Testing for parameter stability in nonlinear autoregressive models
Testing for parameter stability in nonlinear autoregressive models
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DOI：
10.1111/j.1467-9892.2011.00764.x
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发表时间：
2012-05
影响因子：
0.9
通讯作者：
C. Kirch;Joseph Tadjuidje Kamgaing
中科院分区：
文献类型：
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作者：
C. Kirch;Joseph Tadjuidje Kamgaing
在本文中，我们开发了用于检测非线性自回归过程中结构变化的测试程序。对于检测过程，我们通过单层前馈神经网络对回归函数进行建模。我们表明，基于估计残差累积和的 CUSUM 型检验（已针对线性回归进行了深入研究）可以扩展到这种情况。获得原假设下的极限分布，这是构造渐近检验所需要的。对于一大类替代方案，结果表明检验具有渐近幂一。在这种情况下，我们获得了与检验统计量相关的一致变化点估计量。在小型模拟研究中进一步研究了功率和尺寸，特别强调模型指定错误的情况，即数据不是由神经网络而是由其他回归函数生成的。作为说明，给出了尼罗河数据集以及 S&P 对数回报的应用。
In this article we develop testing procedures for the detection of structural changes in nonlinear autoregressive processes. For the detection procedure, we model the regression function by a single layer feedforward neural network. We show that CUSUM‐type tests based on cumulative sums of estimated residuals, that have been intensively studied for linear regression, can be extended to this case. The limit distribution under the null hypothesis is obtained, which is needed to construct asymptotic tests. For a large class of alternatives, it is shown that the tests have asymptotic power one. In this case, we obtain a consistent change‐point estimator which is related to the test statistics. Power and size are further investigated in a small simulation study with a particular emphasis on situations where the model is misspecified, i.e. the data is not generated by a neural network but some other regression function. As illustration, an application on the Nile data set as well as S&P log‐returns is given.