2-tsgraphics.qmd

---
title: "ETC3550/ETC5550 Applied forecasting"
author: "Ch2. Time series graphics"
institute: "OTexts.org/fpp3/"
pdf-engine: pdflatex
fig-width: 7.5
fig-height: 3.5
format:
  beamer:
    theme: monash
    aspectratio: 169
    fontsize: 14pt
    section-titles: false
    knitr:
      opts_chunk:
        dev: "cairo_pdf"
include-in-header: header.tex
execute:
  echo: false
  message: false
  warning: false
---

```{r setup, include=FALSE}
source("setup.R")
library(patchwork)

global_economy <- global_economy |>
  select(Year, Country, GDP, Imports, Exports, Population)
tourism <- tourism |>
  mutate(
    State = recode(State,
      "Australian Capital Territory" = "ACT",
      "New South Wales" = "NSW",
      "Northern Territory" = "NT",
      "Queensland" = "QLD",
      "South Australia" = "SA",
      "Tasmania" = "TAS",
      "Victoria" = "VIC",
      "Western Australia" = "WA"
    )
  )
```

## `tsibble` objects

\fontsize{10}{10.8}\sf

```{r, echo = TRUE}
global_economy
```

\only<2->{\begin{textblock}{.75}(1.65,3.4)
\begin{alertblock}{}\fontsize{9}{9}\sf Index\phantom{dg}\end{alertblock}
\end{textblock}}
\only<3->{\begin{textblock}{1.6}(2.78,3.4)
\begin{alertblock}{}\fontsize{9}{9}\sf Key\phantom{dg}\end{alertblock}
\end{textblock}}
\only<4>{\begin{textblock}{6.7}(4.8,3.4)
\begin{alertblock}{}\fontsize{9}{9}\sf Measured variables\phantom{dg}\end{alertblock}
\end{textblock}}

## `tsibble` objects

\fontsize{10}{10.8}\sf

```{r, echo = TRUE}
tourism
```

\only<3->{\begin{textblock}{.98}(1.65,3.37)
\begin{alertblock}{}\fontsize{9}{9}\sf Index\phantom{dg}\end{alertblock}
\end{textblock}}
\only<4->{\begin{textblock}{3.9}(3,3.37)
\begin{alertblock}{}\fontsize{9}{9}\sf Keys\phantom{dg}\end{alertblock}
\end{textblock}}
\only<5>{\begin{textblock}{1.5}(7.4,3.37)
\begin{alertblock}{}\fontsize{9}{9}\sf Measure\phantom{dg}\end{alertblock}
\end{textblock}}

\only<2->{\begin{textblock}{3}(9,5)
\begin{block}{}\fontsize{10}{10}\sf Domestic visitor nights in thousands by state/region and purpose.\phantom{dg}\end{block}
\end{textblock}}

## `tsibble` objects

* A `tsibble` allows storage and manipulation of multiple time series in R.

* It contains:

  + An index: time information about the observation
  + Measured variable(s): numbers of interest
  + Key variable(s): optional unique identifiers for each series

* It works with tidyverse functions.

## The `tsibble` index

Time index variables can be created with these functions:

###
\vspace*{-0.2cm}

```{r tstable2, echo=FALSE}
tribble(
  ~`Frequency`, ~Function,
  "Annual", "`start:end`",
  "Quarterly", "`yearquarter()`",
  "Monthly", "`yearmonth()`",
  "Weekly", "`yearweek()`",
  "Daily", "`as_date()`, `ymd()`",
  "Sub-daily", "`as_datetime()`"
) |>
  knitr::kable(booktabs = TRUE)
```

## Seasonal or cyclic?

\alert{Differences between seasonal and cyclic patterns:}

  * seasonal pattern constant length; cyclic pattern variable length
  * average length of cycle longer than length of seasonal pattern
  * magnitude of cycle more variable than magnitude of seasonal pattern

\pause

\begin{alertblock}{}
The timing of peaks and troughs is predictable with seasonal data, but unpredictable in the long term with cyclic data.
\end{alertblock}


## Trend and seasonality in ACF plots

- When data have a trend, the autocorrelations for small lags tend to be large and positive.
- When data are seasonal, the autocorrelations will be larger at the seasonal lags (i.e., at multiples of the seasonal frequency)
- When data are trended and seasonal, you see a combination of these effects.


## Which is which?

```{r, fig.height=6, fig.width=12, echo=FALSE, warning=FALSE, out.width="15cm"}
cowtemp <- as_tsibble(fma::cowtemp)
USAccDeaths <- as_tsibble(USAccDeaths)
AirPassengers <- as_tsibble(AirPassengers)
mink <- as_tsibble(fma::mink)
tp1 <- autoplot(cowtemp, value) +
  labs(x = "", y = "chirps per minute", title = "1. Daily temperature of cow")
tp2 <- autoplot(USAccDeaths, value) +
  labs(x = "", y = "thousands", title = "2. Monthly accidental deaths")
tp3 <- autoplot(AirPassengers, value) +
  labs(x = "", y = "thousands", title = "3. Monthly air passengers")
tp4 <- autoplot(mink, value) +
  labs(x = "", y = "thousands", title = "4. Annual mink trappings")
acfb <- ACF(cowtemp, value) |> autoplot() +
  labs(x = "", title = "B") + ylim(-0.4, 1)
acfa <- ACF(USAccDeaths, value) |> autoplot() +
  labs(x = "", title = "A") + ylim(-0.4, 1)
acfd <- ACF(AirPassengers, value) |> autoplot() +
  labs(x = "", title = "D") + ylim(-0.4, 1)
acfc <- ACF(mink, value) |> autoplot() +
  labs(x = "", title = "C") + ylim(-0.4, 1)
(tp1 | tp2 | tp3 | tp4) / (acfa | acfb | acfc | acfd)
```