VAR and back-transformation: A particular case

[nickcox896]

In a bivariate VAR, supose we want one variable to be in first difference [difference(log(Open)] and the other one in levels [log(High)]
The code below

library(fpp3)

 google_stock <- gafa_stock |>
  filter(Symbol == "GOOG", year(Date) >= 2015) |>
  mutate(day = row_number()) |>
  update_tsibble(index = day, regular = TRUE)

google_2015 <- google_stock |> filter(year(Date) == 2015)

case_5 <- google_2015 |>
  model(VARIMA(vars(log(Open), log(High)) ~ pdq(d = 1))) |>
  forecast(h = 3, bootstrap = TRUE, times = 100)

although it allows for difference(log(Open)) it does not accommodate the levels.

[robjhyndman]

You could take cumulative sums of the variable you don't want to difference, then apply differencing to both variables in the model. But the forecasts of the summed variable will then need to be differenced to get back to the levels. If you also have a log or other transformation in the model, this would need to be handled manually.

[nickcox896]

Thank you