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.

Not a finance expert, but there’s nothing wrong with taking a log transform, provided your values are all greater than zero.
I guess your question is more generally about taking log transforms of values which are percentages? Again, I don’t see an issue. If the transform is useful for improving forecasts and there’s a convenient inverse transform for regaining raw values then it’s all good (again assuming you’ll never want to predict a negative/zero value).
