TESTING FOR AUTOCORRELATION IN DYNAMIC LINEAR-MODELS
TESTING FOR AUTOCORRELATION IN DYNAMIC LINEAR-MODELS
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DOI：
10.1111/j.1467-8454.1978.tb00635.x
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发表时间：
1978-01-01
影响因子：
1.9
通讯作者：
BREUSCH, TS
中科院分区：
文献类型：
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作者：
BREUSCH, TS
在第二节中，讨论了德宾推导的一般哲学。在某些地方，论点被简化了，有些观点如果对随后的发展很重要，就会被放大。德宾的要求是只使用那些施加了零假设的估计来获得检验统计量。因此，它可能与Aitchison和Silvey的拉格朗日乘数(LM)方法密切相关[2]。这种关系在第三节和第四节中进行了探讨。第三节在Durbin的一般讨论框架中讨论了LM检验，在第四节中推导了动态模型中抗自回归扰动检验的LM统计量。结论是，Lm统计量和Durbin统计量是渐近等价的，但不同之处在于，Durbin统计量使用自回归参数的估计，而Lm统计量使用OLS残差的简单自相关。在第五节中，考虑了一些特殊情况。除了常见的一阶自相关的Durbin h统计量外，还得到了简单第k阶统计量的一般形式的简化和一、四阶联合统计量的重要情形。Durbin检验与Box和Piells的检验[3]之间的关系并不是一目了然的，但本文说明了后者是如何通过附加近似从LM统计量中获得的。德宾为另一种假设是扰动遵循自回归(AR)过程的情况开发了他的测试。Fitts[6]曾尝试使用相同的一般方法来检验扰动是由移动平均(MA)产生的这一假设，但他的方法并不是非常可行。在第六节中，我们对这种情况进行了LM检验，得到了令人惊讶的结果，即统计量与AR情况下的完全相同。将LM方法应用于复合(ARMA)干扰测试的可能性是...
In section II, the general philosophy of Durbin's derivation is discussed. The argument is, in places, simplified and some points are amplified if they are important for the developments which follow. Durbin's requirement was to obtain a test statistic using only those estimates obtained with the null hypothesis imposed. Therefore, it might be expected to be closely related to the Lagrange multiplier (LM) approach of Aitchison and Silvey [2]. This relationship is explored in sections III and IV. Section III has a discussion of the LM test in the framework adopted by Durbin for his general discussion and in section IV the LM statistic for testing against autoregressive disturbances in a dynamic model is derived. The conclusion is that the LM and Durbin statistics are asymptotically equivalent but differ in that Durbin's statistic uses estimates of autoregressive parameters while the LM statistic uses simple autocorrelations of the OLS residuals. In section V some special cases are considered. Apart from the familiar Durbin h-statistic for first order autocorrelation, the simplifications of the general form of the statistic for simple kth order and the important case of joint first and fourth are obtained. The relationship between Durbin's test and that of Box and Pierce [3] is not immediately apparent but it is shown how the latter may be obtained from the LM statistic by additional approximations. Durbin developed his test for the case where the alternative hypothesis is that the disturbances follow an autoregressive (AR) process. Fitts [6] has attempted to use the same general method to obtain a test against the hypothesis that the disturbances are generated by a moving average (MA) but his procedure is not very practicable. In section VI the LM test is obtained for this situation with the surprising result that the statistic is exactly the same as in the AR case. The possibility of applying the LM approach to testing for composite (ARMA) disturbances is...