The multipole moment method not only conduces to the understanding of the deformation of the space-time, but also serves as an effective tool to approximately solve the Einstein field equation with. However, the usual...The multipole moment method not only conduces to the understanding of the deformation of the space-time, but also serves as an effective tool to approximately solve the Einstein field equation with. However, the usual multipole moments are recursively determined by a sequence of symmetric and trace-free tensors, which is inconvenient for practical resolution. In this paper, we develop a simplified procedure to generate the series solutions to the metric of the stationary vacuum with axisymmetry, and show its validity. In order to understand the free parameters in the solution, we propose to take the Schwarzschild metric as a standard ruler, and some well- known examples are analysed and compared with the series solutions in detail.展开更多
The paper deals with the application of Volterra bound Interval type−2 fuzzy logic techniques in power quality assessment.This work proposes a new layout for detection,localization and classification of various types ...The paper deals with the application of Volterra bound Interval type−2 fuzzy logic techniques in power quality assessment.This work proposes a new layout for detection,localization and classification of various types of power quality events.The proposed method exploits Volterra series for the extraction of relevant features,which are used to recognize different PQ events by Interval type-2 fuzzy logic based classifier.Numerous single as well as multiple powers signal disturbances have been simulated to testify the efficiency of the proposed technique.This time–frequency analysis results in the clear visual detection,localization,and classification of the different power quality events.The simulation results signify that the proposed scheme has a higher recognition rate while classifying single and multiple power quality events unlike other methods.Finally,the proposed method is compared with SVM,feed forward neural network and type−1 Fuzzy logic system based classifier to show the efficacy of the proposed technique in classifying the Power quality events.展开更多
Depending on the asymptotical independence of periodograms,exponential tilted(ET)likelihood,as an effective nonparametric statistical method,is developed to deal with time series in this paper.Similar to empirical lik...Depending on the asymptotical independence of periodograms,exponential tilted(ET)likelihood,as an effective nonparametric statistical method,is developed to deal with time series in this paper.Similar to empirical likelihood(EL),it still suffers from two drawbacks:the nondefinition problem of the likelihood function and the under-coverage probability of confidence region.To overcome these two problems,we further proposed the adjusted ET(AET)likelihood.With a specific adjustment level,our simulation studies indicate that the AET method achieves a higher-order coverage precision than the unadjusted ET method.In addition,due to the good performance of ET under moment model misspecification[Schennach,S.M.(2007).Point estimation with exponentially tilted empirical likelihood.The Annals of Statistics,35(2),634–672.https://doi.org/10.1214/009053606000001208],we show that the one-order property of point estimate is preserved for the misspecified spectral estimating equations of the autoregressive coefficient of AR(1).The simulation results illustrate that the point estimates of the ET outperform those of the EL and their hybrid in terms of standard deviation.A real data set is analyzed for illustration purpose.展开更多
A new method for forecasting non stationary series is developed. Its steps are as follows: Step 1. Data delaminating. Non stationary series is delaminated into several multi scale steady data layers and one trend laye...A new method for forecasting non stationary series is developed. Its steps are as follows: Step 1. Data delaminating. Non stationary series is delaminated into several multi scale steady data layers and one trend layer. Step 2. Modeling and forecasting each stationary data layer. Step 3. Imitating trend layer using polynomial. Step 4. Combining the forecasting layers and imitating layer into one series. The EMD (Empirical Mode Decomposition) method suitable to process non stationary series is selected to delaminate data, while ARMA (Auto Regressive Moving Average) model is employed to model and forecast stationary data layer and least square error method for trend layer regression. Aiming at forecasting length, forecasting orientation and selective method, experiments are performed for SAR (Synthetic Aperture Radar) images. Finally, an example is provided, in which the whole SAR image is restored via the method proposed by this paper.展开更多
This paper considers the problem of smoothing a non-stationary time series(having either deterministic and/or stochastic trends) using the discrete cosine transform(DCT).The DCT is a powerful tool which has found frui...This paper considers the problem of smoothing a non-stationary time series(having either deterministic and/or stochastic trends) using the discrete cosine transform(DCT).The DCT is a powerful tool which has found fruitful applications in filtering and smoothing as it can closely approximate the optimal Karhunen-Loeve transform(KLT).In fact,it is known that it almost corresponds to the KLT for first-order autoregressive processes with a root close to unity:This is the case with most economic and financial time series.A number of new results are derived in the paper:(a) The explicit form of the linear smoother based on the DCT,which is found to have time-varying weights and that uses all observations;(b) the extrapolation of the DCT-smoothed series;(c) the form of the average frequency response function,which is shown to approximate the frequency response of the ideal low pass filter;(d) the asymptotic distribution of the DCT coefficients under the assumptions of deterministic or stochastic trends;(e) two news method for selecting an appropriate degree of smoothing,in general and under the assumptions in(d).These findings are applied and illustrated using several real world economic and financial time series.The results indicate that the DCT-based smoother that is proposed can find many useful applications in economic and financial time series.展开更多
Although the Cointegration Theory was founded by the C.W.J Granger and other economists in the 1980s, it was not widely used in China until C.W.J Granger was awarded with Nobel Prize in 2003. Since then, a lot of econ...Although the Cointegration Theory was founded by the C.W.J Granger and other economists in the 1980s, it was not widely used in China until C.W.J Granger was awarded with Nobel Prize in 2003. Since then, a lot of economic papers introducing or applying Cointegration Theory have emerged, but the phenomenon of misuse of this theory possibly arose at the same time. Based on some of these papers obtained from web site （www.cnki.net）, this paper explores the applications of Cointegration Theory in China and draws some initial conclusions. Most of these applications are reasonable, but some of them are a bit blindfold or even contradictory in conclusions, which indicates that the overall application quality has a large room to get improved and should be paid more attention by academe.展开更多
文摘The multipole moment method not only conduces to the understanding of the deformation of the space-time, but also serves as an effective tool to approximately solve the Einstein field equation with. However, the usual multipole moments are recursively determined by a sequence of symmetric and trace-free tensors, which is inconvenient for practical resolution. In this paper, we develop a simplified procedure to generate the series solutions to the metric of the stationary vacuum with axisymmetry, and show its validity. In order to understand the free parameters in the solution, we propose to take the Schwarzschild metric as a standard ruler, and some well- known examples are analysed and compared with the series solutions in detail.
文摘The paper deals with the application of Volterra bound Interval type−2 fuzzy logic techniques in power quality assessment.This work proposes a new layout for detection,localization and classification of various types of power quality events.The proposed method exploits Volterra series for the extraction of relevant features,which are used to recognize different PQ events by Interval type-2 fuzzy logic based classifier.Numerous single as well as multiple powers signal disturbances have been simulated to testify the efficiency of the proposed technique.This time–frequency analysis results in the clear visual detection,localization,and classification of the different power quality events.The simulation results signify that the proposed scheme has a higher recognition rate while classifying single and multiple power quality events unlike other methods.Finally,the proposed method is compared with SVM,feed forward neural network and type−1 Fuzzy logic system based classifier to show the efficacy of the proposed technique in classifying the Power quality events.
基金supported by Natural Science Foundation of Shanghai(17ZR1409000)National Natural Science Foundation of China(11831008,11971171)the Open Research Fundof KeyLaboratory of Advanced Theory andApplication in Statistics and Data Science-MOE,ECNU.
文摘Depending on the asymptotical independence of periodograms,exponential tilted(ET)likelihood,as an effective nonparametric statistical method,is developed to deal with time series in this paper.Similar to empirical likelihood(EL),it still suffers from two drawbacks:the nondefinition problem of the likelihood function and the under-coverage probability of confidence region.To overcome these two problems,we further proposed the adjusted ET(AET)likelihood.With a specific adjustment level,our simulation studies indicate that the AET method achieves a higher-order coverage precision than the unadjusted ET method.In addition,due to the good performance of ET under moment model misspecification[Schennach,S.M.(2007).Point estimation with exponentially tilted empirical likelihood.The Annals of Statistics,35(2),634–672.https://doi.org/10.1214/009053606000001208],we show that the one-order property of point estimate is preserved for the misspecified spectral estimating equations of the autoregressive coefficient of AR(1).The simulation results illustrate that the point estimates of the ET outperform those of the EL and their hybrid in terms of standard deviation.A real data set is analyzed for illustration purpose.
文摘A new method for forecasting non stationary series is developed. Its steps are as follows: Step 1. Data delaminating. Non stationary series is delaminated into several multi scale steady data layers and one trend layer. Step 2. Modeling and forecasting each stationary data layer. Step 3. Imitating trend layer using polynomial. Step 4. Combining the forecasting layers and imitating layer into one series. The EMD (Empirical Mode Decomposition) method suitable to process non stationary series is selected to delaminate data, while ARMA (Auto Regressive Moving Average) model is employed to model and forecast stationary data layer and least square error method for trend layer regression. Aiming at forecasting length, forecasting orientation and selective method, experiments are performed for SAR (Synthetic Aperture Radar) images. Finally, an example is provided, in which the whole SAR image is restored via the method proposed by this paper.
文摘This paper considers the problem of smoothing a non-stationary time series(having either deterministic and/or stochastic trends) using the discrete cosine transform(DCT).The DCT is a powerful tool which has found fruitful applications in filtering and smoothing as it can closely approximate the optimal Karhunen-Loeve transform(KLT).In fact,it is known that it almost corresponds to the KLT for first-order autoregressive processes with a root close to unity:This is the case with most economic and financial time series.A number of new results are derived in the paper:(a) The explicit form of the linear smoother based on the DCT,which is found to have time-varying weights and that uses all observations;(b) the extrapolation of the DCT-smoothed series;(c) the form of the average frequency response function,which is shown to approximate the frequency response of the ideal low pass filter;(d) the asymptotic distribution of the DCT coefficients under the assumptions of deterministic or stochastic trends;(e) two news method for selecting an appropriate degree of smoothing,in general and under the assumptions in(d).These findings are applied and illustrated using several real world economic and financial time series.The results indicate that the DCT-based smoother that is proposed can find many useful applications in economic and financial time series.
文摘Although the Cointegration Theory was founded by the C.W.J Granger and other economists in the 1980s, it was not widely used in China until C.W.J Granger was awarded with Nobel Prize in 2003. Since then, a lot of economic papers introducing or applying Cointegration Theory have emerged, but the phenomenon of misuse of this theory possibly arose at the same time. Based on some of these papers obtained from web site （www.cnki.net）, this paper explores the applications of Cointegration Theory in China and draws some initial conclusions. Most of these applications are reasonable, but some of them are a bit blindfold or even contradictory in conclusions, which indicates that the overall application quality has a large room to get improved and should be paid more attention by academe.
