The contribution of this work is twofold： （1） a multimodality prediction method of chaotic time series with the Gaussian process mixture （GPM） model is proposed, which employs a divide and conquer strategy. It au...The contribution of this work is twofold： （1） a multimodality prediction method of chaotic time series with the Gaussian process mixture （GPM） model is proposed, which employs a divide and conquer strategy. It automatically divides the chaotic time series into multiple modalities with different extrinsic patterns and intrinsic characteristics, and thus can more precisely fit the chaotic time series. （2） An effective sparse hard-cut expec- tation maximization （SHC-EM） learning algorithm for the GPM model is proposed to improve the prediction performance. SHO-EM replaces a large learning sample set with fewer pseudo inputs, accelerating model learning based on these pseudo inputs. Experiments on Lorenz and Chua time series demonstrate that the proposed method yields not only accurate multimodality prediction, but also the prediction confidence interval SHC-EM outperforms the traditional variational 1earning in terms of both prediction accuracy and speed. In addition, SHC-EM is more robust and insusceptible to noise than variational learning.展开更多
Building the prediction model(s) from the historical time series has attracted many researchers in last few decades. For example, the traders of hedge funds and experts in agriculture are demanding the precise models ...Building the prediction model(s) from the historical time series has attracted many researchers in last few decades. For example, the traders of hedge funds and experts in agriculture are demanding the precise models to make the prediction of the possible trends and cycles. Even though many statistical or machine learning (ML) models have been proposed, however, there are no universal solutions available to resolve such particular problem. In this paper, the powerful forward-backward non-linear filter and wavelet-based denoising method are introduced to remove the high level of noise embedded in financial time series. With the filtered time series, the statistical model known as autoregression is utilized to model the historical times aeries and make the prediction. The proposed models and approaches have been evaluated using the sample time series, and the experimental results have proved that the proposed approaches are able to make the precise prediction very efficiently and effectively.展开更多
Water level prediction of river runoff is an important part of hydrological forecasting.The change of water level not only has the trend and seasonal characteristics,but also contains the noise factors.And the water l...Water level prediction of river runoff is an important part of hydrological forecasting.The change of water level not only has the trend and seasonal characteristics,but also contains the noise factors.And the water level prediction ability of a single model is limited.Since the traditional ARIMA(Autoregressive Integrated Moving Average)model is not accurate enough to predict nonlinear time series,and the WNN(Wavelet Neural Network)model requires a large training set,we proposed a new combined neural network prediction model which combines the WNN model with the ARIMA model on the basis of wavelet decomposition.The combined model fit the wavelet transform sequences whose frequency are high with the WNN,and the scale transform sequence which has low frequency is fitted by the ARIMA model,and then the prediction results of the above are reconstructed by wavelet transform.The daily average water level data of the Liuhe hydrological station in the Chu River Basin of Nanjing are used to forecast the average water level of one day ahead.The combined model is compared with other single models with MATLAB,and the experimental results show that the accuracy of the combined model is improved by 7%compared with the traditional wavelet network under the appropriate wavelet decomposition function and the combined model parameters.展开更多
Structural health monitoring(SHM)is a vast,interdisciplinary research field whose literature spans several decades with focusing on condition assessment of different types of structures including aerospace,mechanical ...Structural health monitoring(SHM)is a vast,interdisciplinary research field whose literature spans several decades with focusing on condition assessment of different types of structures including aerospace,mechanical and civil structures.The need for quantitative global damage detection methods that can be applied to complex structures has led to vibration-based inspection.Statistical time series methods for SHM form an important and rapidly evolving category within the broader vibration-based methods.In the literature on the structural damage detection,many time series-based methods have been proposed.When a considered time series model approximates the vibration response of a structure and model coefficients or residual error are obtained,any deviations in these coefficients or residual error can be inferred as an indication of a change or damage in the structure.Depending on the technique employed,various damage sensitive features have been proposed to capture the deviations.This paper reviews the application of time series analysis for SHM.The different types of time series analysis are described,and the basic principles are explained in detail.Then,the literature is reviewed based on how a damage sensitive feature is formed.In addition,some investigations that have attempted to modify and/or combine time series analysis with other approaches for better damage identification are presented.展开更多
In the paper,the autoregressive moving average model for matrix time series(MARMA)is inves-tigated.The properties of the MARMA model are investigated by using the conditional least square estimation,the conditional ma...In the paper,the autoregressive moving average model for matrix time series(MARMA)is inves-tigated.The properties of the MARMA model are investigated by using the conditional least square estimation,the conditional maximum likelihood estimation,the projection theorem in Hilbert space and the decomposition technique of time series,which include necessary and suf-ficient conditions for stationarity and invertibility,model parameter estimation,model testing and model forecasting.展开更多
The paper proposes and studies some diagnostic tools for checking the goodness-of-fit of general parametric vector autoregressive models in time series. The resulted tests are asymptotically chi-squared under the null...The paper proposes and studies some diagnostic tools for checking the goodness-of-fit of general parametric vector autoregressive models in time series. The resulted tests are asymptotically chi-squared under the null hypothesis and can detect the alternatives converging to the null at a parametric rate. The tests involve weight functions,which provides us with the flexibility to choose scores for enhancing power performance,especially under directional alternatives. When the alternatives are not directional,we construct asymptotically distribution-free maximin tests for a large class of alternatives. A possibility to construct score-based omnibus tests is discussed when the alternative is saturated. The power performance is also investigated. In addition,when the sample size is small,a nonparametric Monte Carlo test approach for dependent data is proposed to improve the performance of the tests. The algorithm is easy to implement. Simulation studies and real applications are carried out for illustration.展开更多
When linear regressive models such as AR or ARMA model are used for fitting and predicting climatic time series,results are often not sufficiently good because nonlinear variations in the time series.In this paper, a ...When linear regressive models such as AR or ARMA model are used for fitting and predicting climatic time series,results are often not sufficiently good because nonlinear variations in the time series.In this paper, a nonlinear self-exciting threshold autoregressive(SETAR)model is applied to modeling and predicting the time series of flood/drought runs in Beijing,which were derived from the graded historical flood/drought records in the last 511 years(1470—1980).The results show that the modeling and predicting with the SETAR model are much better than that of the AR model.The latter can predict the flood/drought runs with a length only less than two years,while the formal can predict more than three-year length runs.This may be due to the fact that the SETAR model can renew the model according to the run-turning points in the process of predic- tion,though the time series is nonstationary.展开更多
This paper is devoted to the goodness-of-fit test for the general autoregressive models in time series. By averaging for the weighted residuals, we construct a score type test which is asymptotically standard chi-squa...This paper is devoted to the goodness-of-fit test for the general autoregressive models in time series. By averaging for the weighted residuals, we construct a score type test which is asymptotically standard chi-squared under the null and has some desirable power properties under the alternatives. Specifically, the test is sensitive to alternatives and can detect the alternatives approaching, along a direction, the null at a rate that is arbitrarily close to n-1/2. Furthermore, when the alternatives are not directional, we construct asymptotically distribution-free maximin tests for a large class of alternatives. The performance of the tests is evaluated through simulation studies.展开更多
A new method is proposed to determine the optimal embedding dimension from a scalar time series in this paper. This method determines the optimal embedding dimension by optimizing the nonlinear autoregressive predicti...A new method is proposed to determine the optimal embedding dimension from a scalar time series in this paper. This method determines the optimal embedding dimension by optimizing the nonlinear autoregressive prediction model parameterized by the embedding dimension and the nonlinear degree. Simulation results show the effectiveness of this method. And this method is applicable to a short time series, stable to noise, computationally efficient, and without any purposely introduced parameters.展开更多
Time headway is an important index used in characterizing dangerous driving behaviors. This research focuses on the decreasing tendency of time headway and investigates its association with crash occurrence. An autore...Time headway is an important index used in characterizing dangerous driving behaviors. This research focuses on the decreasing tendency of time headway and investigates its association with crash occurrence. An autoregressive（AR） time-series model is improved and adopted to describe the dynamic variations of average daily time headway. Based on the model, a simple approach for dangerous driving behavior recognition is proposed with the aim of significantly decreasing headway. The effectivity of the proposed approach is validated by means of empirical data collected from a medium-sized city in northern China. Finally, a practical early-warning strategy focused on both the remaining life and low headway is proposed to remind drivers to pay attention to their driving behaviors and the possible occurrence of crash-related risks.展开更多
We consider a time series following a simple linear regression with first-order autoregressive errors belonging to the class of heavy-tailed distributions. The proposed model provides a useful generalization of the sy...We consider a time series following a simple linear regression with first-order autoregressive errors belonging to the class of heavy-tailed distributions. The proposed model provides a useful generalization of the symmetrical linear regression models with independent error, since the error distribution covers both correlated innovations following a Generalized Exponential distribution. Furthermore, we derive the modified maximum likelihood (MML) estimators as an efficient alternative for estimating model parameters. Finally, we investigate the asymptotic properties of the proposed estimators. Our findings are also illustrated through a simulation study.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No 60972106the China Postdoctoral Science Foundation under Grant No 2014M561053+1 种基金the Humanity and Social Science Foundation of Ministry of Education of China under Grant No 15YJA630108the Hebei Province Natural Science Foundation under Grant No E2016202341
文摘The contribution of this work is twofold： （1） a multimodality prediction method of chaotic time series with the Gaussian process mixture （GPM） model is proposed, which employs a divide and conquer strategy. It automatically divides the chaotic time series into multiple modalities with different extrinsic patterns and intrinsic characteristics, and thus can more precisely fit the chaotic time series. （2） An effective sparse hard-cut expec- tation maximization （SHC-EM） learning algorithm for the GPM model is proposed to improve the prediction performance. SHO-EM replaces a large learning sample set with fewer pseudo inputs, accelerating model learning based on these pseudo inputs. Experiments on Lorenz and Chua time series demonstrate that the proposed method yields not only accurate multimodality prediction, but also the prediction confidence interval SHC-EM outperforms the traditional variational 1earning in terms of both prediction accuracy and speed. In addition, SHC-EM is more robust and insusceptible to noise than variational learning.
文摘Building the prediction model(s) from the historical time series has attracted many researchers in last few decades. For example, the traders of hedge funds and experts in agriculture are demanding the precise models to make the prediction of the possible trends and cycles. Even though many statistical or machine learning (ML) models have been proposed, however, there are no universal solutions available to resolve such particular problem. In this paper, the powerful forward-backward non-linear filter and wavelet-based denoising method are introduced to remove the high level of noise embedded in financial time series. With the filtered time series, the statistical model known as autoregression is utilized to model the historical times aeries and make the prediction. The proposed models and approaches have been evaluated using the sample time series, and the experimental results have proved that the proposed approaches are able to make the precise prediction very efficiently and effectively.
文摘Water level prediction of river runoff is an important part of hydrological forecasting.The change of water level not only has the trend and seasonal characteristics,but also contains the noise factors.And the water level prediction ability of a single model is limited.Since the traditional ARIMA(Autoregressive Integrated Moving Average)model is not accurate enough to predict nonlinear time series,and the WNN(Wavelet Neural Network)model requires a large training set,we proposed a new combined neural network prediction model which combines the WNN model with the ARIMA model on the basis of wavelet decomposition.The combined model fit the wavelet transform sequences whose frequency are high with the WNN,and the scale transform sequence which has low frequency is fitted by the ARIMA model,and then the prediction results of the above are reconstructed by wavelet transform.The daily average water level data of the Liuhe hydrological station in the Chu River Basin of Nanjing are used to forecast the average water level of one day ahead.The combined model is compared with other single models with MATLAB,and the experimental results show that the accuracy of the combined model is improved by 7%compared with the traditional wavelet network under the appropriate wavelet decomposition function and the combined model parameters.
文摘Structural health monitoring(SHM)is a vast,interdisciplinary research field whose literature spans several decades with focusing on condition assessment of different types of structures including aerospace,mechanical and civil structures.The need for quantitative global damage detection methods that can be applied to complex structures has led to vibration-based inspection.Statistical time series methods for SHM form an important and rapidly evolving category within the broader vibration-based methods.In the literature on the structural damage detection,many time series-based methods have been proposed.When a considered time series model approximates the vibration response of a structure and model coefficients or residual error are obtained,any deviations in these coefficients or residual error can be inferred as an indication of a change or damage in the structure.Depending on the technique employed,various damage sensitive features have been proposed to capture the deviations.This paper reviews the application of time series analysis for SHM.The different types of time series analysis are described,and the basic principles are explained in detail.Then,the literature is reviewed based on how a damage sensitive feature is formed.In addition,some investigations that have attempted to modify and/or combine time series analysis with other approaches for better damage identification are presented.
基金This paper is partially supported by the basic scientific research business expenses of Universities in Xinjiang,China[Grant Number XQZX20230057]the National Natural Science Foundation of China[Grant Number 11671142].
文摘In the paper,the autoregressive moving average model for matrix time series(MARMA)is inves-tigated.The properties of the MARMA model are investigated by using the conditional least square estimation,the conditional maximum likelihood estimation,the projection theorem in Hilbert space and the decomposition technique of time series,which include necessary and suf-ficient conditions for stationarity and invertibility,model parameter estimation,model testing and model forecasting.
基金supported by Research Grants Council of Hong Kong (Grant No. HKBU2-030/07P)Wu Jianhong was also supported by a grant from Humanities and Social Sciences in Chinese University(Grant No.07JJD790154)+1 种基金Science Fund for Young Scholars of Zhejiang Gongshang University (Grant No. Q09-12)Zhejiang Provincial Natural Science Foundation of China (Grant No.Y6090172)
文摘The paper proposes and studies some diagnostic tools for checking the goodness-of-fit of general parametric vector autoregressive models in time series. The resulted tests are asymptotically chi-squared under the null hypothesis and can detect the alternatives converging to the null at a parametric rate. The tests involve weight functions,which provides us with the flexibility to choose scores for enhancing power performance,especially under directional alternatives. When the alternatives are not directional,we construct asymptotically distribution-free maximin tests for a large class of alternatives. A possibility to construct score-based omnibus tests is discussed when the alternative is saturated. The power performance is also investigated. In addition,when the sample size is small,a nonparametric Monte Carlo test approach for dependent data is proposed to improve the performance of the tests. The algorithm is easy to implement. Simulation studies and real applications are carried out for illustration.
文摘When linear regressive models such as AR or ARMA model are used for fitting and predicting climatic time series,results are often not sufficiently good because nonlinear variations in the time series.In this paper, a nonlinear self-exciting threshold autoregressive(SETAR)model is applied to modeling and predicting the time series of flood/drought runs in Beijing,which were derived from the graded historical flood/drought records in the last 511 years(1470—1980).The results show that the modeling and predicting with the SETAR model are much better than that of the AR model.The latter can predict the flood/drought runs with a length only less than two years,while the formal can predict more than three-year length runs.This may be due to the fact that the SETAR model can renew the model according to the run-turning points in the process of predic- tion,though the time series is nonstationary.
基金grant from the Research Grants Council of Hong Kong
文摘This paper is devoted to the goodness-of-fit test for the general autoregressive models in time series. By averaging for the weighted residuals, we construct a score type test which is asymptotically standard chi-squared under the null and has some desirable power properties under the alternatives. Specifically, the test is sensitive to alternatives and can detect the alternatives approaching, along a direction, the null at a rate that is arbitrarily close to n-1/2. Furthermore, when the alternatives are not directional, we construct asymptotically distribution-free maximin tests for a large class of alternatives. The performance of the tests is evaluated through simulation studies.
基金Project supported by the Scientific Research Foundation for the Returned 0verseas Chinese Scholars of China （Grant No 2004.176.4） and the Natural Science Foundation of Shandong Province of China （Grant No Z2004G01）.
文摘A new method is proposed to determine the optimal embedding dimension from a scalar time series in this paper. This method determines the optimal embedding dimension by optimizing the nonlinear autoregressive prediction model parameterized by the embedding dimension and the nonlinear degree. Simulation results show the effectiveness of this method. And this method is applicable to a short time series, stable to noise, computationally efficient, and without any purposely introduced parameters.
文摘Time headway is an important index used in characterizing dangerous driving behaviors. This research focuses on the decreasing tendency of time headway and investigates its association with crash occurrence. An autoregressive（AR） time-series model is improved and adopted to describe the dynamic variations of average daily time headway. Based on the model, a simple approach for dangerous driving behavior recognition is proposed with the aim of significantly decreasing headway. The effectivity of the proposed approach is validated by means of empirical data collected from a medium-sized city in northern China. Finally, a practical early-warning strategy focused on both the remaining life and low headway is proposed to remind drivers to pay attention to their driving behaviors and the possible occurrence of crash-related risks.
文摘We consider a time series following a simple linear regression with first-order autoregressive errors belonging to the class of heavy-tailed distributions. The proposed model provides a useful generalization of the symmetrical linear regression models with independent error, since the error distribution covers both correlated innovations following a Generalized Exponential distribution. Furthermore, we derive the modified maximum likelihood (MML) estimators as an efficient alternative for estimating model parameters. Finally, we investigate the asymptotic properties of the proposed estimators. Our findings are also illustrated through a simulation study.
