Logarithmic transformations instead of Box-Cox

[AhmedThahir]

Hi team
This is regarding Mathematical Transformations: https://otexts.com/fpp3/transformations.html#mathematical-transformations

For positive forecasts, I can think of an alternative to the modified Box-Cox transformation:

$$ w_t = \log_b y_t $$

where $b=$ base of logarithm operation

• When $b=1$, we get no change
• When $b=e$, we get a natural logarithm
• When $b<e$, we get a weaker stabilization than natural logarithm
• When $b>e$, we get a stronger stabilization than natural logarithm

We would run a solver to get the b closest to 1 such that it stabilizes the series.

This way we can get the ease-of-interpretation that we get from logarithms while stabilizing the series. For eg, if $b=10$, we get powers of 10

I would like to get your team's opinion on this.

[robjhyndman]

Note that $\log_b y_t = \log_e y_t / \log_e b$, so taking a different base is only scaling the resulting transformation, not making it stronger or weaker.

[AhmedThahir]

Yes, that would make sense. Got it!