week 7 seminar code and slides

week7/seminar_code.R

@@ -4,32 +4,35 @@ library(fpp3)
 
 # Facebook stock
 fb <- gafa_stock |>
-  filter(Symbol == "FB") |>
-  select(Date, Close) |>
-  fill_gaps()
+  filter(Symbol == "FB")
 fb |>
   gg_tsdisplay(Close)
 fb |>
-  gg_tsdisplay(Close |> difference())
+  gg_tsdisplay(difference(Close))
 
 # aus_production Bricks
 
+aus_production |>
+  gg_tsdisplay(Bricks)
 aus_production |>
   gg_tsdisplay(
     box_cox(Bricks, lambda = 0.3)
   )
 aus_production |>
   gg_tsdisplay(
-    box_cox(Bricks, lambda = 0.3) |> difference(lag = 4)
+    box_cox(Bricks, lambda = 0.3) |>
+      difference(lag = 4)
   )
 aus_production |>
   gg_tsdisplay(
-    box_cox(Bricks, lambda = 0.3) |> difference(lag = 4) |> difference()
+    box_cox(Bricks, lambda = 0.3) |>
+      difference(lag = 4) |>
+      difference()
   )
 
 # Unit root tests
 fb  |> features(Close, unitroot_kpss)
-fb  |> features(Close |> difference(), unitroot_kpss)
+fb  |> features(difference(Close), unitroot_kpss)
 fb  |> features(Close, unitroot_ndiffs)
 
 ## Seasonal strength
@@ -43,24 +46,10 @@ aus_production  |>
     box_cox(Bricks, lambda = 0.3),
     unitroot_nsdiffs
   )
-
-## Unit root
-aus_production  |>
-  features(
-    box_cox(Bricks, lambda = 0.3) |> difference(lag = 4),
-    unitroot_kpss
-  )
 aus_production  |>
   features(
-    box_cox(Bricks, lambda = 0.3) |> difference(lag = 4),
+    box_cox(Bricks, lambda = 0.3) |>
+      difference(lag = 4),
     unitroot_ndiffs
   )
 
-# Random walks
-
-tsibble(
-  time = 1:500,
-  value = cumsum(rnorm(500) + 0.1),
-  index = time
-) |>
-  gg_tsdisplay(value)

week7/slides.qmd

@@ -89,52 +89,3 @@ If $F_s > 0.64$, do one seasonal difference.
 ## Your turn
 
 3. Do the unit root tests for the `Gas` series from `aus_accommodation`. Do they give the same numbers of difference as you chose?
-
-# Random walks
-
-## Random walk model
-
-If differenced series is white noise with zero mean:
-
-\begin{block}{}
-\centerline{$y_t-y_{t-1}=\varepsilon_t$ \hspace{0.4cm} or \hspace{0.4cm} $y_t=y_{t-1}+\varepsilon_t$}
-\end{block}\vspace*{-0.3cm}
-where $\varepsilon_t \sim NID(0,\sigma^2)$.
-
-* Model behind the \alert{naïve method}.
-* Forecast are equal to the last observation (future movements up or down are equally likely).
-
-\vspace*{10cm}
-
-## Random walk model
-
-\begin{block}{}
-\centerline{$y_t=y_{t-1}+\varepsilon_t$ \qquad
-where $\varepsilon_t \sim NID(0,\sigma^2)$.}
-\end{block}\pause
-\vspace*{-1.3cm}
-\begin{align*}
-y_{T+h} &= y_{T+h-1} + \varepsilon_{T+h} \\
-  &= y_{T+h-2} + \varepsilon_{T+h-1} + \varepsilon_{T+h} \\
-  &= \dots \\
-  &= y_T + \varepsilon_{T+1} + \dots + \varepsilon_{T+h}
-\end{align*}
-\pause\vspace*{-1cm}
-\begin{align*}
-\text{So}\qquad &\text{E}(y_{T+h}|y_1,\dots,y_T)  = y_T \\
-\text{and}\qquad &\text{Var}(y_{T+h}|y_1,\dots,y_T) = h\sigma^2
-\end{align*}\vspace*{10cm}
-
-## Random walk with drift model
-
-If differenced series is white noise with non-zero mean:
-
-\begin{block}{}
-\centerline{$y_t-y_{t-1}=c+\varepsilon_t$ \hspace{0.4cm} or \hspace{0.4cm} $y_t=c+y_{t-1}+\varepsilon_t$}
-\end{block}\vspace*{-0.3cm}
-where $\varepsilon_t \sim NID(0,\sigma^2)$.
-
-* $c$ is the \alert{average change} between consecutive observations.
-* Model behind the \alert{drift method}.
-
-\vspace*{10cm}

week8/slides.qmd

@@ -23,6 +23,57 @@ library(purrr)
 ```
 
 
+# Random walks
+
+## Random walk model
+
+If differenced series is white noise with zero mean:
+
+\begin{block}{}
+\centerline{$y_t-y_{t-1}=\varepsilon_t$ \hspace{0.4cm} or \hspace{0.4cm} $y_t=y_{t-1}+\varepsilon_t$}
+\end{block}\vspace*{-0.3cm}
+where $\varepsilon_t \sim NID(0,\sigma^2)$.
+
+* Model behind the \alert{naïve method}.
+* Forecast are equal to the last observation (future movements up or down are equally likely).
+
+\vspace*{10cm}
+
+## Random walk model
+
+\begin{block}{}
+\centerline{$y_t=y_{t-1}+\varepsilon_t$ \qquad
+where $\varepsilon_t \sim NID(0,\sigma^2)$.}
+\end{block}\pause
+\vspace*{-1.3cm}
+\begin{align*}
+y_{T+h} &= y_{T+h-1} + \varepsilon_{T+h} \\
+  &= y_{T+h-2} + \varepsilon_{T+h-1} + \varepsilon_{T+h} \\
+  &= \dots \\
+  &= y_T + \varepsilon_{T+1} + \dots + \varepsilon_{T+h}
+\end{align*}
+\pause\vspace*{-1cm}
+\begin{align*}
+\text{So}\qquad &\text{E}(y_{T+h}|y_1,\dots,y_T)  = y_T \\
+\text{and}\qquad &\text{Var}(y_{T+h}|y_1,\dots,y_T) = h\sigma^2
+\end{align*}\vspace*{10cm}
+
+## Random walk with drift model
+
+If differenced series is white noise with non-zero mean:
+
+\begin{block}{}
+\centerline{$y_t-y_{t-1}=c+\varepsilon_t$ \hspace{0.4cm} or \hspace{0.4cm} $y_t=c+y_{t-1}+\varepsilon_t$}
+\end{block}\vspace*{-0.3cm}
+where $\varepsilon_t \sim NID(0,\sigma^2)$.
+
+* $c$ is the \alert{average change} between consecutive observations.
+* Model behind the \alert{drift method}.
+
+\vspace*{10cm}
+
+# Backshift operator notation
+
 ## Backshift operator notation
 
 * $B$ shifts the data back one period. $B y_{t} = y_{t - 1}$
@@ -32,6 +83,8 @@ library(purrr)
 * A seasonal difference followed by a first difference can be written as
 $(1-B)(1-B^m)y_t$
 
+# Autoregressive (AR) models
+
 ## AR(1) model
 
 \begin{block}{}
@@ -73,6 +126,8 @@ We normally restrict autoregressive models to stationary data, and then some con
 * More complicated conditions hold for $p\ge3$.
 * fable takes care of this.
 
+# Moving Average (MA) models
+
 ## Moving Average (MA) models
 A multiple regression with \textbf{past \emph{errors}} as predictors.
 
@@ -98,6 +153,7 @@ A multiple regression with \textbf{past \emph{errors}} as predictors.
 * More complicated conditions hold for $q\ge3$.
 * fable takes care of this.
 
+# ARIMA models
 ## ARIMA models
 
 \fontsize{14}{14.5}\sf\vspace*{0.2cm}