Asymptotic normality of error density estimator in stationary and explosive autoregressive models

In this paper,we consider the limit distribution of the error density function estima-tor in the rst-order autoregressive models with negatively associated and positively associated random errors.Under mild regularity assumptions,some asymptotic normality results of the residual density estimator are obtained when the autoregressive models are stationary process and explosive process.In order to illustrate these results,some simulations such as con dence intervals and mean integrated square errors are provided in this paper.It shows that the residual density estimator can replace the density\estimator"which contains errors.

Constructing Confidence Regions for Autoregressive-Model Parameters

We discuss formulas and techniques for finding maximum-likelihood estimators of parameters of autoregressive (with particular emphasis on Markov and Yule) models, computing their asymptotic variance-covariance matrix and displaying the resulting confidence regions;Monte Carlo simulation is then used to establish the accuracy of the corresponding level of confidence. The results indicate that a direct application of the Central Limit Theorem yields errors too large to be acceptable;instead, we recommend using a technique based directly on the natural logarithm of the likelihood function, verifying its substantially higher accuracy. Our study is then extended to the case of estimating only a subset of a model’s parameters, when the remaining ones (called nuisance) are of no interest to us.

Trend Autoregressive Model Exact Run Length Evaluation on a Two-Sided Extended EWMA Chart

The Extended Exponentially Weighted Moving Average(extended EWMA)control chart is one of the control charts and can be used to quickly detect a small shift.The performance of control charts can be evaluated with the average run length(ARL).Due to the deriving explicit formulas for the ARL on a two-sided extended EWMA control chart for trend autoregressive or trend AR(p)model has not been reported previously.The aim of this study is to derive the explicit formulas for the ARL on a two-sided extended EWMA con-trol chart for the trend AR(p)model as well as the trend AR(1)and trend AR(2)models with exponential white noise.The analytical solution accuracy was obtained with the extended EWMA control chart and was compared to the numer-ical integral equation(NIE)method.The results show that the ARL obtained by the explicit formula and the NIE method is hardly different,but the explicit for-mula can help decrease the computational(CPU)time.Furthermore,this is also expanded to comparative performance with the Exponentially Weighted Moving Average(EWMA)control chart.The performance of the extended EWMA control chart is better than the EWMA control chart for all situations,both the trend AR(1)and trend AR(2)models.Finally,the analytical solution of ARL is applied to real-world data in the healthfield,such as COVID-19 data in the United Kingdom and Sweden,to demonstrate the efficacy of the proposed method.

A modified stochastic model for LS+AR hybrid method and its application in polar motion short-term prediction

Short-term(up to 30 days)predictions of Earth Rotation Parameters(ERPs)such as Polar Motion(PM:PMX and PMY)play an essential role in real-time applications related to high-precision reference frame conversion.Currently,least squares(LS)+auto-regressive(AR)hybrid method is one of the main techniques of PM prediction.Besides,the weighted LS+AR hybrid method performs well for PM short-term prediction.However,the corresponding covariance information of LS fitting residuals deserves further exploration in the AR model.In this study,we have derived a modified stochastic model for the LS+AR hybrid method,namely the weighted LS+weighted AR hybrid method.By using the PM data products of IERS EOP 14 C04,the numerical results indicate that for PM short-term forecasting,the proposed weighted LS+weighted AR hybrid method shows an advantage over both the LS+AR hybrid method and the weighted LS+AR hybrid method.Compared to the mean absolute errors(MAEs)of PMX/PMY sho rt-term prediction of the LS+AR hybrid method and the weighted LS+AR hybrid method,the weighted LS+weighted AR hybrid method shows average improvements of 6.61%/12.08%and 0.24%/11.65%,respectively.Besides,for the slopes of the linear regression lines fitted to the errors of each method,the growth of the prediction error of the proposed method is slower than that of the other two methods.

Classification of Conversational Sentences Using an Ensemble Pre-Trained Language Model with the Fine-Tuned Parameter

Sentence classification is the process of categorizing a sentence based on the context of the sentence.Sentence categorization requires more semantic highlights than other tasks,such as dependence parsing,which requires more syntactic elements.Most existing strategies focus on the general semantics of a conversation without involving the context of the sentence,recognizing the progress and comparing impacts.An ensemble pre-trained language model was taken up here to classify the conversation sentences from the conversation corpus.The conversational sentences are classified into four categories:information,question,directive,and commission.These classification label sequences are for analyzing the conversation progress and predicting the pecking order of the conversation.Ensemble of Bidirectional Encoder for Representation of Transformer(BERT),Robustly Optimized BERT pretraining Approach(RoBERTa),Generative Pre-Trained Transformer(GPT),DistilBERT and Generalized Autoregressive Pretraining for Language Understanding(XLNet)models are trained on conversation corpus with hyperparameters.Hyperparameter tuning approach is carried out for better performance on sentence classification.This Ensemble of Pre-trained Language Models with a Hyperparameter Tuning(EPLM-HT)system is trained on an annotated conversation dataset.The proposed approach outperformed compared to the base BERT,GPT,DistilBERT and XLNet transformer models.The proposed ensemble model with the fine-tuned parameters achieved an F1_score of 0.88.

Utilizing the Vector Autoregression Model (VAR) for Short-Term Solar Irradiance Forecasting

Forecasting solar irradiance is a critical task in the renewable energy sector, as it provides essential information regarding the potential energy production from solar panels. This study aims to utilize the Vector Autoregression (VAR) model to forecast solar irradiance levels and weather characteristics in the San Francisco Bay Area. The results demonstrate a correlation between predicted and actual solar irradiance, indicating the effectiveness of the VAR model for this task. However, the model may not be sufficient for this region due to the requirement of additional weather features to reduce disparities between predictions and actual observations. Additionally, the current lag order in the model is relatively low, limiting its ability to capture all relevant information from past observations. As a result, the model’s forecasting capability is limited to short-term horizons, with a maximum horizon of four hours.

AUTOREGRESSIVE MODEL AND POWER SPECTRUM CHARATERISTICS OF CURRENT SIGNAL IN HIGH FREQUENCY GROUP PULSE MICRO-ELECTROCHEMICAL MACHINING

The identification of the inter-electrode gap size in the high frequency group pulse micro-electrochemical machining （HGPECM） is mainly discussed. The auto-regressive（AR） model of group pulse current flowing across the cathode and the anode are created under different situations with different processing parameters and inter-electrode gap size. The AR model based on the current signals indicates that the order of the AR model is obviously different relating to the different processing conditions and the inter-electrode gap size; Moreover, it is different about the stability of the dynamic system, i.e. the white noise response of the Green＇s function of the dynamic system is diverse. In addition, power spectrum method is used in the analysis of the dynamic time series about the current signals with different inter-electrode gap size, the results show that there exists a strongest power spectrum peak, characteristic power spectrum（CPS）, to the current signals related to the different inter-electrode gap size in the range of 0～5 kHz. Therefore, the CPS of current signals can implement the identification of the inter-electrode gap.

Prediction of earth rotation parameters based on improved weighted least squares and autoregressive model

In this paper, an improved weighted least squares （WLS）, together with autoregressive （AR） model, is proposed to improve prediction accuracy of earth rotation parameters（ERP）. Four weighting schemes are developed and the optimal power e for determination of the weight elements is studied. The results show that the improved WLS-AR model can improve the ERP prediction accuracy effectively, and for different prediction intervals of ERP, different weight scheme should be chosen.

JUMP DETECTION BY WAVELET IN NONLINEAR AUTOREGRESSIVE MODELS

Wavelets are applied to detection of the jump points of a regression function in nonlinear autoregressive model x(t) = T(x(t-1)) + epsilon t. By checking the empirical wavelet coefficients of the data,which have significantly large absolute values across fine scale levels, the number of the jump points and locations where the jumps occur are estimated. The jump heights are also estimated. All estimators are shown to be consistent. Wavelet method ia also applied to the threshold AR(1) model(TAR(1)). The simple estimators of the thresholds are given,which are shown to be consistent.

PARTICLE FILTERING BASED AUTOREGRESSIVE CHANNEL PREDICTION MODEL

A particle filtering based AutoRegressive (AR) channel prediction model is presented for cognitive radio systems. Firstly, this paper introduces the particle filtering and the system model. Secondly, the AR model of order p is used to approximate the flat Rayleigh fading channels; its stability is discussed, and an algorithm for solving the AR model parameters is also given. Finally, an AR channel prediction model based on particle filtering and second-order AR model is presented. Simulation results show that the performance of the proposed AR channel prediction model based on particle filtering is better than that of Kalman filtering.

Identification of Denatured Biological Tissues Based on Improved Variational Mode Decomposition and Autoregressive Model during HIFU Treatment

During high-intensity focused ultrasound(HIFU)treatment,the accurate identification of denatured biological tissue is an important practical problem.In this paper,a novel method based on the improved variational mode decomposition(IVMD)and autoregressive(AR)model was proposed,which identified denatured biological tissue according to the characteristics of ultrasonic scattered echo signals during HIFU treatment.Firstly,the IVMD method was proposed to solve the problem that the VMD reconstruction signal still has noise due to the limited number of intrinsic mode functions(IMF).The ultrasonic scattered echo signals were reconstructed by the IVMD to achieve denoising.Then,the AR model was introduced to improve the recognition rate of denatured biological tissues.The AR model order parameter was determined by the Akaike information criterion(AIC)and the characteristics of the AR coefficients were extracted.Finally,the optimal characteristics of the AR coefficients were selected according to the results of receiver operating characteristic(ROC).The experiments showed that the signal-to-noise ratio(SNR)and root mean square error(RMSE)of the reconstructed signal obtained by IVMD was better than those obtained by variational mode decomposition(VMD).The IVMD-AR method was applied to the actual ultrasonic scattered echo signals during HIFU treatment,and the support vectormachine(SVM)was used to identify the denatured biological tissue.The results show that compared with sample entropy,information entropy,and energy methods,the proposed IVMD-AR method can more effectively identify denatured biological tissue.The recognition rate of denatured biological tissue was higher,up to 93.0%.

Multivariate Generalized Autoregressive Conditional Heteroscedastic Model

In this paper, by making use of the Hadamard product of matrices, a natural and reasonable generalization of the univariate GARCH (Generalized Autoregressive Conditional heteroscedastic) process introduced by Bollerslev (J. Econometrics 31(1986), 307-327) to the multivariate case is proposed. The conditions for the existence of strictly stationary and ergodic solutions and the existence of higher-order moments for this class of parametric models are derived.

SOME LEAST SQUARES ESTIMATES OF THE AUTOREGRESSIVE MODELS

In this paper, we present some iterative methods for solving lth order autoregressive models, prove global convergence for l=1 case, and the numerical results of new algorithms seem to be more efficient than the ones of Cochrane-Orcutt iterative method.

PC-VAR Estimation of Vector Autoregressive Models

In this paper PC-VAR estimation of vector autoregressive models (VAR) is proposed. The estimation strategy successfully lessens the curse of dimensionality affecting VAR models, when estimated using sample sizes typically available in quarterly studies. The procedure involves a dynamic regression using a subset of principal components extracted from a vector time series, and the recovery of the implied unrestricted VAR parameter estimates by solving a set of linear constraints. PC-VAR and OLS estimation of unrestricted VAR models show the same asymptotic properties. Monte Carlo results strongly support PC-VAR estimation, yielding gains, in terms of both lower bias and higher efficiency, relatively to OLS estimation of high dimensional unrestricted VAR models in small samples. Guidance for the selection of the number of components to be used in empirical studies is provided.

Sleep spindles detection from human sleep EEG signals using autoregressive (AR) model: a surrogate data approach

A new algorithm for the detection of sleep spindles from human sleep EEG with surrogate data approach is presented. Surrogate data ap-proach is the state of the art technique for nonlinear spectral analysis. In this paper, by developing autoregressive (AR) models on short segment of the EEG is described as a superposition of harmonic oscillating with damping and frequency in time. Sleep spindle events are detected, whenever the damping of one or more frequencies falls below a prede-fined threshold. Based on a surrogate data, a method was proposed to test the hypothesis that the original data were generated by a linear Gaussian process. This method was tested on human sleep EEG signal. The algorithm work well for the detection of sleep spindles and in addition the analysis reveals the alpha and beta band activities in EEG. The rigorous statistical framework proves essential in establishing these results.

Comparison of the Sampling Efficiency in Spatial Autoregressive Model

A random walk Metropolis-Hastings algorithm has been widely used in sampling the parameter of spatial interaction in spatial autoregressive model from a Bayesian point of view. In addition, as an alternative approach, the griddy Gibbs sampler is proposed by [1] and utilized by [2]. This paper proposes an acceptance-rejection Metropolis-Hastings algorithm as a third approach, and compares these three algorithms through Monte Carlo experiments. The experimental results show that the griddy Gibbs sampler is the most efficient algorithm among the algorithms whether the number of observations is small or not in terms of the computation time and the inefficiency factors. Moreover, it seems to work well when the size of grid is 100.

Asymptotic Normality of Pseudo-LS Estimator of Error Variance in Partly Linear Autoregressive Models

Consider the model Y_t=βY_t-1+g(Y_(t-2))+ε_t for 3＜=t＜=T.Here g is an unknown function,βis an unknown parameter,ε_t are i.i.d,random errors with mean 0 and varianceσ~2 and the fourth momentα_4,andε_t are independent of Y_s for all t＞=3 and s=1,2. Pseudo-LS estimators■_T^2,■4T and■_T^2 ofσ~s,α_4 and Var(ε_3~2)are respectively constructed based on piecewise polynomial approximator of g.The weak consistency of■4T and■_T^2 are proved.The asymptotic normality of■_T^2 is given,i.e.T^(1/2)(■_T^2-σ~2)/■_T converges in distribution to N(0,1).The result can be used to establish large sample interval estimates ofσ~2 or to make large sample tests forσ~2.

基于AR-ECM平均差异模型的串联电池组SOC、容量多尺度联合估计方法

考虑电池单体老化差异所致的电池组不一致性,针对串联电池组荷电状态(state of charge,SOC)、容量估计问题,提出一种基于自回归等效电路模型(autoregression equivalent circuit model,AR-ECM)的平均差异模型(mean-difference model,MDM)。基于此模型,提出串联电池组SOC、容量多尺度联合估计算法。该算法由2个部分组成,一是基于AR-ECM的MDM及差异化模型参数辨识策略:条件辨识策略和定频分组辨识策略;二是基于多时间尺度H无穷滤波(multi-timescale H infinity filter,Mts-HIF)的电池组SOC、容量联合估计算法。通过将所提出MDM中的自回归平均模型(autoregression mean model,AR-MM)与传统MDM中的n阶RC平均模型(nRC mean model,nRC-MM)比较,结果表明所提出的AR-MM在复杂运行工况下具有更优的动态跟随性能。依据最小化信息量准则(akaike information criterion,AIC),AR-MM具有更优的复杂度与精度的权衡。通过与基于多时间尺度扩展卡尔曼滤波(multi-timescale extended Kalman filter,Mts-EKF)联合状态估计算法比较,结果表明所提出的Mts-HIF状态估计算法具有更优的鲁棒性、精度和收敛速度。