Question regarding CRPS:
The CRPS averages the quantile scores over all values of p i.e. the whole the forecast distribution. But exactly what is the whole the forecast distribution? Because if I do an autoplot of a fan chart with level = 100, the fan is all the way from the top to the bottom; does this mean the CRPS is a measure for 100% prediction interval's ? Or is the CRPS a measure of the whole distribution given the parameters of the model i.e. a fan chart as one would plot from 10,000 simulated futures?
library(fpp3) # Re-index based on trading days google_stock <- gafa_stock |> filter(Symbol == "GOOG", year(Date) >= 2015) |> mutate(day = row_number()) |> update_tsibble(index = day, regular = TRUE) # Filter the year of interest google_2015 <- google_stock |> filter(year(Date) == 2015) # forecast OOS google_2015 |> model(NAIVE(Close)) |> forecast(h = 10) |> autoplot(google_2015, level = c(80, 95, 100)) + labs(title="Google daily closing stock price", y="$US" )