forecast package: cross-validation, forecast combination and RMSSE

[newsagent]

In a previews discussion (link), you showed very clearly how to calculate RMSEs for a combination of models in a cross-validation setting using the forecast package. I display the code here again

`library(forecast)
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)

google_tscv_m1 <- tsCV(google_2015$Close, h = 8, function(x, h) {
auto.arima(x) |>
forecast(h = h)
})
google_tscv_m2 <- tsCV(google_2015$Close, h = 8, function(x, h) {
Arima(x, order = c(1, 1, 0), lambda = 0, biasadj = TRUE) |>
forecast(h = h)
})
google_tscv_comb <- tsCV(google_2015$Close, h = 8, function(x, h) {
fc1 <- Arima(x, order = c(1, 1, 0), lambda = 0, biasadj = TRUE) |>
forecast(h = h)
fc2 <- auto.arima(x) |> forecast(h = h)
fc2$mean <- 0.5 * (fc1$mean + fc2$mean)
return(fc2)
})

common_times <- apply(
!is.na(google_tscv_m1) &
!is.na(google_tscv_m2) &
!is.na(google_tscv_comb),
1,
all
)

mse <- rbind(
m1 = colMeans(google_tscv_m1[common_times, ]^2),
m2 = colMeans(google_tscv_m2[common_times, ]^2),
comb = colMeans(google_tscv_comb[common_times, ]^2)
)
mse
#> h=1 h=2 h=3 h=4 h=5 h=6 h=7 h=8
#> m1 138.8834 300.1304 444.5767 575.8839 691.6277 800.2433 918.4026 1022.969
#> m2 133.9775 297.6269 448.3832 581.2425 698.6947 796.2140 909.7168 1005.752
#> comb 135.7658 297.3055 443.5407 573.8943 688.6614 790.0591 904.4725 1003.522`

My question now is how I can calculate the scaled RMSEs for each model separately and for their combination using the forecast package

[robjhyndman]

You just need to divide the results by the scaling factor. See https://robjhyndman.com/hyndsight/rolling_mase.html for a discussion of this issue -- that is about MASE, but the same principles apply to RMSSE.