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乔若羽 · 2025年06月07日

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NO.PZ202405210200000102

问题如下:

When Morgan considers the limitations of historical estimates, which of the following is most likely correct?

选项:

A.When many variables are considered, a larger number of observations is not a statistical necessity. B.The analyst should use the longest data history for which there is a reasonable assurance of stationarity. C.Using higher-frequency data (e.g., monthly, rather than annual observations) will provide more precise estimates, since this will improve the precision of the sample mean.

解释:

Answer Choice (A) is incorrect: when many variables are considered, a large number of observations may be a statistical necessity. Answer Choice (C) is also incorrect: although it is tempting to assume that using higher-frequency data (e.g., monthly rather than annual observations) will also provide more precise estimates, this assumption is not necessarily true. Although higher-frequency data improve the precision of sample variances, covariances and correlations, they do not improve the precision of the sample mean.

选项(A)是错误的:当考虑众多变量时,从统计角度而言,大量的观测数据可能是必要的。选项(C)同样错误:尽管人们很容易认为使用更高频率的数据(例如,采用月度观测数据而非年度观测数据)也能得出更精确的估计值,但这一假设并不一定成立。虽然更高频率的数据能提高样本方差、协方差和相关性的精确程度,但它们并不能提高样本均值的精确程度。

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