Distributions of Correlation Coefficients in Economic Time Series
经济时间序列相关系数的分布AI 解读 ↓
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AI 根据所提供的论文材料归类：摘要研究经济时间序列的相关、自相关、趋势处理及线性差分方程，直接对应时间序列。
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经济时间序列相关系数的分布
- 研究问题
- 历史经济时间序列的相关和自相关系数呈现怎样的经验分布，取对数、去除线性趋势及改变滞后会产生什么影响？
- 方法与思路
- 作者从美国历史统计资料随机抽取一百条二十五年序列，计算原始及对数数据在不同趋势处理下的相关系数分布。
- 材料陈述的贡献
- 摘要报告自相关分布的若干经验规律及较高的交叉相关，并提出这些抽样分布可为经济序列相关显著性检验提供依据。
- 阅读关注点
- 应核对序列抽取与分类方式、趋势校正和滞后设置，以及经验显著性基准与低阶差分方程描述的具体构造。
- 阅读边界
- 仅据版本未注明的 OpenAlex 摘要；结果来自特定历史资料和抽样实验，不能视为任意经济序列的分布定律或因果关系证据。
原文摘要
This paper presents results, mainly in tabular form, of a sampling experiment in which 100 economic time series 25 years long were drawn at random from the Historical Statistics for the United States. Sampling distributions of coefficients of correlation and autocorrelation were computed using these series, and their logarithms, with and without correction for linear trend. We find that the frequency distribution of autocorrelation coefficients has the following properties: a. It is roughly invariant under logarithmic transformation of data.b. It is approximated by a Pearson Type XII function.c. It approaches a rectangular distribution symmetric about 0 as the lag increases. The autocorrelation properties observed are not to be explained by linear trends alone. Correlations and lagged cross-correlations are quite high for all classes of data. E.g., given a randomly selected series, it is possible to find, by random drawing, another series which explains at least 50 per cent of the variances of the first one, in from 2 to 6 random trials, depending on the class of data involved. The sampling distributions obtained provide a basis for tests of significance of correlations of economic time series. We also find that our economic series are well described by exact linear difference equations of low order.