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.

River channel flood forecasting method of coupling wavelet neural network with autoregressive model

Based on analyzing the limitations of the commonly used back-propagation neural network （BPNN）, a wavelet neural network （WNN） is adopted as the nonlinear river channel flood forecasting method replacing the BPNN. The WNN has the characteristics of fast convergence and improved capability of nonlinear approximation. For the purpose of adapting the timevarying characteristics of flood routing, the WNN is coupled with an AR real-time correction model. The AR model is utilized to calculate the forecast error. The coefficients of the AR real-time correction model are dynamically updated by an adaptive fading factor recursive least square（RLS） method. The application of the flood forecasting method in the cross section of Xijiang River at Gaoyao shows its effectiveness.

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.

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.

Empirical likelihood for first-order mixed integer-valued autoregressive model

In this paper, we not only construct the confidence region for parameters in a mixed integer-valued autoregressive process using the empirical likelihood method, but also establish the empirical log-likelihood ratio statistic and obtain its limiting distribution. And then, via simulation studies we give coverage probabilities for the parameters of interest. The results show that the empirical likelihood method performs very well.

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.

Examining spatiotemporal distribution and CPUE-environment relationships for the jumbo flying squid Dosidicus gigas offshore Peru based on spatial autoregressive model

The spatiotemporal distribution and relationship between nominal catch-per-unit-ef fort(CPUE) and environment for the jumbo flying squid( Dosidicus gigas) were examined in of fshore Peruvian waters during 2009–2013. Three typical oceanographic factors aff ecting the squid habitat were investigated in this research, including sea surface temperature(SST), sea surface salinity(SSS) and sea surface height(SSH). We studied the CPUE-environment relationships for D. gigas using a spatially-lagged version of spatial autoregressive(SAR) model and a generalized additive model(GAM), with the latter for auxiliary and comparative purposes. The annual fishery centroids were distributed broadly in an area bounded by 79.5°–82.7°W and 11.9°–17.1°S, while the monthly fishery centroids were spatially close and lay in a smaller area bounded by 81.0°–81.2°W and 14.3°–15.4°S. Our results show that the preferred environmental ranges for D. gigas offshore Peru were 20.9°–21.9°C for SST, 35.16–35.32 for SSS and 27.2–31.5 cm for SSH in the areas bounded by 78°–80°W/82–84°W and 15°–18°S. Monthly spatial distributions during October to December were predicted using the calibrated GAM and SAR models and general similarities were found between the observed and predicted patterns for the nominal CPUE of D. gigas. The overall accuracies for the hotspots generated by the SAR model were much higher than those produced by the GAM model for all three months. Our results contribute to a better understanding of the spatiotemporal distributions of D. gigas off shore Peru, and off er a new SAR modeling method for advancing fishery science.

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.

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.

Study of Feature Extraction Based on Autoregressive Modeling in ECG Automatic Diagnosis

This article explores the ability of multivariate autoregressive model(MAR)and scalar AR model to extract the features from two-lead electrocardiogram signals in order to classify certain cardiac arrhythmias.The classification performance of four different ECG feature sets based on the model coefficients are shown.The data in the analysis including normal sinus rhythm, atria premature contraction,premature ventricular contraction,ventricular tachycardia,ventricular fibrillation and superventricular tachyeardia is obtained from the MIT-BIH database.The classification is performed using a quadratic diacriminant function.The results show the MAR coefficients produce the best results among the four ECG representations and the MAR modeling is a useful classification and diagnosis tool.

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.

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.

The First Order Autoregressive Model with Coefficient Contains Non-Negative Random Elements: Simulation and Esimation

This paper considered an autoregressive time series where the slope contains random components with non-negative values. The authors determine the stationary condition of the series to estimate its parameters by the quasi-maximum likelihood method. The authors also simulates and estimates the coefficients of the simulation chain. In this paper, we consider modeling and forecasting gold chain on the free market in Hanoi, Vietnam.

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.

Noise reduction of acoustic Doppler velocimeter data based on Kalman filtering and autoregressive moving average models

Oceanic turbulence measurements made by an acoustic Doppler velocimeter(ADV)suffer from noise that potentially affects the estimates of turbulence statistics.This study examines the abilities of Kalman filtering and autoregressive moving average models to eliminate noise in ADV velocity datasets of laboratory experiments and offshore observations.Results show that the two methods have similar performance in ADV de-noising,and both effectively reduce noise in ADV velocities,even in cases of high noise.They eliminate the noise floor at high frequencies of the velocity spectra,leading to a longer range that effectively fits the Kolmogorov-5/3 slope at midrange frequencies.After de-noising adopting the two methods,the values of the mean velocity are almost unchanged,while the root-mean-square horizontal velocities and thus turbulent kinetic energy decrease appreciably in these experiments.The Reynolds stress is also affected by high noise levels,and de-noising thus reduces uncertainties in estimating the Reynolds stress.

The m-delay Autoregressive Model with Application

The classical autoregressive(AR)model has been widely applied to predict future data usingmpast observations over five decades.As the classical AR model required m unknown parameters,this paper implements the AR model by reducing m parameters to two parameters to obtain a new model with an optimal delay called as the m-delay AR model.We derive the m-delay AR formula for approximating two unknown parameters based on the least squares method and develop an algorithm to determine optimal delay based on a brute-force technique.The performance of them-delay AR model was tested by comparing with the classical AR model.The results,obtained from Monte Carlo simulation using the monthly mean minimum temperature in PerthWestern Australia from the Bureau of Meteorology,are no significant difference compared to those obtained from the classical AR model.This confirms that the m-delay AR model is an effective model for time series analysis.

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

Consider the model Yt = βYt-1＋g（Yt-2）＋εt for 3 〈 t 〈 T. Hereg is anunknown function, β is an unknown parameter, εt are i.i.d, random errors with mean 0 andvariance σ2 and the fourth moment α4, and α4 are independent of Y8 for all t ≥ 3 and s = 1, 2.Pseudo-LS estimators σ, σ2T α4τ and D2T of σ^2,α4 and Var（ε2↑3） are respectively constructedbased on piecewise polynomial approximator of g. The weak consistency of α4T and D2T are proved. The asymptotic normality of σ2T is given, i.e., √T（σ2T -σ^2）/DT converges indistribution to N（0, 1）. The result can be used to establish large sample interval estimatesof σ^2 or to make large sample tests for σ^2.

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.