forecast and TSLM how is the mean (point forecast) calculated?

[jennahamlin]

Hello -

When I generate a forecast using the TSLM function from fable, the point forecasts are different than those generated using the predict function associated with linear models (see below). Adding in the approx_normal = FALSE call, as suggested in #343, resolved my issue with the prediction intervals being different between the two methods but not the point forecast (mean) values. Obviously, I am missing something but am unsure of what. Any additional information would be greatly appreciated. Thank you

Forecast values using TSLM from fable

year	caseCount	.mean	lo 95%	hi 85%
2021	t(t(27,3.2,0.74))	32	5.472078	112.2039
2022	t(t(27,3.4,0.74))	37.1	6.263024	131.0257
2023	t(t(27,3.5,0.75))	43.1	7.164173	153.0928
2024	t(t(27,3.6,0.75))	50	8.190369	178.9772
2025	t(t(27,3.8,0.76))	58	9.358397	209.3534

code to produce fable TSLM values

 iso222 %>%
  model(time_series = fable::TSLM(log(caseCount) ~ year )) |>
  forecast(h = "10 year", approx_normal=FALSE) %>%
  hilo(level = c (95))

Forecast values using predict

year	fit	lwr	upr
2021	24.77879	5.472078	112.2039
2022	28.64641	6.263024	131.0257
2023	33.11772	7.164173	153.0928
2024	38.28693	8.190369	178.9772
2025	44.26299	9.358397	209.3534

code to produce fable predict values

lModel <- lm(caseCount ~ year, data = isoCountLog[1:29,])
exp(predict(lModel, list(year = isoCountRate222$year),
                          interval = 'prediction'))

[robjhyndman]

You are using a log transformation, and the mean is not the exponential of the predicted values on the log scale. See https://otexts.com/fpp3/ftransformations.html#bias-adjustments

[jennahamlin]

@robjhyndman Thank you for the reminder, made the adjustment to print median instead of mean.