Week 11 seminar

week11/activities.md

@@ -1,26 +1,13 @@
-
-
-Repeat the daily electricity example, but instead of using a quadratic function of temperature, use a piecewise linear function with the "knot" around 20 degrees Celsius (use predictors `Temperature` & `Temp2`). How can you optimize the choice of knot?
-
-The data can be created as follows.
-
-```r
-vic_elec_daily <- vic_elec |>
-  filter(year(Time) == 2014) |>
-  index_by(Date = date(Time)) |>
-  summarise(
-    Demand = sum(Demand)/1e3,
-    Temperature = max(Temperature),
-    Holiday = any(Holiday)
-  ) |>
-  mutate(
-    Temp2 = I(pmax(Temperature-20,0)),
-    Day_Type = case_when(
-      Holiday ~ "Holiday",
-      wday(Date) %in% 2:6 ~ "Weekday",
-      TRUE ~ "Weekend"
-    )
-  )
-```
-
-Repeat but using all available data, and handling the annual seasonality using Fourier terms.
+1.  Fit a regression model with a piecewise linear trend and Fourier terms for the US leisure employment data.
+
+    ```r
+    leisure <- us_employment |>
+      filter(Title == "Leisure and Hospitality", year(Month) > 2001) |>
+      mutate(Employed = Employed / 1000) |>
+      select(Month, Employed)
+    ```
+
+2. Add a dynamic regression model with the same predictors.
+3. How do the models compare on AICc?
+4. Does the additional ARIMA component fix the residual autocorrelation problem in the regression model?
+5. How different are the forecasts from each model?

week11/index.qmd

@@ -24,6 +24,17 @@ Complete Exercises 1-7 from [Section 7.10 of the book](https://otexts.com/fpp3/r
 ```{r}
 #| output: asis
 show_slides(week)
-show_activity(week)
+```
+
+## Seminar activities
+
+```{r}
+#| child: activities.md
+```
+
+[**R code used in seminar**](seminar_code.R)
+
+```{r}
+#| output: asis
 show_assignments(week)
 ```

week11/seminar_code.R

@@ -36,6 +36,8 @@ elec_fit <- vic_elec_daily |>
     dhr = ARIMA(log(Demand) ~ Temperature + I(Temperature^2) +
         (Day_Type == "Weekday") + fourier(period = "year", K = 4))
   )
+elec_fit |>
+  pivot_longer(ets:dhr, names_to="model", values_to="model_fit")
 
 accuracy(elec_fit)
 
@@ -87,13 +89,6 @@ elec_fit |>
   geom_line() +
   geom_line(aes(y = .fitted), col = "red")
 
-# Forecast one day ahead
-vic_next_day <- new_data(vic_elec_daily, 1) |>
-  mutate(Temperature = 26, Day_Type = "Holiday")
-forecast(elec_fit, new_data = vic_next_day) |>
-  autoplot(vic_elec_daily |> tail(14), level = 80) +
-  labs(y = "Electricity demand (GW)")
-
 # Forecast 14 days ahead
 vic_elec_future <- new_data(vic_elec_daily, 14) |>
   mutate(
@@ -105,7 +100,8 @@ vic_elec_future <- new_data(vic_elec_daily, 14) |>
       TRUE ~ "Weekend"
     )
   )
-forecast(elec_fit, new_data = vic_elec_future) |>
+elec_fit |>
+  forecast(new_data = vic_elec_future) |>
   autoplot(vic_elec_daily |> tail(14), level = 80) +
   labs(y = "Electricity demand (GW)")
 

week11/slides.qmd

@@ -15,36 +15,15 @@ format:
     include-in-header: ../header.tex
 ---
 
-
-```{r setup, include=FALSE}
-source(here::here("setup.R"))
-library(readr)
-
-vic_elec_daily <- vic_elec |>
-  filter(year(Time) == 2014) |>
-  index_by(Date = date(Time)) |>
-  summarise(
-    Demand = sum(Demand) / 1e3,
-    Temperature = max(Temperature),
-    Holiday = any(Holiday)
-  ) |>
-  mutate(Day_Type = case_when(
-    Holiday ~ "Holiday",
-    wday(Date) %in% 2:6 ~ "Weekday",
-    TRUE ~ "Weekend"
-  ))
-```
-
 ## Regression with ARIMA errors
 
-\vspace*{0.2cm}\begin{block}{Regression models}\vspace*{-0.2cm}
+\begin{block}{Regression models}\vspace*{-0.2cm}
 \[
   y_t = \beta_0 + \beta_1 x_{1,t} + \dots + \beta_k x_{k,t} + \varepsilon_t,
 \]
 \end{block}\vspace*{-0.3cm}
 
-  * $y_t$ modeled as function of $k$ explanatory variables
-$x_{1,t},\dots,x_{k,t}$.
+  * $y_t$ modeled as function of $k$ explanatory variables $x_{1,t},\dots,x_{k,t}$.
   * In regression, we assume that $\varepsilon_t$ is WN.
   * Now we want to allow $\varepsilon_t$ to be autocorrelated.
 \vspace*{0.1cm}
@@ -93,7 +72,7 @@ $y_t' = (1-B)^dy_t$,\quad $x_{i,t}' = (1-B)^dx_{i,t}$,\quad and $\eta_t' = (1-B)
 
 ## Regression with ARIMA errors
 
-  * In R, we can specify an ARIMA($p,d,q$) for the errors, and $d$ levels of differencing will be applied to all variables ($y, x_{1,t},\dots,x_{k,t}$) during estimation.
+  * In R, we can specify an ARIMA($p,d,q$) for the errors, then $d$ levels of differencing will be applied to all variables ($y, x_{1,t},\dots,x_{k,t}$) during estimation.
   * Check that $\varepsilon_t$ series looks like white noise.
   * AICc can be calculated for final model.
   * Repeat procedure for all subsets of predictors to be considered, and select model with lowest AICc value.
@@ -106,3 +85,10 @@ results.
   * Some predictors are known into the future (e.g., time, dummies).
   * Separate forecasting models may be needed for other predictors.
   * Forecast intervals ignore the uncertainty in forecasting the predictors.
+
+## Your turn
+\fontsize{13}{15}\sf\vspace*{-0.2cm}
+
+```{r}
+#| child: activities.md
+```