Time series graphics

BUS 323 Forecasting and Risk Analysis

The pipe operator

The pipe operator (%>%, or |>) allows you to write your code in a more stepwise fashion.
Instead of:

mutate(filter(data, x > 5), 
y = y * 2)

You can write:

data %>%
  filter(x > 5) %>%
  mutate(y = y * 2)

Data manipulation functions: filter

filter(): selects rows based on conditions.
e.g.

data |> filter(x > 5)

will return the observations within object data that match the filter condition.

Data manipulation functions: mutate

mutate(): adds or transforms columns.
e.g.

data |> mutate(y = y*2)

will return data with the observations in column y doubled.

Data manipulation functions: select

select(): chooses specific columns.
e.g.

data |> select(x)

will return only the x column of data.

Data manipulation functions: arrange

arrange(): sorts rows by column values.
e.g.

data |> arrange(desc(x))

will return data with rows sorted by x in descending order.

Data manipulation functions: summarise and group_by

summarise(): aggregates data
group_by(): groups data by a column value
e.g.

data |> 
group_by(x) |> 
summarise(average_y = mean(y))

will return the mean of y conditional on x.

Time series graphics in R

Load up RStudio
Packages tab -> Install -> fpp3
- Check “install dependencies”
Load the fpp3 package by running library(fpp3) in your session.

tsibble objects

tsibble objects format time series in a tidy way.
Suppose we have the following:

Year	Observation
2015	123
2016	39
2017	78
2018	52
2019	110

tsibble objects

We can turn it into a tsibble object with the following command:

y <- tsibble(
  Year = 2015:2019,
  Observation = c(123, 39, 78, 52, 110),
  index = Year
)

Working with tsibble objects

Once you have a tsibble, working with it is simple. Run: PBS

# A tsibble: 67,596 x 9 [1M]
# Key:       Concession, Type, ATC1, ATC2 [336]
      Month Concession   Type      ATC1  ATC1_desc ATC2  ATC2_desc Scripts  Cost
      <mth> <chr>        <chr>     <chr> <chr>     <chr> <chr>       <dbl> <dbl>
 1 1991 Jul Concessional Co-payme… A     Alimenta… A01   STOMATOL…   18228 67877
 2 1991 Aug Concessional Co-payme… A     Alimenta… A01   STOMATOL…   15327 57011
 3 1991 Sep Concessional Co-payme… A     Alimenta… A01   STOMATOL…   14775 55020
 4 1991 Oct Concessional Co-payme… A     Alimenta… A01   STOMATOL…   15380 57222
 5 1991 Nov Concessional Co-payme… A     Alimenta… A01   STOMATOL…   14371 52120
 6 1991 Dec Concessional Co-payme… A     Alimenta… A01   STOMATOL…   15028 54299
 7 1992 Jan Concessional Co-payme… A     Alimenta… A01   STOMATOL…   11040 39753
 8 1992 Feb Concessional Co-payme… A     Alimenta… A01   STOMATOL…   15165 54405
 9 1992 Mar Concessional Co-payme… A     Alimenta… A01   STOMATOL…   16898 61108
10 1992 Apr Concessional Co-payme… A     Alimenta… A01   STOMATOL…   18141 65356
# ℹ 67,586 more rows

Working with tsibble objects

Suppose we are interested in A10 scripts specifically:

PBS |>
  filter(ATC2 == "A10")

# A tsibble: 816 x 9 [1M]
# Key:       Concession, Type, ATC1, ATC2 [4]
      Month Concession   Type     ATC1  ATC1_desc ATC2  ATC2_desc Scripts   Cost
      <mth> <chr>        <chr>    <chr> <chr>     <chr> <chr>       <dbl>  <dbl>
 1 1991 Jul Concessional Co-paym… A     Alimenta… A10   ANTIDIAB…   89733 2.09e6
 2 1991 Aug Concessional Co-paym… A     Alimenta… A10   ANTIDIAB…   77101 1.80e6
 3 1991 Sep Concessional Co-paym… A     Alimenta… A10   ANTIDIAB…   76255 1.78e6
 4 1991 Oct Concessional Co-paym… A     Alimenta… A10   ANTIDIAB…   78681 1.85e6
 5 1991 Nov Concessional Co-paym… A     Alimenta… A10   ANTIDIAB…   70554 1.69e6
 6 1991 Dec Concessional Co-paym… A     Alimenta… A10   ANTIDIAB…   75814 1.84e6
 7 1992 Jan Concessional Co-paym… A     Alimenta… A10   ANTIDIAB…   64186 1.56e6
 8 1992 Feb Concessional Co-paym… A     Alimenta… A10   ANTIDIAB…   75899 1.73e6
 9 1992 Mar Concessional Co-paym… A     Alimenta… A10   ANTIDIAB…   89445 2.05e6
10 1992 Apr Concessional Co-paym… A     Alimenta… A10   ANTIDIAB…   97315 2.23e6
# ℹ 806 more rows

Working with tsibble objects

And suppose we only want to use the variables Month, Concession, Type, and Cost:

PBS |>
  filter(ATC2 == "A10") |>
  select(Month, Concession, Type, Cost)

# A tsibble: 816 x 4 [1M]
# Key:       Concession, Type [4]
      Month Concession   Type           Cost
      <mth> <chr>        <chr>         <dbl>
 1 1991 Jul Concessional Co-payments 2092878
 2 1991 Aug Concessional Co-payments 1795733
 3 1991 Sep Concessional Co-payments 1777231
 4 1991 Oct Concessional Co-payments 1848507
 5 1991 Nov Concessional Co-payments 1686458
 6 1991 Dec Concessional Co-payments 1843079
 7 1992 Jan Concessional Co-payments 1564702
 8 1992 Feb Concessional Co-payments 1732508
 9 1992 Mar Concessional Co-payments 2046102
10 1992 Apr Concessional Co-payments 2225977
# ℹ 806 more rows

Working with tsibble objects

Suppose further we are only interested in total cost regardless of concession or type:

PBS |>
  filter(ATC2 == "A10") |>
  select(Month, Concession, Type, Cost) |>
  summarise(TotalC = sum(Cost))

# A tsibble: 204 x 2 [1M]
      Month  TotalC
      <mth>   <dbl>
 1 1991 Jul 3526591
 2 1991 Aug 3180891
 3 1991 Sep 3252221
 4 1991 Oct 3611003
 5 1991 Nov 3565869
 6 1991 Dec 4306371
 7 1992 Jan 5088335
 8 1992 Feb 2814520
 9 1992 Mar 2985811
10 1992 Apr 3204780
# ℹ 194 more rows

Working with tsibble objects

You can make new variables using mutate(). Let’s convert TotalC to millions of dollars:

PBS |>
  filter(ATC2 == "A10") |>
  select(Month, Concession, Type, Cost) |>
  summarise(TotalC = sum(Cost)) |>
  mutate(Cost = TotalC/1e6)

# A tsibble: 204 x 3 [1M]
      Month  TotalC  Cost
      <mth>   <dbl> <dbl>
 1 1991 Jul 3526591  3.53
 2 1991 Aug 3180891  3.18
 3 1991 Sep 3252221  3.25
 4 1991 Oct 3611003  3.61
 5 1991 Nov 3565869  3.57
 6 1991 Dec 4306371  4.31
 7 1992 Jan 5088335  5.09
 8 1992 Feb 2814520  2.81
 9 1992 Mar 2985811  2.99
10 1992 Apr 3204780  3.20
# ℹ 194 more rows

Working with tsibble objects

To save something for future use, use the assignment operator <-:

a10 <- PBS |>
  filter(ATC2 == "A10") |>
  select(Month, Concession, Type, Cost) |>
  summarise(TotalC = sum(Cost)) |>
  mutate(Cost = TotalC/1e6)

Time plots

Plot thousands of economy passengers flying between Melbourne (MEL) and Sydney (SYD) airports from the ansett dataset in fpp3 using the autoplot() command:

Time plots

Plot thousands of economy passengers flying between Melbourne (MEL) and Sydney (SYD) airports from the ansett dataset in fpp3 using the autoplot() command:

melsyd_economy <- ansett |>
  filter(Airports == "MEL-SYD", Class == "Economy") |>
  mutate(Passengers = Passengers/1000)
autoplot(melsyd_economy, Passengers) +
  labs(title = "Ansett airlines economy class",
       subtitle = "Melbourne-Sydney",
       y = "Passengers ('000)")

Time plots

Plot thousands of economy passengers flying between Melbourne (MEL) and Sydney (SYD) airports from the ansett dataset in fpp3 using the autoplot() command:

Time series patterns

Cyclicality: occurs when the data exhibit rises and falls of regular but not fixed frequency. If a fluctuation occurs with a fixed frequency and is related to the calendar, it’s seasonal.
Exercise time

Exercise: electricity

aus_production |>
  filter(year(Quarter) >= 1980) |>
  autoplot(Electricity) +
  labs(y = "GWh", title = "Australian electricity production")

Exercise: bricks

aus_production |>
  autoplot(Bricks) +
  labs(y = "million units", title = "Australian clay brick production")

Exercise: retail employment

us_employment |>
  filter(Title == "Retail Trade", year(Month) >= 1980) |>
  autoplot(Employed / 1000) +
  labs(y = "Million people", title = "Retail employment, USA")

Exercise: AMZN

gafa_stock |>
  filter(Symbol == "AMZN", year(Date) >= 2018) |>
  autoplot(Close) +
  labs(y = "USD", title = "AMZN closing price")