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Accordingly, there are several nonlinear modeling approaches provided to tackle the complexity of nonlinear time series, the approaches can be generally divided into three categories: parametric, semiparametric, and nonparametric model. Actually nonlinear statistical time series analysis started its research on parametric modeling about two decades ago for the motivation to overcome the limitations of the linear models in revealing nonlinear phenomena such as limit cycle. Two typical parametric nonlinear time series models are the exponential autoregressive (ExpAR) model and the threshold autoregressive model, they have been wellknown in describing several typical nonlinear behaviors. However, it has been argued recently that the parametric models are hard to justify a priori the universal description appropriateness in most real applications to complex dynamic systems analysis. Moreover, the parametric modeling approach as the traditional statistical nonlinear time series analysis methodology has been faced with the serious challenges from neural network techniques and deterministic dynamic theory. In this situation, the nonparametric identification such as non parametric density estimation of nonlinear time series became popular being an alternative paradigm of modeling in recent years. The nonparametric models allow for great flexibility without confining oneself to a special parametric model, however, this approach still has some drawbacks such as the curse of dimensionality, which hinder its wide application. Therefore the semiparametric modeling is introduced in order to evade the limitations of nonparametric approach, although some of the semiparametric models lose their generality simultaneously so that they seem limited to be applicable for some particular cases, and the boundary between parametric and some semiparametric models become not sharp.\u003cbr /\u003e Since the parametric approach can be easily interpreted, and in turn the dynamic mechanism of the underlying systems can be looked for, this study focuses on nonlinear time series analysis by one of the parametric model, the exponential autoregressive model and its general version, with comparison to other approaches. The thesis gives a deep investigation into the properties of the model, and shows the performance of the ExpAR modeling in identification and prediction as two important issues in the statistical analysis of time series. The details of the thesis are summarized as follows.\u003cbr /\u003e First, the classic exponential autoregressive model is introduced to nonlinear time series analysis. The ExpAR model looks very simple in structure, it is basically the AR model but the statedependent coefficients. Then the dynamics of the ExpAR model is investigated. By calculating the Lyapunov exponent and the bifurcation of the ExpAR model, it is found that even very simple ExpAR may behave very complicated dynamics such as fixed point, limit cycle and chaos. Several typical chaotic phenomena like perioddouble bifurcation, intermittency and synchronization occur in the simple ExpAR model too. So we can let the ExpAR model reveal rich different nonlinear behaviors just by controlling the parameters and the delay dimension. This can be a solid evidence to accept the ExpAR model to identify some complex data since the model is originally provided to model time series instead of as an analytical model like Logistic equation and others. However, from the standout of practitioner, the model estimate, as a nonlinear optimization problem, becomes obviously important since minor difference in the values of parameters may result in large different dynamics. Actually the ExpAR model estimate has not been yet well solved. In this study, the genetic algorithm is applied to solve this problem, and several procedures are provided. The procedures take mutual estimation, in which the first one is to use the genetic algorithm to determine the scaling parameter in the model, and then other linear weights are estimated by linear least squares. In another procedure, the genetic algorithm is used to optimize both the model structure and the nonlinear scaling parameter. We therefore name the procedures as the selforganization modeling. As a byproduct of the selforganizing procedure, we can get a subset ExpAR model that is of importance to dimensionality reduction. The efficiency of the estimates is shown by the numerical examples. \u003cbr /\u003e Secondly, the investigation of applying the ExpAR model to machine tool chatter monitoring system design is carried out. According to the fact that machine tool chatter is a nonlinear selfexcited oscillation of limit cycle type, we provide the limit cycle behavior to be the intrinsic index of chatter occurrence, and the ExpAR model is proposed to detect the index from online cutting signal. Consider the actual implementation of the proposal, a realtime estimation of the ExpAR model is provided to satisfy the needs of online monitoring system design. Actual cutting signal analysis shows the effectiveness of the proposal.\u003cbr /\u003e Thirdly, the generalized exponential autoregressive modeling is considered to complex time series analysis. The classic ExpAR model is actually a kind of statedependent AR model in which only the amplitude is taken as the state. However, it can be imagined that the coefficients of the model are not necessarily dependent on one state, for some complex data, the coefficients of ExpAR model should be dependent on several states, say state vector. Therefore we introduce state vectorbased ExpAR model, namely generalized ExpAR model, to nonlinear time series analysis, in which the coefficients are Gaussianproduct functions (Gaussian radial basis function) of state vector. We prove that the geometric ergodic condition of the generalized exponential autoregressive model is still the same as that of the classic Expel model since factorizable property of the Gaussian radial basis function. Thus the stability of the model can be expected. For the estimate of the generalized ExpAR model, we provide a mutual estimating procedure which hybridizes the multiagent random optimization algorithm namely evolutionary programming with the ordinary least squares to estimate the unknown parameters in the model. Simulations show the efficient ability of the generalized ExpAR model to dynamics reconstruction and prediction error reduction.\u003cbr /\u003e Finally, empirical investigation of statistical identification of several actual nonlinear time series is given. We introduce three typical models respectively belonged to nonparametric conditional mean estimator (NadarayaWatson estimator), semiparametric model (radial basis function network) and local linearization model (generalized exponential autoregressive) to analyze the epilepsy EEG (spike and wave) and human pulse wave (quasiperiodicity). Empirical comparisons show that the nonparametric estimator is of advantage to dynamics reconstruction, the local linearization model is good at forecasting for short term horizon, and the semiparametric model has its site between the above models.", "subitem_description_type": "Other"}]}, "item_1_description_7": {"attribute_name": "学位記番号", "attribute_value_mlt": [{"subitem_description": "総研大乙第61号", "subitem_description_type": "Other"}]}, "item_1_select_14": {"attribute_name": "所蔵", "attribute_value_mlt": [{"subitem_select_item": "有"}]}, "item_1_select_8": {"attribute_name": "研究科", "attribute_value_mlt": [{"subitem_select_item": "数物科学研究科"}]}, "item_1_select_9": {"attribute_name": "専攻", "attribute_value_mlt": [{"subitem_select_item": "15 統計科学専攻"}]}, "item_1_text_10": {"attribute_name": "学位授与年度", "attribute_value_mlt": [{"subitem_text_value": "1998"}]}, "item_1_text_20": {"attribute_name": "業務メモ", "attribute_value_mlt": [{"subitem_text_value": "（2018年2月13日）本籍など個人情報の記載がある旧要旨・審査要旨を個人情報のない新しいものに差し替えた。承諾書等未確認。要確認該当項目修正のこと。"}]}, "item_creator": {"attribute_name": "著者", "attribute_type": "creator", "attribute_value_mlt": [{"creatorNames": [{"creatorName": "SHI, Zhaoyun", "creatorNameLang": "en"}], "nameIdentifiers": [{"nameIdentifier": "8962", "nameIdentifierScheme": "WEKO"}]}]}, "item_files": {"attribute_name": "ファイル情報", "attribute_type": "file", "attribute_value_mlt": [{"accessrole": "open_date", "date": [{"dateType": "Available", "dateValue": "20160217"}], "displaytype": "simple", "download_preview_message": "", "file_order": 0, "filename": "乙61_要旨.pdf", "filesize": [{"value": "351.8 kB"}], "format": "application/pdf", "future_date_message": "", "is_thumbnail": false, "licensetype": "license_11", "mimetype": "application/pdf", "size": 351800.0, "url": {"label": "要旨・審査要旨 / Abstract, Screening Result", "url": "https://ir.soken.ac.jp/record/743/files/乙61_要旨.pdf"}, "version_id": "f44aa1273c3b4bd1a3de403da22c06e8"}]}, "item_language": {"attribute_name": "言語", "attribute_value_mlt": [{"subitem_language": "eng"}]}, "item_resource_type": {"attribute_name": "資源タイプ", "attribute_value_mlt": [{"resourcetype": "thesis", "resourceuri": "http://purl.org/coar/resource_type/c_46ec"}]}, "item_title": "Nonlinear time series analysis by the generalized exponentiol autoregressive model and its applications", "item_titles": {"attribute_name": "タイトル", "attribute_value_mlt": [{"subitem_title": "Nonlinear time series analysis by the generalized exponentiol autoregressive model and its applications"}, {"subitem_title": "Nonlinear time series analysis by the generalized exponentiol autoregressive model and its applications", "subitem_title_language": "en"}]}, "item_type_id": "1", "owner": "1", "path": ["17"], "permalink_uri": "https://ir.soken.ac.jp/records/743", "pubdate": {"attribute_name": "公開日", "attribute_value": "20100222"}, "publish_date": "20100222", "publish_status": "0", "recid": "743", "relation": {}, "relation_version_is_last": true, "title": ["Nonlinear time series analysis by the generalized exponentiol autoregressive model and its applications"], "weko_shared_id": 1}
Nonlinear time series analysis by the generalized exponentiol autoregressive model and its applications
https://ir.soken.ac.jp/records/743
https://ir.soken.ac.jp/records/7435040e86935964d2cb58d69385c1e6dbc
名前 / ファイル  ライセンス  アクション 

要旨・審査要旨 / Abstract, Screening Result (351.8 kB)

Item type  学位論文 / Thesis or Dissertation(1)  

公開日  20100222  
タイトル  
タイトル  Nonlinear time series analysis by the generalized exponentiol autoregressive model and its applications  
タイトル  
言語  en  
タイトル  Nonlinear time series analysis by the generalized exponentiol autoregressive model and its applications  
言語  
言語  eng  
資源タイプ  
資源タイプ識別子  http://purl.org/coar/resource_type/c_46ec  
資源タイプ  thesis  
著者名 
施, 招雲
× 施, 招雲 

フリガナ 
セ, ショウウン
× セ, ショウウン 

著者 
SHI, Zhaoyun
× SHI, Zhaoyun 

学位授与機関  
学位授与機関名  総合研究大学院大学  
学位名  
学位名  博士（学術）  
学位記番号  
内容記述タイプ  Other  
内容記述  総研大乙第61号  
研究科  
値  数物科学研究科  
専攻  
値  15 統計科学専攻  
学位授与年月日  
学位授与年月日  19990324  
学位授与年度  
1998  
要旨  
内容記述タイプ  Other  
内容記述  Due to the complexity and nonlinear variety of the real world, nonlinear time series analysis has become one topics of the most popular interest. Accordingly, there are several nonlinear modeling approaches provided to tackle the complexity of nonlinear time series, the approaches can be generally divided into three categories: parametric, semiparametric, and nonparametric model. Actually nonlinear statistical time series analysis started its research on parametric modeling about two decades ago for the motivation to overcome the limitations of the linear models in revealing nonlinear phenomena such as limit cycle. Two typical parametric nonlinear time series models are the exponential autoregressive (ExpAR) model and the threshold autoregressive model, they have been wellknown in describing several typical nonlinear behaviors. However, it has been argued recently that the parametric models are hard to justify a priori the universal description appropriateness in most real applications to complex dynamic systems analysis. Moreover, the parametric modeling approach as the traditional statistical nonlinear time series analysis methodology has been faced with the serious challenges from neural network techniques and deterministic dynamic theory. In this situation, the nonparametric identification such as non parametric density estimation of nonlinear time series became popular being an alternative paradigm of modeling in recent years. The nonparametric models allow for great flexibility without confining oneself to a special parametric model, however, this approach still has some drawbacks such as the curse of dimensionality, which hinder its wide application. Therefore the semiparametric modeling is introduced in order to evade the limitations of nonparametric approach, although some of the semiparametric models lose their generality simultaneously so that they seem limited to be applicable for some particular cases, and the boundary between parametric and some semiparametric models become not sharp.<br /> Since the parametric approach can be easily interpreted, and in turn the dynamic mechanism of the underlying systems can be looked for, this study focuses on nonlinear time series analysis by one of the parametric model, the exponential autoregressive model and its general version, with comparison to other approaches. The thesis gives a deep investigation into the properties of the model, and shows the performance of the ExpAR modeling in identification and prediction as two important issues in the statistical analysis of time series. The details of the thesis are summarized as follows.<br /> First, the classic exponential autoregressive model is introduced to nonlinear time series analysis. The ExpAR model looks very simple in structure, it is basically the AR model but the statedependent coefficients. Then the dynamics of the ExpAR model is investigated. By calculating the Lyapunov exponent and the bifurcation of the ExpAR model, it is found that even very simple ExpAR may behave very complicated dynamics such as fixed point, limit cycle and chaos. Several typical chaotic phenomena like perioddouble bifurcation, intermittency and synchronization occur in the simple ExpAR model too. So we can let the ExpAR model reveal rich different nonlinear behaviors just by controlling the parameters and the delay dimension. This can be a solid evidence to accept the ExpAR model to identify some complex data since the model is originally provided to model time series instead of as an analytical model like Logistic equation and others. However, from the standout of practitioner, the model estimate, as a nonlinear optimization problem, becomes obviously important since minor difference in the values of parameters may result in large different dynamics. Actually the ExpAR model estimate has not been yet well solved. In this study, the genetic algorithm is applied to solve this problem, and several procedures are provided. The procedures take mutual estimation, in which the first one is to use the genetic algorithm to determine the scaling parameter in the model, and then other linear weights are estimated by linear least squares. In another procedure, the genetic algorithm is used to optimize both the model structure and the nonlinear scaling parameter. We therefore name the procedures as the selforganization modeling. As a byproduct of the selforganizing procedure, we can get a subset ExpAR model that is of importance to dimensionality reduction. The efficiency of the estimates is shown by the numerical examples. <br /> Secondly, the investigation of applying the ExpAR model to machine tool chatter monitoring system design is carried out. According to the fact that machine tool chatter is a nonlinear selfexcited oscillation of limit cycle type, we provide the limit cycle behavior to be the intrinsic index of chatter occurrence, and the ExpAR model is proposed to detect the index from online cutting signal. Consider the actual implementation of the proposal, a realtime estimation of the ExpAR model is provided to satisfy the needs of online monitoring system design. Actual cutting signal analysis shows the effectiveness of the proposal.<br /> Thirdly, the generalized exponential autoregressive modeling is considered to complex time series analysis. The classic ExpAR model is actually a kind of statedependent AR model in which only the amplitude is taken as the state. However, it can be imagined that the coefficients of the model are not necessarily dependent on one state, for some complex data, the coefficients of ExpAR model should be dependent on several states, say state vector. Therefore we introduce state vectorbased ExpAR model, namely generalized ExpAR model, to nonlinear time series analysis, in which the coefficients are Gaussianproduct functions (Gaussian radial basis function) of state vector. We prove that the geometric ergodic condition of the generalized exponential autoregressive model is still the same as that of the classic Expel model since factorizable property of the Gaussian radial basis function. Thus the stability of the model can be expected. For the estimate of the generalized ExpAR model, we provide a mutual estimating procedure which hybridizes the multiagent random optimization algorithm namely evolutionary programming with the ordinary least squares to estimate the unknown parameters in the model. Simulations show the efficient ability of the generalized ExpAR model to dynamics reconstruction and prediction error reduction.<br /> Finally, empirical investigation of statistical identification of several actual nonlinear time series is given. We introduce three typical models respectively belonged to nonparametric conditional mean estimator (NadarayaWatson estimator), semiparametric model (radial basis function network) and local linearization model (generalized exponential autoregressive) to analyze the epilepsy EEG (spike and wave) and human pulse wave (quasiperiodicity). Empirical comparisons show that the nonparametric estimator is of advantage to dynamics reconstruction, the local linearization model is good at forecasting for short term horizon, and the semiparametric model has its site between the above models.  
所蔵  
値  有 