近单位根近白噪声下 $M$-检验的一个刻画
A Characterization of the $M$-tests Under Nearly Integrated Nearly White Noise
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中文总结 AI 辅助
本文刻画了近单位根近白噪声下 $M$-检验的极限分布，证明其保守性及功效低于高斯包络，并指出 LRV 估计高估问题，模拟显示对大负 MA 系数无统一满意方案。
中文摘要 AI 辅助
我们在 Nabeya 和 Perron (1994) 引入的近单位根近白噪声 (NINW) 框架下，针对未知线性时间趋势的情形，推导了 $M$-检验族单位根统计量的极限分布。在已知长期方差 (LRV) 的情形下，$M^{GLS}$ 检验的极限分布因准差分而受到额外噪声项的污染，而这些项在 $M^{OLS}$ 的极限分布中较少出现，两者在常规临界值下均表现出保守性质。此外，我们证明了 NINW 模型中的高斯功效包络渐近等价于 Elliott, Rothenberg, 和 Stock (1996) 的标准包络，并且 oracle $M$-检验相对于该基准具有低效的功效。接着，我们推导了可行统计量的极限分布，并表明常用的自回归 LRV 估计会高估 LRV，从而产生改变的极限分布。最后，有限样本模拟表明，在所考虑的方法中，对于具有大负移动平均系数的序列，不存在统一令人满意的解决方案。
英文摘要
We derive the limiting distributions of the $M$-test family of unit root statistics in the nearly integrated nearly white noise (NINW) framework introduced by Nabeya and Perron (1994) in the case of an unknown linear time trend. In the case of known long run variance (LRV), the limiting distributions of the $M^{GLS}$ tests are contaminated by additional noise terms as a result of quasi differencing whereas these terms are less present in the $M^{OLS}$ limiting distributions, both of which display conservative properties under conventional critical values. Furthermore, we prove the Gaussian power envelope in the NINW model is asymptotically equivalent to the standard envelope of Elliott, Rothenberg, and Stock (1996), and that the oracle $M$-tests have inefficient power relative to this benchmark. We then derive the limiting distributions of the feasible statistics and show that the autoregressive estimate of the LRV commonly used overestimates the LRV, creating altered limiting distributions. Finally, finite sample simulations illustrate that, of the procedures considered, no uniformly satisfactory solution exists for handling a series with a large negative moving average coefficient.
