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
The energy sector is the second largest emitter of greenhouse (GHG) gases in Kenya, emitting about 31.2% of GHG emissions in the country. The aim of this study was to model Kenya’s GHG emissions by the energy sector ...The energy sector is the second largest emitter of greenhouse (GHG) gases in Kenya, emitting about 31.2% of GHG emissions in the country. The aim of this study was to model Kenya’s GHG emissions by the energy sector using ARIMA models for forecasting future values. The data used for the study was that of Kenya’s GHG emissions by the energy sector for the period starting from 1970 to 2022 obtained for the International Monetary Fund (IMF) database that was split into training and testing sets using the 80/20 rule for modelling purposes. The best specification for the ARIMA model was identified using Akaike Information Criterion (AIC), root mean squared error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE) and mean absolute scaled error (MASE). ARIMA (1, 1, 1) was identified as the best model for modelling Kenya’s GHG emissions and forecasting future values. Using this model, Kenya’s GHG emissions by the energy sector were forecasted to increase to a value of about 43.13 million metric tons of carbon dioxide equivalents by 2030. The study, therefore, recommends that Kenya should accelerate the adjustment of industry structure and improve the efficient use of energy, optimize the energy structure and accelerate development and promotion of energy-efficient products to reduce the emission of GHGs by the country’s energy sector.展开更多
As one of the main characteristics of atmospheric pollutants,PM_(2.5) severely affects human health and has received widespread attention in recent years.How to predict the variations of PM_(2.5) concentrations with h...As one of the main characteristics of atmospheric pollutants,PM_(2.5) severely affects human health and has received widespread attention in recent years.How to predict the variations of PM_(2.5) concentrations with high accuracy is an important topic.The PM_(2.5) monitoring stations in Xinjiang Uygur Autonomous Region,China,are unevenly distributed,which makes it challenging to conduct comprehensive analyses and predictions.Therefore,this study primarily addresses the limitations mentioned above and the poor generalization ability of PM_(2.5) concentration prediction models across different monitoring stations.We chose the northern slope of the Tianshan Mountains as the study area and took the January−December in 2019 as the research period.On the basis of data from 21 PM_(2.5) monitoring stations as well as meteorological data(temperature,instantaneous wind speed,and pressure),we developed an improved model,namely GCN−TCN−AR(where GCN is the graph convolution network,TCN is the temporal convolutional network,and AR is the autoregression),for predicting PM_(2.5) concentrations on the northern slope of the Tianshan Mountains.The GCN−TCN−AR model is composed of an improved GCN model,a TCN model,and an AR model.The results revealed that the R2 values predicted by the GCN−TCN−AR model at the four monitoring stations(Urumqi,Wujiaqu,Shihezi,and Changji)were 0.93,0.91,0.93,and 0.92,respectively,and the RMSE(root mean square error)values were 6.85,7.52,7.01,and 7.28μg/m^(3),respectively.The performance of the GCN−TCN−AR model was also compared with the currently neural network models,including the GCN−TCN,GCN,TCN,Support Vector Regression(SVR),and AR.The GCN−TCN−AR outperformed the other current neural network models,with high prediction accuracy and good stability,making it especially suitable for the predictions of PM_(2.5)concentrations.This study revealed the significant spatiotemporal variations of PM_(2.5)concentrations.First,the PM_(2.5) concentrations exhibited clear seasonal fluctuations,with higher levels typically observed in winter and differences presented between months.Second,the spatial distribution analysis revealed that cities such as Urumqi and Wujiaqu have high PM_(2.5) concentrations,with a noticeable geographical clustering of pollutions.Understanding the variations in PM_(2.5) concentrations is highly important for the sustainable development of ecological environment in arid areas.展开更多
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
Food and non-alcoholic beverages are highly important for individuals to continue staying alive and living healthy lives. The increase in the prices of food and non-alcoholic beverages experienced across the world ove...Food and non-alcoholic beverages are highly important for individuals to continue staying alive and living healthy lives. The increase in the prices of food and non-alcoholic beverages experienced across the world over years has continued to make food and non-alcoholic beverages not to be accessible and affordable to individuals and families having a low income. The aim of this particular research study was to identify how Kenya’s CPI of food and non-alcoholic beverages could be modelled using Autoregressive Integrated Moving Average (ARIMA) models for forecasting future values for the next two years. The data used for the study was that of Kenya’s CPI of food and non-alcoholic beverages for the period starting from February 2009 to April 2024 obtained from the International Monetary Fund (IMF) database. The best specification for the ARIMA model was identified using Akaike Information Criterion (AIC), root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE) and mean absolute scaled error (MASE) and assessing whether residuals of the model were independent and normally distributed with a variance that is constant an whether the model has most of its coefficients being significant statistically. ARIMA (3, 1, 0) (1, 0, 0) model was identified as the best ARIMA model for modeling Kenya’s CPI of food and non-beverages for forecasting future values among the ARIMA models considered. Using this particular model, Kenya’s CPI of food and non-alcoholic beverages was forecasted to increase only slightly with time to reach a value of about 165.70 by March 2026.展开更多
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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....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.展开更多
基金supported by the National Natural Science Foundation of China(12131015,12071422)。
文摘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.
文摘The energy sector is the second largest emitter of greenhouse (GHG) gases in Kenya, emitting about 31.2% of GHG emissions in the country. The aim of this study was to model Kenya’s GHG emissions by the energy sector using ARIMA models for forecasting future values. The data used for the study was that of Kenya’s GHG emissions by the energy sector for the period starting from 1970 to 2022 obtained for the International Monetary Fund (IMF) database that was split into training and testing sets using the 80/20 rule for modelling purposes. The best specification for the ARIMA model was identified using Akaike Information Criterion (AIC), root mean squared error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE) and mean absolute scaled error (MASE). ARIMA (1, 1, 1) was identified as the best model for modelling Kenya’s GHG emissions and forecasting future values. Using this model, Kenya’s GHG emissions by the energy sector were forecasted to increase to a value of about 43.13 million metric tons of carbon dioxide equivalents by 2030. The study, therefore, recommends that Kenya should accelerate the adjustment of industry structure and improve the efficient use of energy, optimize the energy structure and accelerate development and promotion of energy-efficient products to reduce the emission of GHGs by the country’s energy sector.
基金supported by the Program of Support Xinjiang by Technology(2024E02028,B2-2024-0359)Xinjiang Tianchi Talent Program of 2024,the Foundation of Chinese Academy of Sciences(B2-2023-0239)the Youth Foundation of Shandong Natural Science(ZR2023QD070).
文摘As one of the main characteristics of atmospheric pollutants,PM_(2.5) severely affects human health and has received widespread attention in recent years.How to predict the variations of PM_(2.5) concentrations with high accuracy is an important topic.The PM_(2.5) monitoring stations in Xinjiang Uygur Autonomous Region,China,are unevenly distributed,which makes it challenging to conduct comprehensive analyses and predictions.Therefore,this study primarily addresses the limitations mentioned above and the poor generalization ability of PM_(2.5) concentration prediction models across different monitoring stations.We chose the northern slope of the Tianshan Mountains as the study area and took the January−December in 2019 as the research period.On the basis of data from 21 PM_(2.5) monitoring stations as well as meteorological data(temperature,instantaneous wind speed,and pressure),we developed an improved model,namely GCN−TCN−AR(where GCN is the graph convolution network,TCN is the temporal convolutional network,and AR is the autoregression),for predicting PM_(2.5) concentrations on the northern slope of the Tianshan Mountains.The GCN−TCN−AR model is composed of an improved GCN model,a TCN model,and an AR model.The results revealed that the R2 values predicted by the GCN−TCN−AR model at the four monitoring stations(Urumqi,Wujiaqu,Shihezi,and Changji)were 0.93,0.91,0.93,and 0.92,respectively,and the RMSE(root mean square error)values were 6.85,7.52,7.01,and 7.28μg/m^(3),respectively.The performance of the GCN−TCN−AR model was also compared with the currently neural network models,including the GCN−TCN,GCN,TCN,Support Vector Regression(SVR),and AR.The GCN−TCN−AR outperformed the other current neural network models,with high prediction accuracy and good stability,making it especially suitable for the predictions of PM_(2.5)concentrations.This study revealed the significant spatiotemporal variations of PM_(2.5)concentrations.First,the PM_(2.5) concentrations exhibited clear seasonal fluctuations,with higher levels typically observed in winter and differences presented between months.Second,the spatial distribution analysis revealed that cities such as Urumqi and Wujiaqu have high PM_(2.5) concentrations,with a noticeable geographical clustering of pollutions.Understanding the variations in PM_(2.5) concentrations is highly important for the sustainable development of ecological environment in arid areas.
基金This project is supported by the 10th Five-year Plan Pre-research Project Foundation of China Weapon Industry Company, China(No.42001080701).
文摘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.
文摘Food and non-alcoholic beverages are highly important for individuals to continue staying alive and living healthy lives. The increase in the prices of food and non-alcoholic beverages experienced across the world over years has continued to make food and non-alcoholic beverages not to be accessible and affordable to individuals and families having a low income. The aim of this particular research study was to identify how Kenya’s CPI of food and non-alcoholic beverages could be modelled using Autoregressive Integrated Moving Average (ARIMA) models for forecasting future values for the next two years. The data used for the study was that of Kenya’s CPI of food and non-alcoholic beverages for the period starting from February 2009 to April 2024 obtained from the International Monetary Fund (IMF) database. The best specification for the ARIMA model was identified using Akaike Information Criterion (AIC), root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE) and mean absolute scaled error (MASE) and assessing whether residuals of the model were independent and normally distributed with a variance that is constant an whether the model has most of its coefficients being significant statistically. ARIMA (3, 1, 0) (1, 0, 0) model was identified as the best ARIMA model for modeling Kenya’s CPI of food and non-beverages for forecasting future values among the ARIMA models considered. Using this particular model, Kenya’s CPI of food and non-alcoholic beverages was forecasted to increase only slightly with time to reach a value of about 165.70 by March 2026.
基金supported by the Foundation for the Author of National Excellent Doctoral Dissertation of China (2007B51)Natural Science Foundation of China (41174008)
文摘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.
文摘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.
基金Supported by National Natural Science Foundation of China (No. 60972038)The Open Research Fund of Na-tional Mobile Communications Research Laboratory, Southeast University (N200911)+3 种基金The Jiangsu Province Universities Natural Science Research Key Grant Project (No. 07KJA51006)ZTE Communications Co., Ltd. (Shenzhen) Huawei Technology Co., Ltd. (Shenzhen)The Research Fund of Nanjing College of Traffic Voca-tional Technology (JY0903)
文摘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.
基金The authors thank the financial support of Natural Science Foundation of China(U2031112)Natural Science Foundation of Hunan Province(2021JJ30469)Natural Science Youth Foundation of Hunan Province(2020JJ5396).
文摘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%.
文摘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.
文摘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.
基金Supported by the National Natural Science Foundation of China
文摘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.
文摘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.
文摘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.
基金Supported by the National Natural Science Foundation of China（60375003） Supported by the Chinese Aviation Foundation（03153059）
文摘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.
文摘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.
基金Thailand Science ResearchInnovation Fund,and King Mongkut's University of Technology North Bangkok Contract No.KMUTNB-FF-65-45.
文摘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.
文摘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.
文摘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.
基金The National Natural Science Foundation of China(No.50479017).
文摘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.
