How can I return to my raw data, after using BoxCox transformation?

I am working on a forecasting project. After inspecting my time series, i decided to apply linear transformation by using R's forecast package's BoxCox function.

This function created an output variable which includes my transformed data. Afterwards I built my ARIMA model to forecast future values. However these forecasts are also in transformed scale. As BoxCox function makes calculations with precise lambda values, I am unable to specify functional form of my series (for example; i can't say if transformation is logaritmic or not).

So, I wonder if there is a function to transform series processed with BoxCox function to their orginal scale? Because I need to report forecasted values in orginal scale.

Solution

Use the lambda argument in the modelling function and don't transform your data yourself. All the modelling functions in the forecast package will do the BoxCox transformation for you, and back-transform the forecasts when you need them (including bias-adjustment if required). Here is a simple example:

library(forecast)
AirPassengers %>%
  auto.arima(lambda=0, biasadj=TRUE) %>%
  forecast() %>%
  autoplot()