| ASYMPTOTIC CANONICAL FORMS AND ITERATED LOGARITHM RATE RESULTS OF LEAST SQUARES ESTIMATES FOR UNSTABLE ARMA MODELS |
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| 引用本文： | 张虎明. ASYMPTOTIC CANONICAL FORMS AND ITERATED LOGARITHM RATE RESULTS OF LEAST SQUARES ESTIMATES FOR UNSTABLE ARMA MODELS[J]. 应用数学学报(英文版), 1996, 12(3): 257-277. DOI: 10.1007/BF02011891 |
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| 作者姓名： | 张虎明 |
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| 作者单位： | Department of Mathematics，Shanxi University，Taiyuan 030006，China |
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| 摘 要： | ＡＳＹＭＰＴＯＴＩＣＣＡＮＯＮＩＣＡＬＦＯＲＭＳＡＮＤＩＴＥＲＡＴＥＤＬＯＧＡＲＩＴＨＭＲＡＴＥＲＥＳＵＬＴＳＯＦＬＥＡＳＴＳＱＵＡＲＥＳＥＳＴＩＭＡＴＥＳＦＯＲＵＮＳＴＡＢＬＥＡＲＭＡＭＯＤＥＬＳＺＨＡＮＧＨＵＭＩＮＧ（张虎明）（Ｄｅｐａｒｔｍｅｎ...
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| 收稿时间： | 1992-11-27 |
Asymptotic canonical forms and iterated logarithm rate results of least squares estimates for unstable ARMA models |
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| Huming Zhang. Asymptotic canonical forms and iterated logarithm rate results of least squares estimates for unstable ARMA models[J]. Acta Mathematicae Applicatae Sinica, 1996, 12(3): 257-277. DOI: 10.1007/BF02011891 |
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| Authors: | Huming Zhang |
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| Affiliation: | (1) Department of Mathematics, Shanxi University, 030006 Taiyuan, China |
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| Abstract: | Herein we give the asymptotic canonical forms of the design mains Pn where is an unstable ARMA process B denotes the backshift operator such that B, and p is the order of the polynomial having all roots outside or on the unit circle. These asymptotic canonical forms for Pn, which behave a.s. approximately diagonally, are then used to obtain the itersted logarithm rates of almost sure convergence of the least-squares estimates to the unknown true parameter for an unstable time series. |
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| Keywords: | Unstable ARMA models design matrices asymptotic canonical forms leastsquares estimates iterated logarithm rates |
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