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在网上用中文搜索“ARMA模型的自协方差”怎么也找不到想要的东西，出来的结果大都是要付钱的期刊论文。我只想找一个入门级的教程而已。

Finding the Autocovariance Function (AVCF) for a general ARMA model

(from the lecture 1.3.2006)

In a general ARMA model we have: , where for convenience of notation.                                          (1)

Let and . Note that for , since future noise values are independent of the observed values.

Determining the cross covariances Multiplying both sides of (1) with and taking expectations, we obtain: ,                                                                                                                               (2)

Since unless .

Since for , (2) is a triangular system of linear equations, and we get: (3)

Thus, the cross-covariances can be obtained by a simple recursion.

Determining the covariances Multiplying both sides of (1) with and taking expectations, we obtain: (4)

The right hand sum in (4) goes from (not ), since for .

(4) is a system of linear equations for the unknown covariances . Note that the same covariance can occur twice in each equation: the first few equations look as follows:    (5)

Note that the right hand sides contain only known values, after the have been found using (3).

Collecting the terms that contain the same covariances, and rearranging into an equation system for the , (5) can be rewritten: (6)

Where the denotes the right hand sand of the equations given by (5). Solving (6) gives the required covariances.

Eivind Damsleth

2006-3-1