| 时间序列模型Back算子多项式的可逆性 |
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| 引用本文： | 陈勇明,戴奇华,尹音频. 时间序列模型Back算子多项式的可逆性[J]. 数学的实践与认识, 2009, 39(13) |
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| 作者姓名： | 陈勇明 戴奇华 尹音频 |
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| 作者单位： | 1. 成都信息工程学院,数学学院,四川,成都,610225
2. 西南财经大学,财税学院,四川,成都,610074 |
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| 基金项目： | 国家社会科学基金，成都信息工程学院科研基金 |
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| 摘 要： | 定义零算子和单位算子,并定义Back算子多项式的加法运算和乘法运算规则,加法类似于普通的加法运算,乘法为算子的复合运算,于是Back算子多项式构成一个环.回答了时间序列分析中Back算子多项式作除法运算的含义,Back算子多项式和它作用的时间序列Xt之间并非乘积关系,除法运算实质是等式两边同时用算子的逆作用.AR(1)模型、AR(2)模型等的Back算子多项式具有可逆性.
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| 关 键 词： | Back算子 多项式 环 AR(p)模型 ARMA(p,q)模型 可逆性 |
The Invertibility of the Polynomial of Back-operator for Time Series Models |
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| CHEN Yong-ming,DAI Qi-hua,YIN Yin-pin. The Invertibility of the Polynomial of Back-operator for Time Series Models[J]. Mathematics in Practice and Theory, 2009, 39(13) |
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| Authors: | CHEN Yong-ming DAI Qi-hua YIN Yin-pin |
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| Abstract: | Zero operator and identity operator are defined,and the additive operation and multiplying operation are defined for the polynomial of back-operator (PBO),where the additive operation is similar to the normal one while the multiplying operation is a kind of composition operation,then the PBO constructs a ring. The essence of division of PBO is explained as to be the inverse operation of operator. The PBO in AR(1)、AR(2) model and some others are invertible. |
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| Keywords: | ARMA(p |
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