TESTING FOR A CHANGE IN THE PARAMETER VALUES AND ORDER OF AN AUTOREGRESSIVE MODEL
TESTING FOR A CHANGE IN THE PARAMETER VALUES AND ORDER OF AN AUTOREGRESSIVE MODEL
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DOI：
10.1214/aos/1176324468
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发表时间：
1995-02-01
影响因子：
4.5
通讯作者：
YAO, YC
中科院分区：
文献类型：
--
作者：
DAVIS, RA;HUANG, DW;YAO, YC
研究了自回归模型的参数值和阶数是否发生变化的检验问题。研究表明，如果AR模型中的白色噪声具有有限的四阶矩弱平稳，则在无变点的原假设下，归一化高斯似然比检验统计量服从Gumbel极值分布.本文还提出了一种检验AR模型中系数、白色噪声方差或阶数变化的渐近无分布检验方法。在噪声三阶矩为零的假设下，得到了该检验的渐近零分布。这些结果的证明依赖于Horvath对Darling-Erdos关于k维Ornstein-Uhlenbeck过程范数最大值的结果的推广和对相依随机变量部分和的几乎必然逼近。
The problem of testing whether or not a change has occurred in the parameter values and order of an autoregressive model is considered. It is shown that if the white noise in the AR model is weakly stationary with finite fourth moments, then under the null hypothesis of no changepoint, the normalized Gaussian likelihood ratio test statistic converges in distribution to the Gumbel extreme value distribution. An asymptotically distribution-free procedure for testing a change of either the coefficients in the AR model, the white noise variance or the order is also proposed. The asymptotic null distribution of this test is obtained under the assumption that the third moment of the noise is zero. The proofs of these results rely on Horvath's extension of Darling-Erdos' result for the maximum of the norm of a k-dimensional Ornstein-Uhlenbeck process and an almost sure approximation to partial sums of dependent random variables.