# Prediction Intervals on Test Set: Forecasting with Fable

Hello,
In the online text books (2nd and 3rd editions) there is a section devoted to the test and train approach to determining model accuracy. I am following the 3rd edition and would like to extract confidence intervals on the from the one-step forecast done on the test set. I am unable to share data because this is for work. However I am able to obtain the fitted values with the code below

fit%>%####ie the model fitted on the train data
refit(test)%>%###ie apply the model to the test data or one step forecast on the test data
fitted()###give the fitted values

The code above returns a tsible object with .model, Date, and .fitted parameters.

But shouldn't there be prediction intervals as well?
Am I totally off here and there are no prediction intervals for 1-step forecasts?

Thank You!

Referred here by Forecasting: Principles and Practice, by Rob J Hyndman and George Athanasopoulos

The one step forecast variance is simply the residual variance, so it is easy to construct prediction intervals if you need them. Here is an example where 95% prediction intervals are computed assuming Gaussian residuals.

``````library(fpp3)
#> ── Attaching packages ──────────────────────────────────────────── fpp3 0.4.0 ──
#> ✓ tibble      3.1.3      ✓ tsibble     1.0.1
#> ✓ dplyr       1.0.7      ✓ tsibbledata 0.3.0
#> ✓ tidyr       1.1.3      ✓ feasts      0.2.2
#> ✓ lubridate   1.7.10     ✓ fable       0.3.1
#> ✓ ggplot2     3.3.5
#> ── Conflicts ───────────────────────────────────────────────── fpp3_conflicts ──

train <- aus_production %>%
filter(Quarter < yearquarter("2006 Q1"))
test <- aus_production %>%
filter(Quarter >= yearquarter("2006 Q1"))

fit <- train %>%
model(ets = ARIMA(Beer))
sigma2 <- glance(fit) %>% pull(sigma2)
fit %>%
refit(test) %>%
fitted() %>%
mutate(
lo = .fitted - 1.96*sqrt(sigma2),
hi = .fitted + 1.96*sqrt(sigma2)
)
#> # A tsibble: 18 x 5 [1Q]
#> # Key:       .model 
#>    .model Quarter .fitted    lo    hi
#>    <chr>    <qtr>   <dbl> <dbl> <dbl>
#>  1 ets    2006 Q1    438.  407.  469.
#>  2 ets    2006 Q2    386.  355.  417.
#>  3 ets    2006 Q3    405.  374.  436.
#>  4 ets    2006 Q4    491.  460.  522.
#>  5 ets    2007 Q1    428.  397.  459.
#>  6 ets    2007 Q2    379.  347.  410.
#>  7 ets    2007 Q3    396.  365.  427.
#>  8 ets    2007 Q4    482.  451.  513.
#>  9 ets    2008 Q1    420.  389.  451.
#> 10 ets    2008 Q2    371.  340.  402.
#> 11 ets    2008 Q3    387.  356.  418.
#> 12 ets    2008 Q4    475.  444.  506.
#> 13 ets    2009 Q1    427.  396.  458.
#> 14 ets    2009 Q2    391.  360.  422.
#> 15 ets    2009 Q3    405.  374.  436.
#> 16 ets    2009 Q4    486.  455.  518.
#> 17 ets    2010 Q1    430.  399.  461.
#> 18 ets    2010 Q2    397.  366.  428.
``````

Created on 2021-08-07 by the reprex package (v2.0.0)

Ah, of course! Thank you Dr. Hyndman!

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