Parameters Of Autoregressive Model Research Articles

Energy Price Inflation, Geopolitical Risk, and Bitcoin Dependence Structure: Evidence from BRICS

ABSTRACT This study examines the co-movement between geopolitical risk (GPR), energy price, and bitcoin (BTC) in BRICS countries, namely Brazil, Russia, India, China, and South Africa. Previous studies have focused on the impact of GPR on the volatility and risk premium of BTC investment. However, very limited studies have focused on integrating BTC as an extension of the mix of GPR on the co-movement with energy price. The analysis is based on monthly data of GPR index for BRICS countries, brent oil futures, natural gas futures and BTCs covering the period between March 2012 and Jun 2021. We employ the Bayesian graphical structural vector autoregressive model and time-varying parameter vector autoregressions-based dynamic connectedness to investigate the network-dependence structure. This research project provides useful empirical evidence for assessing the impact of both BTC and GPR on energy prices. Nonetheless, it will also be informative about the likelihood of co-movements occurring at different stages.

Imputed quantile vector autoregressive model for multivariate spatial–temporal data

AbstractImputing missing values in multivariate spatial–temporal data is important in many fields. Existing low rank tensor learning methods are popular for handling this task but are sensitive to high level of skewness. The aim of this paper is to develop an alternative method with robustness and high imputation accuracy for multivariate spatial–temporal data. In view of the fact that quantile regression is robust to noises and outliers, we propose an imputed quantile vector autoregressive (IQVAR) model. IQVAR can simultaneously impute missing values and estimate parameters of quantile vector autoregressive model. The objective function includes check loss and nuclear norm penalization. We develop an ADMM (Alternating Direction Method of Multipliers) algorithm to solve the resulting optimization problem. Simulation studies and real data analysis are conducted to verify the efficiency of IQVAR. Compared with other approaches, IQVAR is more robust and accurate.

Fast and asymptotically-efficient estimation in an autoregressive process with fractional type noise

This paper considers the joint estimation of the parameters of a first-order fractional autoregressive model. A one-step procedure is considered in order to obtain an asymptotically-efficient estimator with an initial guess estimator with convergence speed lower than n and singular asymptotic joint distribution. This estimator is computed faster than the maximum likelihood estimator or the Whittle estimator and therefore allows for faster inference on large samples. The paper also illustrates the performance of this method on finite-size samples via Monte Carlo simulations.

Locally robust inference for non‐Gaussian SVAR models

All parameters in structural vector autoregressive (SVAR) models are locally identified when the structural shocks are independent and follow non‐Gaussian distributions. Unfortunately, standard inference methods that exploit such features of the data for identification fail to yield correct coverage for structural functions of the model parameters when deviations from Gaussianity are small. To this extent, we propose a locally robust semiparametric approach to conduct hypothesis tests and construct confidence sets for structural functions in SVAR models. The methodology fully exploits non‐Gaussianity when it is present, but yields correct size/coverage for local‐to‐Gaussian densities. Empirically, we revisit two macroeconomic SVAR studies where we document mixed results. For the oil price model of Kilian and Murphy (2012), we find that non‐Gaussianity can robustly identify reasonable confidence sets, whereas for the labor supply–demand model of Baumeister and Hamilton (2015) this is not the case. Moreover, these exercises highlight the importance of using weak identification robust methods to assess estimation uncertainty when using non‐Gaussianity for identification.

Research on the Design and Practice of Civics Teaching in College Physical Education Courses Based on VAR Modeling

Abstract In this paper, a penalty function is added in the construction of the VAR model to control the accuracy of the model prediction, and considering the nature of the correlation between the variables, a weight fusion with Laplace penalty is introduced to generate a sparse solution to complete the construction of the vector autoregressive model. The basic types of vector autoregressive models under panel data are divided, the number of parameters to be estimated is determined, the parameters of the vector autoregressive model are estimated by the generalized method of moments estimation, and the parameter fitting effect of the model is improved by the great likelihood parameter estimation method, and the vector autoregressive model for panel data is constructed. Based on the VAR model, we propose a design scheme for the teaching of Civics in college sports courses and analyze the development of sports + Civics and the teaching effect of the courses through simulation and empirical analysis. The results of the study showed that OSI and OPCI rejected the original hypothesis at the significance level of 5% after second-order differencing, at which time both p-values were less than 0.1, and the series was smooth. The elasticity coefficient of the starting value of the sports response path is 0.0342, and the error interval is [0.0564, 0.06], indicating that the future development of the scale of “Sports + Civics” is stable.

Micro-expression recognition based on EEG signals

Research into micro-expression recognition is increasingly motivated by its potential applications to mental-health diagnosis and policing. Thus far, micro-expression recognition research and applications have been based on computer vision processing technology, with notable limitations. For instance, changes in ambient lighting or in the head posture and facial occlusion can all affect micro-expression recognition. The high temporal resolution of EEG technology captures brain activity associated with micro-expressions, and hence objectively identifies micro-expressions from a neurophysiological perspective. Herein, we report a real-time supervision and emotional expression suppression (SEES) experimental paradigm. We collected micro-expression video and EEG data from 68 subjects under positive emotion induction. Thereafter, the EEG frequency-band power, statistical features, autoregressive (AR) model parameters, and wavelet entropy were extracted as features. We ranked all 128 channels based on the micro-expression recognition task classification accuracy using all the features extracted for each channel. Based on the channel ranking, different sizes of channel combinations were chosen. Subsequently, the optimal subset of these features from different combinations was selected using a sequential backward selection (SBS) algorithm and fed into different classifiers, including a support vector machine (SVM), K-nearest neighbor (KNN), gradient-boosted decision tree (GBDT), and back-propagation (BP) neuron network. The different classifiers achieve promising accuracy for micro-expression recognition, with GBDT exhibiting the highest accuracy of 85.96 % when 11 channels were selected. This demonstrates the feasibility of recognizing micro-expressions based on EEG signals.

Parameter Estimation in Spectral Resolution Enhancement Based on Forward-Backward Linear Prediction Total Least Square Method.

In a Fourier transform infrared (IR) spectrometer, the Michelson interference signal extrapolation method based on linear prediction is often used to improve spectral resolution. In this method, an autoregressive (AR) model is established for the Michelson interference signal in the spectrometer. Once the AR model parameters are determined, the AR process is predictable. The interference signal can be used to figure out the AR model's parameters. Based on this, the AR model can be used to extrapolate the interference signal to improve the spectral resolution. In this paper, the forward-backward linear prediction total least squares (FB-TLS) method is proposed to estimate the parameters of the AR model. The parameters that are estimated are used to improve the IR spectral resolution. By simulating different order and signal-to-noise ratio situations, the effects of the Burg, the least square, and the FB-TLS parameter estimation methods on spectral resolution enhancement are studied. The simulation results demonstrate that the FB-TLS parameter estimation method can effectively suppress noise and avoid spurious peaks. The experimental results demonstrate that the FB-TLS parameter estimation method is effective for spectral resolution enhancement technology based on linear prediction. When the FB-TLS method is used to enhance NH3 IR spectral resolution from 2 cm-1 to 1 cm-1, the spectral prediction error in the NH3 characteristic band is only 0.21% compared with the measured NH3 spectrum, whose spectral resolution is 1 cm-1.

Least Absolute Deviation Estimation for Uncertain Vector Autoregressive Model with Imprecise Data

The uncertain vector autoregressive model is able to model the interrelationships between different variables, which is more advantageous compared to the traditional autoregressive model, when modeling real-life objects and where the observed values are imprecise. In this paper, the parameters of the uncertain vector autoregressive model are estimated by using least absolute deviation estimation (LAD) to obtain a fitted uncertain vector autoregressive model, and residual analysis is performed to obtain estimates of expected values and variances of the residuals. In addition, future values are modeled by using forecasting methods, i.e., point estimation and interval estimation. The order of the uncertain vector autoregressive model is also determined by the indicator summation of test errors (STE) in the cross-validation, and we also analyze that the least absolute deviation estimation outperforms the least squares estimation method in the presence of outliers.

Eigenanalysis of vector autoregressive model for optimal fitting of a predefined cross power spectral density matrix: Application to numeric generation of stationary homogeneous isotropic/anisotropic turbulent wind fields

Turbulent wind fields representing realistic atmospheric conditions are required for wind turbine load calculations. For a statistically stationary situation, the wind loads on a wind turbine depend, among other wind characteristics, on the spectra and spatial coherences of the velocity field in the rotor plane (i.e. the cross-power spectral density matrix). In this study, a novel approach is proposed to optimally calibrate the parameters of a vector autoregressive model for reproducing a predefined target cross-power spectral density matrix to be used for the synthetic generation of turbulent wind fields. This approach is based on the eigenanalysis of the companion matrix of the vector autoregressive model. In this work, the cross-power spectral density matrix, for different turbulent wind conditions, is considered as targets. This approach is compared to the state-of-the-art approaches for calibration of parameters of vector autoregressive models. The discussion covers the implications derived from approaching the vector autoregressive model determination in the frequency domain or in the time domain.

Estimating function method for nonnegative autoregressive models

A stationary sequence of nonnegative random variables generated by autoregressive (AR) models may be used to describe the inter‐arrival times between events in counting processes. Even though, several such models are available in the literature, there is no unified approach to estimate their parameters. In this paper, we propose a class of combined estimating function method to estimate the model parameters of AR models with gamma marginals. The proposed method is compared with other estimation procedures and are illustrated by simulation and data analysis.

Indirect inference estimation of higher-order spatial autoregressive models

This paper proposes estimating parameters in higher-order spatial autoregressive models, where the error term also follows a spatial autoregression and its innovations are heteroskedastic, by matching the simple ordinary least squares estimator with its analytical approximate expectation, following the principle of indirect inference. The resulting estimator is shown to be consistent, asymptotically normal, simulation-free, and robust to unknown heteroskedasticity. Monte Carlo simulations demonstrate its good finite-sample properties in comparison with existing estimators. An empirical study of Airbnb rental prices in the city of Asheville illustrates that the structure of spatial correlation and effects of various factors at the early stage of the COVID-19 pandemic are quite different from those during the second summer. Notably, during the pandemic, safety is valued more and on-line reviews are valued much less.

Uncertain Threshold Autoregressive Model via LASSO Procedure

Uncertain time series models have been proposed to forecast future data based on imprecise known data. As an uncertain time series model, the uncertain threshold autoregressive model was proposed to deal with nonlinear data. The previous study estimated the unknown parameters in the uncertain threshold autoregressive model with the least-squares estimation. However, for nonlinear time series models, the least-squares estimation may cause overfitting of the model. To deal with this problem, this paper adds the least absolute shrinkage and selection operator penalty to the uncertain threshold autoregressive model to alleviate the level of overfitting. In addition, this paper uses the sum of square errors criterion to select the optimum order of the model. Finally, a real stock price example is provided to compare two different parameter estimation methods.

Сравнительный анализ устойчивости различных методов оценивания параметров билинейной авторегрессионной модели

The purpose of this work is to compare various methods in evaluating parameters of a bilinear autoregressive model. Least squares estimate, least absolute deviations estimate and estimate based on the Huber function were used as the parameter estimates. Computer simulation was introduced to study the indicated estimates precision depending on probability distribution of the bilinear autoregressive model upgrading process. Probable distribution of the upgrading process was simulated by normal and uniform distributions, Student distribution with various degrees of freedom, Laplace distribution (double exponential distribution), and Tukey distribution known as the polluted normal distribution. Their mean square error served as the evaluation precision measure. Results of the conducted computational experiment showed that precision of three methods used in evaluating parameters of the bilinear autoregressive series significantly depended on probability distribution of the model upgrading process. In particular, it concerns the number of degrees of freedom of the Student distribution, as well as the Tukey distribution pollution share and amount. If the upgrading process possesses normal and uniform distributions, Student’s distribution with sufficiently high number of degrees of freedom, the least squares method works more efficiently. Estimate based on the Huber function and the least absolute deviations estimate are becoming more efficient compared to the least squares estimation for the Laplace distribution, with a decrease in the number of degrees of freedom --- for the Student distribution, and with an increase in the pollution share and amount --- for the Tukey distribution

A Method for Improving the Prediction of Outpatient Visits for Hospital Management: Bayesian Autoregressive Analysis.

The number of outpatient visits is generally influenced by various factors that are difficult to quantify and obtain, resulting in some irregular fluctuations. The traditional statistical methodology seldom considers these uncertainties. Accordingly, this paper presents a Bayesian autoregressive (AR) analysis to propose a forecasting framework to cope with the strict requirements. The AR model was conducted to identify the linear and autocorrelation relationships of historical series, and Bayesian inference was used to correct and optimize the AR model parameters. Posterior distribution of parameters was stably and reliably obtained by Gibbs sampling on the condition of the convergent Markov chain. Meanwhile, the lag orders of the AR model were adjusted based on the series characteristics. To increase the variability and generality of the dataset, the developed Bayesian AR model was evaluated at seven hospitals in China. The results demonstrated that the Bayesian AR model had varying degrees of decline in the MAPE value in the seven sets of experimental data. The reductions ranged from 0.1431% to 0.0342%, indicating effective optimization of the Bayesian inference in the AR model parameters and reflecting the useful correction of the lag order adjustment strategy. The proposed Bayesian AR framework showed high accuracy index and stable prediction accuracy, thereby outperforming the traditional AR model.

A novel feature extraction method using chemosensory EEG for Parkinson's disease classification

Parkinson’s disease (PD) is an incurable nervous system disease that affects millions of people all around the world. The loss of smell is one of the first symptoms that come into prominence in the early diagnosis of PD. The main motivation of this study is to provide a more accurate diagnosis in the early period of the disease using chemosensory electroencephalography (EEG) signals, which are difficult to study and also less studied. For this purpose, we proposed a hybrid feature extraction method called EEMD_VAR that combines Ensemble Empirical Mode Decomposition (EEMD) and Vector Autoregressive Model (VAR). In contrast to conventional feature extraction methods, the proposed method is to prevent arbitrary selection of features and to determine the number of features. The pre-processed EEG signals were decomposed using EEMD and the obtained intrinsic mode functions (IMFs) used as independent variables in VAR. The coefficients of the VAR model were employed as features in frequently used supervised classification algorithms. The performance metrics of the EEMD_VAR were compared to the performance metrics of the autoregressive (AR) model and Hjorth parameters. The maximum classification accuracy of the proposed method was 100% using artificial neural networks (ANN) in C2 electrode, while the AR method and Hjorth parameters only obtained a maximum of 72%. The other metrics also corroborate the proposed method's ability to perform well in the classification. In addition, the higher results from right side electrodes may lead to the conclusion that the right side of the brain is more sensitive to odor stimuli.

Intelligent Scanning Detection System of Muscle Exercise Fatigue Based on Surface Electromyography.

In order to use the surface EMG signal to automatically detect the muscle fatigue state, a research method of the muscle exercise fatigue intelligent scanning detection system based on surface EMG was proposed, and the sEMG signal features of 10 subjects before and after fatigue were extracted. A time-varying parameter autoregressive model is established. By introducing the Legendre basis function, the parameter identification of the linear nonstationary process is transformed into the parameter identification of the linear time-invariant system. Combined with the correlation index, the optimal Legendre base function dimension of the time-varying system parameter estimation can be obtained, then the best model fitting effect can be obtained, and the time-invariant parameters are solved by the least square method. Using the rate of change of the first time-varying parameter (ARC1) of the autoregressive model before and after fatigue as an index to detect muscle fatigue sensitivity, a two-tailed t test was used to compare the mean power frequency (MPF) and the median frequency (MF) with the rate of change. The results showed that the change rates of ARC1, MPF, and MF before and after fatigue were34.33% ± 2.5%, 68% + 2.03%, and 22.80% + 2.19%, which were 41% and 25%, respectively. The rate of change of ACR1 was significantly higher than that of MPF and MF (P < 0.05). When detecting muscle fatigue by sEMG signal, it has the advantages of short time and high sensitivity. It can be used for online real-time analysis of muscle fatigue, providing a potential analysis tool for limb muscle strain, rehabilitation, and ergonomics assessment.

Statistical Inference of Spatial Econometric Models Based on Likelihood Functions

This paper is devoted to studying the probabilistic and statistical properties of maximum likelihood estimation of parameters in spatially mixed autoregressive models. When the response variable in the mixed autoregressive model obeys a continuous distribution, this paper verifies the monotonicity of the likelihood function of the mixed autoregressive model with respect to the autoregressive parameter P, which proves the existence and uniqueness of the maximum likelihood estimation of the autoregressive parameter. The results show that when the condition n &gt; rank(x+1) is satisfied, the quasi-likelihood function of the mixed autoregressive model has a unique maximum value with probability 1 in the parameter space; when n &gt; rank(x+1) and the regression coefficient When the matrix column is full rank, the maximum likelihood estimates of all parameters in the spatial mixed autoregressive model exist with probability 1 and are unique in the parameter space. In order to detect the strong influence points and abnormal points in the spatial mixed autoregressive model, this paper uses the first derivative method in the local influence analysis to obtain the statistics of the strong influence points and abnormal points in the spatial mixed autoregressive model in the form of variance perturbation. Simulation studies have shown that the first derivative of the maximum likelihood estimate of variance in the spatial mixed autoregressive model should be chosen to obtain the test statistic, which can effectively avoid the mearing and masking effects that often occur and are difficult to handle in local influence analysis. . As application and verification, this paper analyzes a real data to show that the conclusions obtained in this paper are reliable and practical.

Assessment of submentalis muscle activity for sleep-wake classification of healthy individuals and patients with sleep disorders.

This work proposes a method utilizing only the submentalis EMG channel for the classification of sleep and wake states among the healthy individuals and patients with various sleep disorders such as sleep apnea hypopnea syndrome, dyssomnia, etc. We extracted autoregressive model parameters, discrete wavelet transform coefficients, Hjorth's complexity and mobility, relative bandpowers, Poincaré plot descriptors and statistical features from the EMG signal. We also used the energy of each epoch as a feature to distinguish between the sleep and wake states. Mutual information based feature selection approach was considered to obtain the top 25 features which provided maximum accuracy. For classification, we employed an ensemble of decision trees with random undersampling and boosting technique to deal with the class-imbalance problem in the sleep data. We achieved an overall accuracy of about 85% for the healthy population and about 70% on an average across different pathological groups. This work shows the potential of EMG chin activity for sleep analysis. Clinical Relevance- Automatic and reliable sleep-wake classification can reduce the burden of sleep experts in analyzing overnight sleep data (~ 8 hours) and also assist them to diagnose various neurological disorders at an early stage. Utilizing EMG channel provides an easier and convenient long-term recording of data without causing much disturbance in sleepunlike EEG which is inconvenient and hampers the natural sleep.

On bank return and volatility spillovers: Identifying transmitters and receivers during crisis periods

This study investigates dynamic bank-return correlation and spillovers among G7 advanced markets, employing an asymmetric multivariate GARCH approach and the forecast-error variance decomposition framework of a generalized VAR model and using a time-varying parameter autoregressive model. We utilize weekly bank stock indices over a long period (2000–2020) covering the recent Global Financial Crisis (GFC) and the subsequent European Sovereign Debt Crisis (ESDC). Dynamic spillover analysis reveals evidence of contagion effects during recent episodes. It is also shown that the impact of the GFC is notably higher than that of the ESDC. Major spillover transmitters are the markets of France, Germany and the UK, with the US market being vulnerable to shocks from European markets. Useful implications arise for policy makers and investors.

Reversible Jump MCMC Algorithm for Transformed Laplacian AR: Application in Modeling CO&lt;sub&gt;2&lt;/sub&gt; Emission Data

Autoregressive (AR) model is applied to model various types of data. For confidential data, data confusion is very important to protect the data from being known by other unauthorized parties. This paper aims to find data modeling with transformations in the AR model. In this AR model, the noise has a Laplace distribution. AR model parameters include order, coefficients, and variance of the noise. The estimation of the AR model parameter is proposed in a Bayesian method by using the reversible jump Markov Chain Monte Carlo (MCMC) algorithm. This paper shows that the posterior distribution of AR model parameters has a complicated equation, so the Bayes estimator cannot be determined analytically. Bayes estimators for AR model parameters are calculated using the reversible jump MCMC algorithm. This algorithm was validated through a simulation study. This algorithm can accurately estimate the parameters of the transformed AR model with Laplacian noise. This algorithm produces an AR model that satisfies the stationary conditions. The novelty in this paper is the use of transformations in the Laplacian AR model to secure research data when the research results are published in a scientific journal. As an example application, the Laplacian AR model was used to model CO₂ emission data. The results of this paper can be applied to modeling and forecasting confidential data in various sectors.