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In the textbook “Forecasting: Principles and Practice (3rd ed)”, at https://otexts.com/fpp3/transformations.html , I see:

“3.1 Transformations and adjustments ...

Mathematical transformations
If the [time series] data shows variation that increases or decreases with the level of the series, then a transformation can be useful. ...

A useful family of transformations, that includes both logarithms and power transformations, is the family of Box-Cox transformations (Box & Cox, 1964), which depend on the parameter λ ...

The guerrero feature (Guerrero, 1993) can be used to choose a value of lambda for you.”

Q. Why do the authors use the Guerrero method, rather than the maximum likelihood estimation (MLE) method (or some other method)?

Q. When the goal is to stabilize the variance of a time series, what are the pros and cons of various methods (Guerrero, MLE, others)?

(Here is the R documentation for feasts:guerrerostrong text guerrero {feasts}, Guerrero's method for Box Cox lambda selection https://search.r-project.org/CRAN/refmans/feasts/html/guerrero.html)

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Maximum likelihood estimation needs a model. What model do you propose? Transformations are usually done as a pre-processing step before modelling.

Guerrero's method does not need a model. It simply tries to balance the coefficient of variation across the subseries.

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  • $\begingroup$ Thanks, I greatly appreciate your response! search.r-project.org/CRAN/refmans/forecast/html/… states "If method=="loglik", the value of lambda is chosen to maximize the profile log likelihood of a linear model fitted to x. For non-seasonal data, a linear time trend is fitted while for seasonal data, a linear time trend with seasonal dummy is used." To clarify my question, what are the pros and cons of estimating lambda using forecast::BoxCox.lambda(x = aus_production_gas_ts, method = "guerrero") vs forecast::BoxCox.lambda(x = aus_production_gas_ts, method = "loglik")? $\endgroup$ Commented Jul 23 at 15:47
  • $\begingroup$ The MLE approach is sensitive to the assumed model. $\endgroup$ Commented Jul 23 at 23:37
  • $\begingroup$ Thanks again for your insights! $\endgroup$ Commented Jul 25 at 13:15
  • $\begingroup$ Hi Dr. Hyndman, I posted a question about time series models , can you please take a look? stats.stackexchange.com/questions/670804/… $\endgroup$ Commented Oct 23 at 2:17

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