A Large‐Sample Test for the Goodness of Fit of Autoregressive Schemes
A Large‐Sample Test for the Goodness of Fit of Autoregressive Schemes
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DOI：
10.1111/j.2397-2335.1947.tb04730.x
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发表时间：
1947-03
影响因子：
--
通讯作者：
M. H. Quenouille
中科院分区：
文献类型：
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作者：
M. H. Quenouille
A similar application confirms that R, and Rt are uncorrelated. Thus, if we wish to test the legitimacy of assuming an autoregressive'scheme Un+ 2+-aUn+? J+ bun=? n2'we can use the estimates a 1l-r12, b= 1 r2--1 and test that-r 2 I-r12 r8+ 2+ 2a rs+?,-(a2+ 2b) r,-L 2abr, _1+ b2r82= R,, s-1, 2, are distributed with mean zero, and variance! This approximation are L~~~~~~~~~~~~ 1+ b Ti prxmto can be improved still further by the use of ns instead of n. To illustrate the method we shall consider firstly artificial series, for which a and b are known, and secondly series experienced in practice, for which a and b have been calculated. The adequacy of the usual methods of fitting an autoregressive scheme and its suitability for the representation of practical results will not be discussed here, but a discussion of these problems will be given elsewhere (Quenouille and Orcutt, 1947b).
