以下这个解答很精彩，原汁原味借鉴过来，供大家参考交流。

First difference of LOG = percentage change: When used inconjunction with differencing, logging converts absolute differences into relative (i.e., percentage)differences. Thus, the series DIFF(LOG(Y)) represents the percentage change in Y from period toperiod. Strictly speaking, the percentage change in Y at period t is defined as (Y(t)-Y(t-1))/Y(t-1),which is only approximately equal to LOG(Y(t)) - LOG(Y(t-1)),but the approximation is almost exact if the percentage change is small. In Statgraphics terms, this means that DIFF(Y)/LAG(Y,1) is virtually identical to DIFF(LOG(Y)). If you don't believe me, the attached below is a plot of the percent change in auto sales versus the first difference of its logarithm, zooming in on the last 5 years. The blue and red lines are virtually indistinguishable except at the highest and lowest points.

Data source:https://faculty.fuqua.duke.edu/~rnau/Decision411_2007/411log.htm

另外：论坛上也有其他精彩帖子，可参考：https://bbs.pinggu.org/forum.php?mod=viewthread&tid=982649&page=1
一点感受：要想彻底理解这个问题，需要对数学上”等价无穷小“这一概念有所掌握。