时间序列模型Back算子多项式的可逆性

The Invertibility of the Polynomial of Back-operator for Time Series Models

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.

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 he the inverse operation of operator. The PBO in AR （1）, AR （2） model and some others are invertible.