Forecasting and back transformation with TSLM

If you put the transformations inside the model() function, then fable will automatically undo the transformations for you. In this case, the model is equivalent to a regression on the log variables with an ARIMA(0,1,0) error. Your TSLM model included an insignificant intercept, which you probably don't want/need here, as it induces a small trend in the forecasts.

library(fpp3)
#> ── Attaching packages ──────────────────────────────────────────── fpp3 1.0.3 ──
#> ✔ tibble      3.3.1     ✔ tsibble     1.2.0
#> ✔ dplyr       1.2.1     ✔ tsibbledata 0.4.1
#> ✔ tidyr       1.3.2     ✔ ggtime      0.2.0
#> ✔ lubridate   1.9.5     ✔ feasts      0.5.0
#> ✔ ggplot2     4.0.2     ✔ fable       0.5.0
#> ── Conflicts ───────────────────────────────────────────────── fpp3conflicts ──
#> ✖ lubridate::date()    masks base::date()
#> ✖ dplyr::filter()      masks stats::filter()
#> ✖ tsibble::intersect() masks base::intersect()
#> ✖ tsibble::interval()  masks lubridate::interval()
#> ✖ dplyr::lag()         masks stats::lag()
#> ✖ tsibble::setdiff()   masks base::setdiff()
#> ✖ tsibble::union()     masks base::union()
googlestock 
  filter(Symbol == "GOOG", year(Date) >= 2015) |>
  mutate(day = rownumber()) |>
  updatetsibble(index = day, regular = TRUE)
google2015  filter(year(Date) == 2015)
fit 
  filter(Date < "2015-12-23") |>
  model(ARIMA(log(Open) ~ log(High) + pdq(0, 1, 0)))
report(fit)
#> Series: Open 
#> Model: LM w/ ARIMA(0,1,0) errors 
#> Transformation: log(Open) 
#> 
#> Coefficients:
#>       log(High)
#>          0.9267
#> s.e.     0.0401
#> 
#> sigma^2 estimated as 0.0001211:  log likelihood=757.67
#> AIC=-1511.35   AICc=-1511.3   BIC=-1504.34
forecast 
  forecast(newdata = google2015 |> filter(Date >= "2015-12-23"))
autoplot(forecast) +
  autolayer(
    google2015 |> filter(Date > "2015-11-01"),
    Open
  ) +
  labs(
    x = "Date",
    y = "Google Stock Price",
    title = "Google Stock Price Forecast"
  )

^{Created on 2026-04-20 with reprex v2.1.1}