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.

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.

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.

Deep Learning-Based Stock Price Prediction Using LSTM Model

The stock market is a vital component of the broader financial system,with its dynamics closely linked to economic growth.The challenges associated with analyzing and forecasting stock prices have persisted since the inception of financial markets.By examining historical transaction data,latent opportunities for profit can be uncovered,providing valuable insights for both institutional and individual investors to make more informed decisions.This study focuses on analyzing historical transaction data from four banks to predict closing price trends.Various models,including decision trees,random forests,and Long Short-Term Memory(LSTM)networks,are employed to forecast stock price movements.Historical stock transaction data serves as the input for training these models,which are then used to predict upward or downward stock price trends.The study’s empirical results indicate that these methods are effective to a degree in predicting stock price movements.The LSTM-based deep neural network model,in particular,demonstrates a commendable level of predictive accuracy.This conclusion is reached following a thorough evaluation of model performance,highlighting the potential of LSTM models in stock market forecasting.The findings offer significant implications for advancing financial forecasting approaches,thereby improving the decision-making capabilities of investors and financial institutions.

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.

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。

相干累加与AR滤波相结合的舰船轴频电场信号处理方法

针对采用电场传感器阵列测量舰船电场的应用场景,为提升目标轴频电场的信噪比,提出一种相干累加结合自回归(autoregressive,AR)模型滤波的方法对阵列电场信号进行处理。对测量得到的阵列电场信号进行时延补偿后累加,同时对环境电场信号进行AR建模,并利用AR模型参数构造滤波器,以对累加后的信号实施滤波处理。为验证所提方法在低信噪比条件下的有效性,对实测阵列式电场信号进行处理,结果表明,所提方法能够在信噪比为-25.39 dB的条件下有效压制噪声频谱,保留轴频线谱,处理后信噪比提高约21.92 dB。

基于ARIMA-TCN混合模型的高速铁路时间同步方法

列控系统作为高速铁路的核心系统,保持其系统的时间同步对于行车安全至关重要。针对现有时间同步方法易受时变上下行传输时延、随机时钟跳变等影响,导致主从时钟偏移估计不准确的问题,提出一种基于差分自回归移动平均-时域卷积神经网络(ARIMA-TCN)混合模型的高速铁路时间同步方法。首先,根据上下行链路传输速率的不对称比,建立高速铁路时钟的数学理论和实际观测模型。然后,使用拉依达准则识别处理跳变异常值,完成实际时间序列的预处理。再次,使用ARIMA模型平滑时间序列中不确定时延带来的噪声抖动,获得平稳的时间序列。最后,通过提出的注意力增强TCN模型进行预测补偿,完成时钟偏移的补偿校正。通过实验仿真,得到基站区间内位置、基站间距以及车速对高速铁路时间同步的影响性分析。实验结果表明:与对比方法相比,所提方法补偿后的均方根误差较最小二乘法减少了75%、较最大似然估计方法误差减少了44.4%,较BP神经网络方法误差减少了16.7%,验证所提方法具有更低的同步误差和更高的同步精度。

基于小波分解和ARIMA-GARCH-GRU组合模型的制造业PMI预测

制造业采购经理人指数(PMI)是反映国家经济运行情况的重要指标,而传统预测模型对该类时序数据预测精度不高。针对制造业PMI指数的非线性、波动性和数据量少的特点,提出一种基于一维离散小波变换进行数据预处理的组合模型。时序数据经过小波变换,由整合移动平均自回归–广义自回归条件异方差模型(ARIMA-GARCH)处理稳态低频数据,门控循环单元(GRU)处理波动性强的高频数据,将各频段预测结果进行融合得到最终预测结果。为验证模型有效性,选取一定数据量的PMI指数进行实验。结果表明,与其他常见模型对比,本文构建的组合模型具有较好的预测精度与性能,平均绝对误差(MAE)、均方根误差(RMSE)、平均绝对百分比误差(MAPE)分别达到0.00329、0.004162、0.65%。

基于季节ARIMA模型对某三级综合性医院门诊量的预测研究

目的 通过建立季节ARIMA模型,对浙江省某三级综合性医院门诊量进行预测,为医院合理配备门诊人力资源提供依据。方法 以2013年1—6月浙江省某医院门诊量数据为基线,利用SPSS软件构建季节ARIMA模型,对2023年7—12月的门诊量进行预测,通过对比门诊量实测值,评价季节ARIMA模型预测门诊人次的精度。结果 该综合性医院门诊量呈现逐年上升趋势,并呈现周期性波动的特征。拟合的最优季节ARIMA模型为ARIMA(0,1,1)(1,0,1)12,BIC(贝叶斯信息准则)为5.273,MAPE(平均绝对百分误差)为14.265,R2(模块决定系数)为0.408,总体相对误差为1.83%,预测结果良好。结论 季节ARIMA模型较好地模拟了该三级综合性医院门诊量在时间序列上的变化趋势,为该院门诊量的短期预测提供理论依据。

基于自适应AR模型巡航飞行参数预测研究

为更准确实现飞行参数趋势预测,提出一种基于自适应自回归(AR)模型的稳定巡航飞行参数预测方法。根据稳定巡航参数筛选条件,获取建模所需飞行参数。利用卡尔曼滤波原理估计AR模型参数,并与飞行参数构建系统方程,利用无迹卡尔曼滤波实时更新、修正AR模型参数估计值,将自适应AR模型的预测值与曲线拟合模型和灰色模型的预测值进行对比。以波音B777-300ER飞机的快速存取记录器数据样本进行仿真验证,结果表明:自适应AR模型在数据预测和收敛速率方面均更优,可有效降低预报模型随步数增加导致的精度误差,提高参数预测准确性。研究在飞机维修保障、状态监控与预测等方面具有重要作用。

基于D3AR的半球共形阵低空风切变风速估计方法

针对半球共形阵体制下进行低空风切变检测时会受到强地杂波信号的干扰,导致风切变信号难以检测的问题,提出了一种基于空时自回归的直接数据域算法(Space-Time Autoregressive Direct Data Domain,D3AR)的低空风切变风速估计方法。该方法首先将待检测距离单元的数据从空域、时域以及空时域进行信号对消处理;然后将处理后的数据矩阵描述为空时自回归(Autoregression,AR)模型并估计模型参数;再通过构造与杂波子空间正交的空间来实现对杂波的抑制,最后通过提取待检测单元的最大多普勒频率来估计风场速度。根据仿真结果显示,该方法有效地实现了地杂波抑制,并且能够精确估计风速。

基于MS(2)-AR-TVTP模型的I_(BD)波动周期非对称性和持续性分析

国际干散货运输市场源于国际贸易的衍生需求,受世界经济的影响,是一个典型的周期性市场。选取1999年11月~2021年12月的波罗的海干散货运价指数(I_(BD))月度数据,在检验序列平稳性的基础上,确定最优滞后长度,构建两区制的时变转换概率马尔科夫转换自回归模型,分析I_(BD)波动周期的持续时间、转换拐点和非对称性等主要特征。研究结果表明:模型能有效拟合I_(BD)波动周期的主要特征,周期平均持续时间为33.7个月,自2008年9月之后呈缩短态势,上升期和下降期交互更频繁;I_(BD)波动周期具有非对称性,周期内上升期持续时间比下降期长,I_(BD)维持上升期更具有稳定性。周期性特征结果可为干散货航运业造船投资和市场经营提供决策依据。

基于R语言时间序列的ARIMA模型预测某三甲综合医院人均月住院费用和住院日的研究

目的运用自回归积分滑动平均模型(Autoregressive Intergrated Moving Average,ARIMA)建立月平均住院费用和住院日的医学经济学模型,为医院精细化管理提供依据。方法利用R4.0.2软件对2017年1月—2021年12月四川大学华西医院宜宾医院(宜宾市第二人民医院)的平均住院费用和住院日数据建立时间序列ARIMA预测模型。结果住院费用最优模型为ARIMA(0,1,1),赤池信息准则(Akaike information criterion,AIC)=924.35,贝叶斯信息准则(Bayesian Information Criterion,BIC)=928.51,残差Ljung-Box Q=12.51(P=0.768),可认为残差序列为白噪声。平均住院日的最优模型为ARIMA(5,1,1),AIC=87.49,BIC=104.11,残差Ljung-Box Q=10.05(P=0.612),可认为残差序列为白噪声。2022年1—12月实际值与预测值基本吻合,月人均住院费用和人均住院日的平均相对误差为0.55%、0.29%。结论建立基于时间序列ARIMA模型能够为合理配置卫生资源提供强有力的数据支撑。

基于WPD-ARIMA-GARCH组合模型的酱卤肉制品安全风险区间预测

针对传统确定性预测不能提供不确定性信息的难题,本研究提出了一种点估计和区间估计组合预测模型,并将其创新性地应用在食品安全风险预警领域。在点估计部分,使用小波包分解(wavelet packet decomposition,WPD)对周风险等级序列分解后,应用差分自回归移动平均(autoregressive integrated moving average,ARIMA)模型进行预测;在区间估计部分,使用广义自回归条件异方差(generalized autoregressive conditional heteroskedast,GARCH)模型对残差进行预测。本实验将建立的WPD-ARIMA-GARCH组合模型运用于某地区酱卤肉制品的风险预测,结果表明2019年的3月底和7月底该地区的酱卤肉制品安全风险较高,与实际情况相符;同时,该模型在10个不同地区的酱卤肉制品风险预测中,均方误差、平均绝对误差和平均绝对百分比误差分别为1.626、0.806和20.824;其90%置信区间的预测区间平均宽度和覆盖宽度标准值均为0.024,可以覆盖所有真实值。该模型具有较高的预测精度和较低的误差,能对酱卤肉制品质量安全起到风险防控作用,可为日常食品安全监管提供相应的技术支持。

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.