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首页> 外文期刊>Journal of Time Series Analysis >PROPERTIES OF THE POWER ENVELOPE FOR TESTS AGAINST BOTH STATIONARY AND EXPLOSIVE ALTERNATIVES: THE EFFECT OF TRENDS
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PROPERTIES OF THE POWER ENVELOPE FOR TESTS AGAINST BOTH STATIONARY AND EXPLOSIVE ALTERNATIVES: THE EFFECT OF TRENDS

机译：针对平稳和爆炸性替代品的测试的功率包络的性质：趋势的影响

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摘要

This article details a precise analytic effect that inclusion of a linear trend has on the power of Neyman-Pearson point optimal unit root tests and thence the power envelope. Both stationary and explosive alternatives are considered. The envelope can be characterized by probabilities for two, related, sums of Chi-square random variables. A stochastic expansion, in powers of the local-to-unity parameter, of the difference between these loses its leading term when a linear trend is included. This implies that the power envelope converges to size at a faster rate, which can then be exploited to prove that the power envelope must necessarily be lower. This effect is shown to be, analytically, greater asymptotically than in small samples and numerically far greater for explosive than for stationary alternatives. Only a linear trend has a specific rate effect on the power envelope, however other deterministic variables will have some effect. The methods of the article lead to a simple direct measure of this effect which is then informative about power, in practice.
机译：本文详细介绍了精确的分析效果，包括线性趋势对Neyman-Pearson点最优单位根检验的功效以及因此的功效包络。固定式和爆炸式替代品均被考虑。包络可以通过两个相关的卡方随机变量之和的概率来表征。当包含线性趋势时，局部变量到局部变量的幂的随机扩展将失去它们之间的先导项。这意味着功率包络以更快的速率收敛到尺寸，然后可以利用它证明功率包络必须更低。从分析上看，这种影响在渐近性上要比小样本大，而对于爆炸物，在数值上要远大于固定的选择。只有线性趋势对功率包络有特定的速率影响，但是其他确定性变量也会有一定影响。本文的方法可导致对该效果的简单直接测量，然后在实践中提供有关功率的信息。

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