation for VAR models with explosive roots. Our SUR estimator is consistent in the case of both distinct explosive roots and common explosive root. We also consider models with drift in the system for generalization. Simulations show that the SUR estimate performs better than OLS and IV estimate in the case of both a common explosive root and distinct explosive roots case. In structural FEVD analysis, simulations show that SUR yields a different result from OLS and IV. We demonstrate the use of SUR in FEVD for agricultural commodity markets between 3 July 2010, and 29 January 2011.

EMG-Based Estimation of Lower Limb Joint Angles and Moments Using Long Short-Term Memory Network.

One of the fundamental limitations in human biomechanics is that we cannot directly obtain joint moments during natural movements without affecting the motion. However, estimating these values is feasible with inverse dynamics computation by employing external force plates, which can cover only a small area of the plate. This work investigated the Long Short-Term Memory (LSTM) network for the kinetics and kinematics prediction of human lower limbs when performing different activities without using force plates after the learning. We measured surface electromyography (sEMG) signals from 14 lower extremities muscles to generate a 112-dimensional input vector from three sets of features: root mean square, mean absolute value, and sixth-order autoregressive model coefficient parameters for each muscle in the LSTM network. With the recorded experimental data from the motion capture system and the force plates, human motions were reconstructed in a biomechanical simulation created using OpenSim v4.1, from which the joint kinematics and kinetics from left and right knees and ankles were retrieved to serve as output for training the LSTM. The estimation results using the LSTM model deviated from labels with average R2 scores (knee angle: 97.25%, knee moment: 94.9%, ankle angle: 91.44%, and ankle moment: 85.44%). These results demonstrate the feasibility of the joint angle and moment estimation based solely on sEMG signals for multiple daily activities without requiring force plates and a motion capture system once the LSTM model is trained.

On testing for bubbles during hyperinflations

Abstract We consider testing for the presence of rational bubbles during hyperinflations via an analysis of the non-stationarity properties of relevant observable time series. The test procedure is based on a Markov regime-switching model with independent stochastic changes in its intercept, error variance and autoregressive coefficients. This model formulation allow us to disentangle fundamentals-driven changes in the drift, bubble-driven explosiveness, and volatility changes that may be fundamentals-driven and/or bubble-driven. The testing methodology is illustrated by applying it to data from hyperinflations in Argentina, Brazil, Germany and Poland.

Asymptotic Properties of the M-estimation for an AR(1) Process with a General Autoregressive Coefficient

Asymptotic Properties of the M-estimation for an AR(1) Process with a General Autoregressive Coefficient

Impact of Bias Correction of the Least Squares Estimation on Bootstrap Confidence Intervals for Bifurcating Autoregressive Models

The least squares (LS) estimator of the autoregressive coefficient in the bifurcating autoregressive (BAR) model was recently shown to suffer from substantial bias, especially for small to moderate samples. This study investigates the impact of the bias in the LS estimator on the behavior of various types of bootstrap confidence intervals for the autoregressive coefficient and introduces methods for constructing bias-corrected bootstrap confidence intervals. We first describe several bootstrap confidence interval procedures for the autoregressive coefficient of the BAR model and present their bias-corrected versions. The behavior of uncorrected and corrected confidence interval procedures is studied empirically through extensive Monte Carlo simulations and two real cell lineage data applications. The empirical results show that the bias in the LS estimator can have a significant negative impact on the behavior of bootstrap confidence intervals and that bias correction can significantly improve the performance of bootstrap confidence intervals in terms of coverage, width, and symmetry.

On Semiparametrically Dynamic Functional-Coefficient Autoregressive Spatio-Temporal Models with Irregular Location Wide Nonstationarity

Nonlinear dynamic modeling of spatio-temporal data is often a challenge, especially due to irregularly observed locations and location-wide nonstationarity. In this article we propose a semiparametric family of Dynamic Functional-coefficient Autoregressive Spatio-Temporal (DyFAST) models to address the difficulties. We specify the autoregressive smoothing coefficients depending dynamically on both a concerned regime and location so that the models can characterize not only the dynamic regime-switching nature but also the location-wide nonstationarity in real data. Different smoothing schemes are then proposed to model the dynamic neighboring-time interaction effects with irregular locations incorporated by (spatial) weight matrices. The first scheme popular in econometrics supposes that the weight matrix is pre-specified. We show that locally optimal bandwidths by a greedy idea popular in machine learning should be cautiously applied. Moreover, many weight matrices can be generated differently by data location features. Model selection is popular, but may suffer from loss of different candidate features. Our second scheme is thus to suggest a weight matrix fusion to let data combine or select the candidates with estimation done simultaneously. Both theoretical properties and Monte Carlo simulations are investigated. The empirical application to an EU energy market dataset further demonstrates the usefulness of our DyFAST models. Supplementary materials for this article are available online.

Bimodal HAR-An efficient approach to human activity analysis and recognition using bimodal hybrid classifiers

Human activity recognition (HAR) is an emerging field that identifies human actions in different settings. This activity is recognized by sensors placed in the room or residence where we wish to observe human action. Real-world applications and automation employ activity recognition to detect anomalous behavior. For example, the anomalous behavior of patients such as walking while advised to rest in bed and falling elderly people need to be monitored carefully in hospitals as well as in home-based monitoring systems. Security, healthcare, human interaction, and computer vision use it. The activity is monitored through sensors and cameras. There is no general, explicit approach for inferring human activities from sensor data. Sensor data and heuristics present technological challenges. Several elements must be evaluated to build a reliable activity recognition system. Factors such as storage, connectivity, processing, energy efficiency, and system adaptability are important. Deep learning systems can better recognize human activities from earlier datasets. In this study, the hybrid One Dimensional Convolution Neural Network with Long Short Term Memory (LSTM) classifier is employed to improve the performance of HAR. It offers a method for automatically and data-adaptively removing reliable characteristics from raw data. This model proposes a two-way classification for abstract and individual activity monitoring. Human activities such as walking, sitting, walking downstairs, walking upstairs, laying, and standing along with mobile phone usage are considered in this study. We also compare state-of-the-art algorithms such as Support Vector Machine (SVM), K-Nearest Neighbour (KNN), Long Short Term Memory (LSTM), and Convolutional Neural Network (CNN). The UCI-HAR dataset is used for recognizing human activity in the proposed work. Features such as mean, median, and autoregressive coefficients are derived from the raw data and processed with principal component analysis to make them more reliable. The LSTM model accepts a series of activities, whereas the CNN accepts a single input. The CNN takes the single input data and each of the outputs is forwarded to the LSTM model, which classifies the activity. The Hybrid model achieves 97.89% accuracy with the new feature selection methods, whereas the CNN and LSTM individually produce 92.77% and 92.80% accuracy.

On consistency and sparsity for high-dimensional functional time series with application to autoregressions

Modelling a large collection of functional time series arises in a broad spectral of real applications. Under such a scenario, not only the number of functional variables can be diverging with, or even larger than the number of temporally dependent functional observations, but each function itself is an infinite-dimensional object, posing a challenging task. In this paper, we propose a three-step procedure to estimate high-dimensional functional time series models. To provide theoretical guarantees for the three-step procedure, we focus on multivariate stationary processes and propose a novel functional stability measure based on their spectral properties. Such stability measure facilitates the development of some useful concentration bounds on sample (auto)covariance functions, which serve as a fundamental tool for further convergence analysis in high-dimensional settings. As functional principal component analysis (FPCA) is one of the key dimension reduction techniques in the first step, we also investigate the non-asymptotic properties of the relevant estimated terms under a FPCA framework. To illustrate with an important application, we consider vector functional autoregressive models and develop a regularization approach to estimate autoregressive coefficient functions under the sparsity constraint. Using our derived non-asymptotic results, we investigate convergence properties of the regularized estimate under high-dimensional scaling. Finally, the finite-sample performance of the proposed method is examined through both simulations and a public financial dataset.

Spatial dependence in the non-performing loans of small Italian cooperative banks

ABSTRACT This paper investigates the presence of spatial dependence in the non-performing loans (NPLs) ratio of small Italian cooperative banks. As these financial intermediaries operate in a delimited area, the strategies they adopt to recover NPLs can produce spatial spillover effects on the ability of neighbouring banks to recover credit. Furthermore, small banks’ reliance on the relationship lending technique to select and monitor borrowers suggests a similar ability to identify underperforming borrowers, which may have a negative impact on the community in which those banks operate. Our empirical estimations provide strong evidence for both spatial and spatial–temporal variables driving impaired loans in local banks. The results indicate different effects of the spatial terms, showing a direct positive effect of the contemporaneous spatial lag variable and a negative effect of the space–time autoregressive coefficient. Whereas the former effects can be ascribed to changes in the macroeconomic cycle, the latter confirms the insight that the recovery capacities of local banks can be harmed by neighbouring banks’ credit recovery policies.

Endogenous Time Variation in Vector Autoregressions

Abstract We introduce a new class of time-varying parameter vector autoregressions (TVP-VARs) where the identified structural innovations are allowed to influence the dynamics of the coefficients in these models. An estimation algorithm and a parameterization conducive to model comparison are also provided. We apply our framework to the U.S. economy. Scenario analysis suggests that once accounting for the influence of structural shocks on the autoregressive coefficients, the effects of monetary policy on economic activity are larger and more persistent than in an otherwise standard TVP-VAR. Our results also indicate that cost-push shocks play a prominent role in understanding historical changes in inflation-gap persistence.

Bayesian circular lattice filters for computationally efficient estimation of multivariate time-varying autoregressive models

Nonstationary time series data exist in various scientific disciplines, including environmental science, biology, signal processing, econometrics, among others. Many Bayesian models have been developed to handle nonstationary time series. The time-varying vector autoregressive (TV-VAR) model is a well-established model for multivariate nonstationary time series. Nevertheless, in most cases, the large number of parameters presented by the model results in a high computational burden, ultimately limiting its usage. To address this issue, a computationally efficient multivariate Bayesian Circular Lattice Filter is developed, extending the usage of the TV-VAR model to a broader class of high-dimensional problems. The fully Bayesian framework allows both the autoregressive (AR) coefficients and innovation covariance to vary over time. The proposed estimation method is based on the Bayesian lattice filter (BLF), which is extremely computationally efficient and stable in univariate cases. To illustrate the effectiveness of the proposed approach, a comprehensive comparison with other competing methods is conducted through simulation studies and finds that, in most cases, the proposed approach performs superior in terms of the average squared error between the estimated and true time-varying spectral density. Finally, the methodology is demonstrated through applications to quarterly Gross Domestic Product (GDP) data and Northern California wind data.

Sources of residual autocorrelation in multiband task fMRI and strategies for effective mitigation.

Analysis of task fMRI studies is typically based on using ordinary least squares within a voxel- or vertex-wise linear regression framework known as the general linear model. This use produces estimates and standard errors of the regression coefficients representing amplitudes of task-induced activations. To produce valid statistical inferences, several key statistical assumptions must be met, including that of independent residuals. Since task fMRI residuals often exhibit temporal autocorrelation, it is common practice to perform "prewhitening" to mitigate that dependence. Prewhitening involves estimating the residual correlation structure and then applying a filter to induce residual temporal independence. While theoretically straightforward, a major challenge in prewhitening for fMRI data is accurately estimating the residual autocorrelation at each voxel or vertex of the brain. Assuming a global model for autocorrelation, which is the default in several standard fMRI software tools, may under- or over-whiten in certain areas and produce differential false positive control across the brain. The increasing popularity of multiband acquisitions with faster temporal resolution increases the challenge of effective prewhitening because more complex models are required to accurately capture the strength and structure of autocorrelation. These issues are becoming more critical now because of a trend toward subject-level analysis and inference. In group-average or group-difference analyses, the within-subject residual correlation structure is accounted for implicitly, so inadequate prewhitening is of little real consequence. For individual subject inference, however, accurate prewhitening is crucial to avoid inflated or spatially variable false positive rates. In this paper, we first thoroughly examine the patterns, sources and strength of residual autocorrelation in multiband task fMRI data. Second, we evaluate the ability of different autoregressive (AR) model-based prewhitening strategies to effectively mitigate autocorrelation and control false positives. We consider two main factors: the choice of AR model order and the level of spatial regularization of AR model coefficients, ranging from local smoothing to global averaging. We also consider determining the AR model order optimally at every vertex, but we do not observe an additional benefit of this over the use of higher-order AR models (e.g. (AR(6)). To overcome the computational challenge associated with spatially variable prewhitening, we developed a computationally efficient R implementation using parallelization and fast C++ backend code. This implementation is included in the open source R package BayesfMRI. We find that residual autocorrelation exhibits marked spatial variance across the cortex and is influenced by many factors including the task being performed, the specific acquisition protocol, mis-modeling of the hemodynamic response function, unmodeled noise due to subject head motion, and systematic individual differences. We also find that local regularization is much more effective than global averaging at mitigating autocorrelation. While increasing the AR model order is also helpful, it has a lesser effect than allowing AR coefficients to vary spatially. We find that prewhitening with an AR(6) model with local regularization is effective at reducing or even eliminating autocorrelation and controlling false positives. Our analysis revealed dramatic spatial differences in autocorrelation across the cortex. This spatial topology is unique to each session, being influenced by the task being performed, the acquisition technique, various modeling choices, and individual differences. If not accounted for, these differences will result in differential false positive control and power across the cortex and across subjects.

Existence of the money multiplier in a developing economy: a case of Saudi Arabia

In this study, cointegration methods are used to test the existence of the money multiplier model in Saudi Arabia for 1997m1-2020m4 and subperiods before and after the 2008 global financial crisis. Residual-based tests support broad (M2 and M3) multipliers over the full sample and pre-crisis period, albeit the M3 multiplier performs better than the M2 multiplier. Johansen's vector autoregression (VAR) and Pesaran et al. (2001) autoregressive distributed lags (ARDL) cointegration and coefficient restriction tests reveal that broad multipliers perform well. Narrow and broad multipliers are mean-reverting in the pre-crisis period, and the M3 multiplier is mean-reverting over the full sample. These multipliers are stable in a dynamic framework. Therefore, the Saudi Arabian Monetary Authority (SAMA) can control money stock and inflation by controlling base money. Narrow and broad multipliers are also predictable and broad monetary aggregates can influence monetary policy.

Estimating large‐dimensional connectedness tables: The great moderation through the lens of sectoral spillovers

We estimate sectoral spillovers around the Great Moderation with the help of forecast error variance decomposition tables. Obtaining such tables in high dimensions is challenging because they are functions of the estimated vector autoregressive coefficients and the residual covariance matrix. In a simulation study, we compare various regularization methods on both and conduct a comprehensive analysis of their performance. We show that standard estimators of large connectedness tables lead to biased results and high estimation uncertainty, both of which are mitigated by regularization. To explore possible causes for the Great Moderation, we apply a cross‐validated estimator on sectoral spillovers of industrial production in the US from 1972 to 2019. We find that the spillover network has considerably weakened, which hints at structural change, for example, through improved inventory management, as a critical explanation for the Great Moderation.

Analysis of Household Income Dynamics in the Russia Based on the RLMS Database

The goal of the study is to estimate the parameters of the stochastic wage process using data from the Russian Longitudinal Monitoring Survey of Higher School of Economics (RLMS-HSE). The main method of analysis is econometric estimation, which includes two steps. In the first step, the authors estimated a Mincer-type regression. In the second step, they estimated the parameters of the stochastic wage process using the generalized method of moments. As a result, the autoregression coefficient turned out to be lower, and the variance of shocks was higher than in similar foreign studies. The results of the research allow to conclude that labor incomes in Russia are less stable over time and are marked by great uncertainty. The practical value of the work lies in the possibility of using the obtained estimates when calibrating general equilibrium models with heterogeneous agents, which is demonstrated in the framework of estimation of macroeconomic effects from hypothetical tax maneuvers based on the canonical model with heterogeneous agents.

DETECTION OF AUTISM SPECTRUM DISORDER BY FEATURE EXTRACTION OF EEG SIGNALS AND MACHINE LEARNING CLASSIFIERS

Autism Spectrum Disorder (ASD), a neurodevelopmental disorder, impacts the subject’s social communication and interaction and the subjects exhibit restricted and repetitive behaviors. Subjects with ASD may need assistance throughout their life, depending on the severity. Early diagnosis of ASD is therefore critical for early intervention. ASD is diagnosed clinically based on behavioral assessments of the subjects, which results in delayed diagnosis, since the typical ASD traits due to aberrant brain development take time to develop. Neurological disorders associated with aberrant brain electrical activity have been detected by analyzing Electroencephalogram (EEG) signal patterns. In this study, we used features extracted from EEG brain waves to categorize ASD and normal subjects using Machine Learning (ML) classifiers. Autoregressive (AR) coefficients, Shannon entropy, Multifractal wavelet leader estimates, Multiscale wavelet variance and Discrete Fourier Transform (DFT) coefficients were extracted from EEG brain waves of ASD and normal subjects. Support Vector Machine (SVM), Decision Tree (DT), Logistic Regression (LR), k-Nearest Neighbor (k-NN) and Feed-forward Neural Network (FNN) were utilized as classification algorithms to categorize the ASD subjects and the control subjects. An accuracy of 90% was achieved by k-NN algorithm using AR features, Shannon entropy, Multifractal wavelet leader estimates and Multiscale wavelet variance estimates in ASD categorization. An accuracy of 93% was achieved by k-NN using the DFT features. The findings of this study indicate that features extracted from EEG are sufficient enough for categorization of ASD subjects and the control subjects.