jagartner建议的方法很好，如果您想分析给定术语的季度频率变化，只考虑孤立的术语。它不做的是评估与语料库中所有其他术语相比的相对频率。为此，您可以按季度比较所有术语的频率排名。这是 Zipf 定律中使用的分析。此分析的另一个优点是您可以测试生成过程是否静止（例如，由相同的分布季度到季度控制）。

比较频率等级的优点是它不依赖于每个季度的语料库的相对大小（只要它们都是“大”的）。简单来说，无论（美国英语新闻）语料库是10,000 篇还是1,000,000 篇文章，“圣诞节”这个词在第4 季度出现的频率排名大概都一样。

如果您希望在这种情况下计算一个单词的相对重要性，您可以考虑按季度进行逆文档频率评分： tf-idf

一旦你从一个季度到另一个季度获得了语料库中所有单词的逆频率分数，你就可以通过所有分数的范围进行归一化，然后进行一个季度到一个季度的比较。

如果您尝试进行预测，前几年的历史数据将非常有用。您可以通过对历史数据进行回归并标准化为该年的预测文档输出来找到一年中的趋势。

之前的两个答案都采用了一种有趣的方法，但都没有真正解决我的问题；如何以统计严格的方式比较给定术语频率随时间的变化，并与同一时期的其他术语进行比较，该方法考虑了术语频率随集合大小的幂律分布。

下面的答案是我迄今为止在这个问题上的工作。无论如何，这不是一个完整的答案，但是我将其发布在这里以征求反馈和改进建议。

以齐夫定律的定义为例，

$f(r) \sim z_{max} r^{-\alpha}$

here, $r$ is the rank of a given term, $z_{max}$ is the frequency of the most frequent term, $\alpha$ is Zipf's exponent, and $f(r)$ is the frequency of the r-th ranked term.

Taking the log of both sides, you get a linear relationship between $log(f)$ and $log(r)$, with gradient $-\alpha$ and intercept $z_{max}$

$log(f) \sim log(z_{max}) - \alpha log(r)$

We want to find the expected frequency of a single term over a given period. First, split the period into equal sized windows. For the first window, $i$, we know the frequency of our term $f_i$, and the frequency of the largest term $z_{max,i}$ and $\alpha$. We can use these to find the rank of our term,

$r \sim \left(\frac{f_i(r)}{z_{max,i}}\right)^{-\alpha}$

This rank can then be used to calculate the 'expected' frequency for all subsequent time windows, which I'll indicate with $\hat{f}$,

$\hat{f}_{i+1}(r) \sim z_{max,i+1} r^{\alpha(i+1)}$

The ratio $\frac{\hat{f}}{f}$ represents the normalised frequency.

Some observations:

1. For a stationary underlying distribution, this approach identifies minor deviations from the expected frequency of a term. A moving window could be used if the underlying text distribution changes dramatically, or exhibits seasonal behaviour.
2. The initial choice of $r$ could be calculated for the entire period, rather than the first window.
3. $\alpha$ could be calculated from the raw term and total frequency counts using heap's law (see Lu et al. 2010 for a derivation of Heap's law from Zipf's).
4. This approach assumes a linear relationship between $f$ and $r$ in log space.