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Asymptotic normality of error density estimator in stationary and explosive autoregressive models
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作者 WU Shi-peng YANG Wen-zhi +1 位作者 GAO Min HU Shu-he 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2024年第1期140-158,共19页
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... 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. 展开更多
关键词 explosive autoregressive models residual density estimator asymptotic distribution association sequence
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Constructing Confidence Regions for Autoregressive-Model Parameters
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作者 Jan Vrbik 《Applied Mathematics》 2023年第10期704-717,共14页
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 ... 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. 展开更多
关键词 MarKOV Yule and autoregressive models Maximum Likelihood Function Asymptotic Variance-Covariance Matrix Confidence Intervals Nuisance Parameters
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Trend Autoregressive Model Exact Run Length Evaluation on a Two-Sided Extended EWMA Chart
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作者 Kotchaporn Karoon Yupaporn Areepong Saowanit Sukparungsee 《Computer Systems Science & Engineering》 SCIE EI 2023年第2期1143-1160,共18页
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 a... 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. 展开更多
关键词 Average run length explicit formula extended EWMA chart trend autoregressive model
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AUTOREGRESSIVE MODEL AND POWER SPECTRUM CHARATERISTICS OF CURRENT SIGNAL IN HIGH FREQUENCY GROUP PULSE MICRO-ELECTROCHEMICAL MACHINING 被引量:3
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作者 TANG Xinglun ZHANG Zhijing +1 位作者 ZHOU Zhaoying YANG Xiaodong 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2006年第2期260-264,共5页
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 acros... 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. 展开更多
关键词 Electrochemical machining Inter-electrode gap autoregressive(ar) model Power spectrum
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A modified stochastic model for LS+AR hybrid method and its application in polar motion short-term prediction 被引量:1
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作者 Fei Ye Yunbin Yuan 《Geodesy and Geodynamics》 EI CSCD 2024年第1期100-105,共6页
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.Currentl... 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. 展开更多
关键词 Stochastic model LS+ar Short-term prediction The earth rotation parameter(ERP) Observation model
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Classification of Conversational Sentences Using an Ensemble Pre-Trained Language Model with the Fine-Tuned Parameter
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作者 R.Sujatha K.Nimala 《Computers, Materials & Continua》 SCIE EI 2024年第2期1669-1686,共18页
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 requir... 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. 展开更多
关键词 Bidirectional encoder for representation of transformer conversation ensemble model fine-tuning generalized autoregressive pretraining for language understanding generative pre-trained transformer hyperparameter tuning natural language processing robustly optimized BERT pretraining approach sentence classification transformer models
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Deep Learning-Based Stock Price Prediction Using LSTM Model
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作者 Jiayi Mao Zhiyong Wang 《Proceedings of Business and Economic Studies》 2024年第5期176-185,共10页
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 ... 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. 展开更多
关键词 autoregressive integrated moving average(arIMA)model Long Short-Term Memory(LSTM)network Forecasting Stock market
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Utilizing the Vector Autoregression Model (VAR) for Short-Term Solar Irradiance Forecasting
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作者 Farah Z. Najdawi Ruben Villarreal 《Energy and Power Engineering》 2023年第11期353-362,共10页
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 A... 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. 展开更多
关键词 Vector autoregression model Hyperparameter Parameters Augmented Dickey Fuller Durbin Watson’s Statistics
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Prediction of earth rotation parameters based on improved weighted least squares and autoregressive model 被引量:8
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作者 Sun Zhangzhen Xu Tianhe 《Geodesy and Geodynamics》 2012年第3期57-64,共8页
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 develope... 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. 展开更多
关键词 earth rotation parameters(ERP) PREDICTION autoregressive(ar) WEIGHTED least-square
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JUMP DETECTION BY WAVELET IN NONLINEAR AUTOREGRESSIVE MODELS 被引量:2
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作者 李元 谢衷洁 《Acta Mathematica Scientia》 SCIE CSCD 1999年第3期261-271,共11页
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 signi... 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. 展开更多
关键词 jump points nonlinear autoregressive models WAVELETS
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PARTICLE FILTERING BASED AUTOREGRESSIVE CHANNEL PREDICTION MODEL 被引量:1
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作者 Dong Chunli Dong Yuning +2 位作者 Wang Li Yang Zhen Zhang Hui 《Journal of Electronics(China)》 2010年第3期316-320,共5页
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 o... 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. 展开更多
关键词 Cognitive radio Rayleigh fading channel autoregressive (ar) model Particle filtering
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Identification of Denatured Biological Tissues Based on Improved Variational Mode Decomposition and Autoregressive Model during HIFU Treatment 被引量:2
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作者 Bei Liu Xian Zhang 《Computer Modeling in Engineering & Sciences》 SCIE EI 2022年第3期1547-1563,共17页
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 ... 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%. 展开更多
关键词 HIFU ultrasonic scattered echo signals IVMD ar model
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Multivariate Generalized Autoregressive Conditional Heteroscedastic Model 被引量:1
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作者 史宁中 刘继春 《Northeastern Mathematical Journal》 CSCD 2001年第3期323-332,共10页
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 Bollersl... 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. 展开更多
关键词 generalized autoregressive conditional heteroscedastic model strict stationarity Hadamard product
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SOME LEAST SQUARES ESTIMATES OF THE AUTOREGRESSIVE MODELS
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作者 林正华 盛中平 王嘉松 《Numerical Mathematics A Journal of Chinese Universities(English Series)》 SCIE 1999年第1期113-124,共12页
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 ... 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. 展开更多
关键词 autoregressive model ITERATIVE METHOD convergence.
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PC-VAR Estimation of Vector Autoregressive Models
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作者 Claudio Morana 《Open Journal of Statistics》 2012年第3期251-259,共9页
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 typic... 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. 展开更多
关键词 VECTOR autoregressive model Principal COMPONENTS Analysis STATISTICAL REDUCTION Techniques
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Sleep spindles detection from human sleep EEG signals using autoregressive (AR) model: a surrogate data approach
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作者 Venkatakrishnan Perumalsamy Sangeetha Sankaranarayanan Sukanesh Rajamony 《Journal of Biomedical Science and Engineering》 2009年第5期294-303,共10页
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 p... 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. 展开更多
关键词 ar model LPC SLEEP SPINDLES Surrogate Data
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Asymptotic Normality of Pseudo-LS Estimator of Error Variance in Partly Linear Autoregressive Models
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作者 WU Xin-qian TIAN Zheng JU Yan-wei 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2006年第4期617-622,共6页
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 ... 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. 展开更多
关键词 partly linear autoregressive model error variance piecewise polynomial pseudo-LS estimation weak consistency asymptotic normality
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Comparison of the Sampling Efficiency in Spatial Autoregressive Model
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作者 Yoshihiro Ohtsuka Kazuhiko Kakamu 《Open Journal of Statistics》 2015年第1期10-20,共11页
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,... 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. 展开更多
关键词 Acceptance-Rejection METROPOLIS-HASTINGS ALGORITHM Griddy Gibbs SAMPLER Markov Chain Monte Carlo (MCMC) Random WALK METROPOLIS-HASTINGS ALGORITHM Spatial autoregressive model
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Vector Autoregressive (VAR) Modeling and Projection of DSE
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作者 Ahammad Hossain Md. Kamruzzaman Md. Ayub Ali 《Chinese Business Review》 2015年第6期273-289,共17页
In this paper, vector autoregressive (VAR) models have been recognized for the selected indicators of Dhaka stock exchange (DSE). Bangladesh uses the micro economic variables, such as stock trade, invested stock c... In this paper, vector autoregressive (VAR) models have been recognized for the selected indicators of Dhaka stock exchange (DSE). Bangladesh uses the micro economic variables, such as stock trade, invested stock capital, stock volume, current market value, and DSE general indexes which have the direct impact on DSE prices. The data were collected for the period from June 2004 to July 2013 as the basis on daily scale. But to get the maximum explorative information and reduction of volatility, the data have been transformed to the monthly scale. The outliers and extreme values of the study variables are detected through box and whisker plot. To detect the unit root property of the study variables, various unit root tests have been applied. The forecast performance of the different VAR models is compared to have the minimum residual. Moreover, the dynamics of this financial market is analyzed through Granger causality and impulse response analysis. 展开更多
关键词 vector autoregressive (Var) model impulse response analysis Granger causality
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A Parametric Autoregressive Model for the Extraction of Electric Network Frequency Fluctuations in Audio Forensic Authentication
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作者 Tarek E. Gemayel Martin Bouchard 《Journal of Energy and Power Engineering》 2016年第8期504-512,共9页
This paper proposes a new method for extracting ENF (electric network frequency) fluctuations from digital audio recordings for the purpose of forensic authentication. It is shown that the extraction of ENF componen... This paper proposes a new method for extracting ENF (electric network frequency) fluctuations from digital audio recordings for the purpose of forensic authentication. It is shown that the extraction of ENF components from audio recordings is realizable by applying a parametric approach based on an AR (autoregressive) model. The proposed method is compared to the existing STFT (short-time Fourier transform) based ENF extraction method. Experimental results from recorded electrical grid signals and recorded audio signals show that the proposed approach can improve the time resolution in the extracted ENF fluctuations and improve the detection of tampering with short alterations in longer audio recordings. 展开更多
关键词 Audio forensic authentication electric network frequency fluctuations autoregressive modeling tampering anddiscontinuity detection.
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