I'm doing some class work, and I need to use what is called 'log-return variable'. Which is transform each data value $D_n$ to $R_n = \log\Big(\frac{D_n}{D_{n-1}}\Big)$.
I'm guessing that the interest of this transformation is to see if the data is getting bigger or smaller, depending if $R_n$ is positive or negative.
But I know that I am not understanding something key about it. If that was its use, checking if $\frac{D_n}{D_{n-1}}$ is bigger or smaller than $1$ would do the trick.
Can someone give me some intuition of the log-return transformation? Thank you.
The intuition behind is that the logarithm turns power-like behaviors into linear behaviors. For example if $y=x^2$ the relation between logarithms is linear $$ \log y = 2\log x, $$ so if you see a straight line in the logarithmic plane, the dependence is actually power-like and the power is equal to the slope of the line.