Anything wrong with taking the log of an interest rate? Suppose I am looking to forecast the 2 Year Treasury Bond rate with an ARIMA type model. The series is I(1) but its first difference does not look stationary due to non-constant variance. A general rule of thumb is that one way to stabilize the variance is to take the natural log of the series. Is there anything wrong with taking the natural log of an interest rate series? I don't see it done much and I don't understand why. If not, then in this case, the solution could be to take the natural log first and then first difference it to obtain a stationary looking series.
Here is a professor's opinion (that I do not agree with), in which he says "taking logs of an interest rate is pointless (no exponential trend to linearize), taking logs of an exchange rate can make sense (it can stabilize the variance of the time series)." https://www.researchgate.net/post/Log_transformation_of_variables_in_Rates_or_percentage/58f340875b4952592f7d0ff5/citation/download
Here's a sentence from Brockwell and Davis (page 14)"...if the magnitude of the fluctuations appear to grow roughly linearly with the level of the series, the the transformed series {lnX1,...,lnXn} will have fluctuations of more constant magnitude... If some of the data are negative, add a positive before taking logarithms". So negative rates aren't really much of a concern. We can add 1000 to every rate and move forward.
Here's prof. Hyndman on the topic: "Plot a graph of the data against time. If it looks like the variation increases with the level of the series, take logs. Otherwise model the original data." No statement about how this does not apply to interest rates.
https://stats.stackexchange.com/a/6333/198058
I followed prof. Hyndman's advice and plotted the data. The variation decreases with the level - therefore I took the log.

Let’s say that a very low interest rate is of the order of 0.1% and a high interest rate of the order of 10%, so there is a likely range of say two orders of magnitude.
Then logarithmic thinking commits you to regarding the difference between 0.1 and 1% as equivalent to that between 1 and 10%. Is that sensible or accurate economically?
I know as an individual in the economy I don’t believe that at all. I use logarithmic thinking in thinking about house prices -- participants play with adding or subtracting large sums to buy or sell a house -- but not about interest rates.
The deeper question is surely whether e.g. firms, sectors, economies behave that way. What does your data tell you?
If interest rates are ever negative, then transformations such as cube roots, neglog and asinh are available, but the doubt remains whether logarithms help here.
