Chapter 2 Time Series Graphics

Tyler George

Cornell College
STA 364 Spring 2025 Block 5

Setup

library(patchwork)
library(fpp3)
library(tidyverse)

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"
    )
  )

Time series in R

tsibble objects

global_economy
# A tsibble: 15,150 x 6 [1Y]
# Key:       Country [263]
    Year Country             GDP Imports Exports Population
   <dbl> <fct>             <dbl>   <dbl>   <dbl>      <dbl>
 1  1960 Afghanistan  537777811.    7.02    4.13    8996351
 2  1961 Afghanistan  548888896.    8.10    4.45    9166764
 3  1962 Afghanistan  546666678.    9.35    4.88    9345868
 4  1963 Afghanistan  751111191.   16.9     9.17    9533954
 5  1964 Afghanistan  800000044.   18.1     8.89    9731361
 6  1965 Afghanistan 1006666638.   21.4    11.3     9938414
 7  1966 Afghanistan 1399999967.   18.6     8.57   10152331
 8  1967 Afghanistan 1673333418.   14.2     6.77   10372630
 9  1968 Afghanistan 1373333367.   15.2     8.90   10604346
10  1969 Afghanistan 1408888922.   15.0    10.1    10854428
# ℹ 15,140 more rows

tsibble objects

tourism |> head(5)
# A tsibble: 5 x 5 [1Q]
# Key:       Region, State, Purpose [1]
  Quarter Region   State Purpose  Trips
    <qtr> <chr>    <chr> <chr>    <dbl>
1 1998 Q1 Adelaide SA    Business  135.
2 1998 Q2 Adelaide SA    Business  110.
3 1998 Q3 Adelaide SA    Business  166.
4 1998 Q4 Adelaide SA    Business  127.
5 1999 Q1 Adelaide SA    Business  137.

Domestic visitor nights in thousands by state/region and purpose.

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

Example

mydata <- tsibble(
    year = 2012:2016,
    y = c(123, 39, 78, 52, 110),
    index = year
)
mydata
# A tsibble: 5 x 2 [1Y]
   year     y
  <int> <dbl>
1  2012   123
2  2013    39
3  2014    78
4  2015    52
5  2016   110

The tsibble index

Example

mydata <- tibble(
    year = 2012:2016,
    y = c(123, 39, 78, 52, 110)
  ) |>
  as_tsibble(index = year)
mydata
# A tsibble: 5 x 2 [1Y]
   year     y
  <int> <dbl>
1  2012   123
2  2013    39
3  2014    78
4  2015    52
5  2016   110

The tsibble index

For observations more frequent than once per year, we need to use a time class function on the index.

z
# A tibble: 5 × 2
  Month    Observation
  <chr>          <dbl>
1 2019 Jan          50
2 2019 Feb          23
3 2019 Mar          34
4 2019 Apr          30
5 2019 May          25

The tsibble index

For observations more frequent than once per year, we need to use a time class function on the index.

z |>
  mutate(Month = yearmonth(Month)) |>
  as_tsibble(index = Month)
# A tsibble: 5 x 2 [1M]
     Month Observation
     <mth>       <dbl>
1 2019 Jan          50
2 2019 Feb          23
3 2019 Mar          34
4 2019 Apr          30
5 2019 May          25

The tsibble index

Common time index variables can be created with these functions:

Frequency Function
Annual start:end
Quarterly yearquarter()
Monthly yearmonth()
Weekly yearweek()
Daily as_date(), ymd()
Sub-daily as_datetime()

Example: Australian prison population

Australian prison population

Read a csv file and convert to a tsibble

prison <- readr::read_csv("data/prison_population.csv")
#readr::read_csv("~/STA364/data/prison_population.csv")
# A tibble: 3,072 × 6
   date       state gender legal     indigenous count
   <date>     <chr> <chr>  <chr>     <chr>      <dbl>
 1 2005-03-01 ACT   Female Remanded  ATSI           0
 2 2005-03-01 ACT   Female Remanded  Other          2
 3 2005-03-01 ACT   Female Sentenced ATSI           0
 4 2005-03-01 ACT   Female Sentenced Other          0
 5 2005-03-01 ACT   Male   Remanded  ATSI           7
 6 2005-03-01 ACT   Male   Remanded  Other         58
 7 2005-03-01 ACT   Male   Sentenced ATSI           0
 8 2005-03-01 ACT   Male   Sentenced Other          0
 9 2005-03-01 NSW   Female Remanded  ATSI          51
10 2005-03-01 NSW   Female Remanded  Other        131
# ℹ 3,062 more rows

Read a csv file and convert to a tsibble

prison <- readr::read_csv("data/prison_population.csv") |>
  mutate(Quarter = yearquarter(date))
# A tibble: 3,072 × 7
   date       state gender legal     indigenous count Quarter
   <date>     <chr> <chr>  <chr>     <chr>      <dbl>   <qtr>
 1 2005-03-01 ACT   Female Remanded  ATSI           0 2005 Q1
 2 2005-03-01 ACT   Female Remanded  Other          2 2005 Q1
 3 2005-03-01 ACT   Female Sentenced ATSI           0 2005 Q1
 4 2005-03-01 ACT   Female Sentenced Other          0 2005 Q1
 5 2005-03-01 ACT   Male   Remanded  ATSI           7 2005 Q1
 6 2005-03-01 ACT   Male   Remanded  Other         58 2005 Q1
 7 2005-03-01 ACT   Male   Sentenced ATSI           0 2005 Q1
 8 2005-03-01 ACT   Male   Sentenced Other          0 2005 Q1
 9 2005-03-01 NSW   Female Remanded  ATSI          51 2005 Q1
10 2005-03-01 NSW   Female Remanded  Other        131 2005 Q1
# ℹ 3,062 more rows

Read a csv file and convert to a tsibble

prison <- readr::read_csv("data/prison_population.csv") |>
  mutate(Quarter = yearquarter(date)) |>
  select(-date)
# A tibble: 3,072 × 6
   state gender legal     indigenous count Quarter
   <chr> <chr>  <chr>     <chr>      <dbl>   <qtr>
 1 ACT   Female Remanded  ATSI           0 2005 Q1
 2 ACT   Female Remanded  Other          2 2005 Q1
 3 ACT   Female Sentenced ATSI           0 2005 Q1
 4 ACT   Female Sentenced Other          0 2005 Q1
 5 ACT   Male   Remanded  ATSI           7 2005 Q1
 6 ACT   Male   Remanded  Other         58 2005 Q1
 7 ACT   Male   Sentenced ATSI           0 2005 Q1
 8 ACT   Male   Sentenced Other          0 2005 Q1
 9 NSW   Female Remanded  ATSI          51 2005 Q1
10 NSW   Female Remanded  Other        131 2005 Q1
# ℹ 3,062 more rows

Read a csv file and convert to a tsibble

prison <- readr::read_csv("data/prison_population.csv") |>
  mutate(Quarter = yearquarter(date)) |>
  select(-date) |>
  as_tsibble(
    index = Quarter,
    key = c(state, gender, legal, indigenous)
  )
# A tsibble: 5 x 6 [1Q]
# Key:       state, gender, legal, indigenous [1]
  state gender legal    indigenous count Quarter
  <chr> <chr>  <chr>    <chr>      <dbl>   <qtr>
1 ACT   Female Remanded ATSI           0 2005 Q1
2 ACT   Female Remanded ATSI           1 2005 Q2
3 ACT   Female Remanded ATSI           0 2005 Q3
4 ACT   Female Remanded ATSI           0 2005 Q4
5 ACT   Female Remanded ATSI           1 2006 Q1

Example: Australian pharmaceutical sales

Australian Pharmaceutical Benefits Scheme

Australian Pharmaceutical Benefits Scheme

The Pharmaceutical Benefits Scheme (PBS) is the Australian government drugs subsidy scheme.

  • Many drugs bought from pharmacies are subsidised to allow more equitable access to modern drugs.
  • The cost to government is determined by the number and types of drugs purchased. Currently nearly 1% of GDP.
  • The total cost is budgeted based on forecasts of drug usage.
  • Costs are disaggregated by drug type (ATC1 x15 / ATC2 84), concession category (x2) and patient type (x2), giving \(84\times2\times2=336\) time series.

Working with tsibble objects

PBS |> head(5)
# A tsibble: 5 x 9 [1M]
# Key:       Concession, Type, ATC1, ATC2 [1]
     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-payments A     Alimentary tract … A01   STOMATOL…   18228 67877
2 1991 Aug Concessional Co-payments A     Alimentary tract … A01   STOMATOL…   15327 57011
3 1991 Sep Concessional Co-payments A     Alimentary tract … A01   STOMATOL…   14775 55020
4 1991 Oct Concessional Co-payments A     Alimentary tract … A01   STOMATOL…   15380 57222
5 1991 Nov Concessional Co-payments A     Alimentary tract … A01   STOMATOL…   14371 52120

Working with tsibble objects

We can use the filter() function to select rows.

PBS |>
  filter(ATC2 == "A10")|> 
  head(5)
# A tsibble: 5 x 9 [1M]
# Key:       Concession, Type, ATC1, ATC2 [1]
     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-payments A     Alimentary tract… A10   ANTIDIAB…   89733 2.09e6
2 1991 Aug Concessional Co-payments A     Alimentary tract… A10   ANTIDIAB…   77101 1.80e6
3 1991 Sep Concessional Co-payments A     Alimentary tract… A10   ANTIDIAB…   76255 1.78e6
4 1991 Oct Concessional Co-payments A     Alimentary tract… A10   ANTIDIAB…   78681 1.85e6
5 1991 Nov Concessional Co-payments A     Alimentary tract… A10   ANTIDIAB…   70554 1.69e6

Working with tsibble objects

We can use the select() function to select columns.

PBS |>
  filter(ATC2 == "A10") |>
  select(Month, Concession, Type, Cost)|> 
  head(5)
# A tsibble: 5 x 4 [1M]
# Key:       Concession, Type [1]
     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

Working with tsibble objects

We can use the summarise() function to summarise over keys.

PBS |>
  filter(ATC2 == "A10") |>
  select(Month, Concession, Type, Cost) |>
  summarise(total_cost = sum(Cost))|> 
  head(5)
# A tsibble: 5 x 2 [1M]
     Month total_cost
     <mth>      <dbl>
1 1991 Jul    3526591
2 1991 Aug    3180891
3 1991 Sep    3252221
4 1991 Oct    3611003
5 1991 Nov    3565869

Working with tsibble objects

We can use the mutate() function to create new variables.

PBS |>
  filter(ATC2 == "A10") |>
  select(Month, Concession, Type, Cost) |>
  summarise(total_cost = sum(Cost)) |>
  mutate(total_cost = total_cost / 1e6)|> 
  head(5)
# A tsibble: 5 x 2 [1M]
     Month total_cost
     <mth>      <dbl>
1 1991 Jul       3.53
2 1991 Aug       3.18
3 1991 Sep       3.25
4 1991 Oct       3.61
5 1991 Nov       3.57

Working with tsibble objects

We can use the mutate() function to create new variables.

a10 <- PBS |>
  filter(ATC2 == "A10") |>
  select(Month, Concession, Type, Cost) |>
  summarise(total_cost = sum(Cost)) |>
  mutate(total_cost = total_cost / 1e6) |> 
  head(5)
# A tsibble: 5 x 2 [1M]
     Month total_cost
     <mth>      <dbl>
1 1991 Jul       3.53
2 1991 Aug       3.18
3 1991 Sep       3.25
4 1991 Oct       3.61
5 1991 Nov       3.57

Time plots

Time plots

a10 |>
  autoplot(total_cost)

Ansett airlines

ansett |>
  autoplot(Passengers)

Ansett airlines

ansett |>
  filter(Class == "Economy") |>
  autoplot(Passengers)

Ansett airlines

ansett |>
  filter(Airports == "MEL-SYD") |>
  autoplot(Passengers)

Time series patterns

Trend
pattern exists when there is a long-term increase or decrease in the data.
Seasonal
pattern exists when a series is influenced by seasonal factors (e.g., the quarter of the year, the month, or day of the week).
Cyclic
pattern exists when data exhibit rises and falls that are (duration usually of at least 2 years).

Time series components

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

Time series patterns

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

Time series patterns

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

Time series patterns

us_employment |>
  filter(Title == "Retail Trade", year(Month) >= 1980) |>
  autoplot(Employed / 1e3) +
  labs(y = "Million people", title = "Retail employment, USA")

Time series patterns

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

Time series patterns

pelt |>
  autoplot(Lynx) +
  labs(y="Number trapped", title = "Annual Canadian Lynx Trappings")

Seasonal or cyclic?

  • 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

Seasonal and subseries plots

Seasonal plots

a10 |> gg_season(total_cost, labels = "both") +
  labs(y = "$ million", title = "Seasonal plot: antidiabetic drug sales")

Seasonal plots

  • Data plotted against the individual “seasons” in which the data were observed. (In this case a “season” is a month.)
  • Something like a time plot except that the data from each season are overlapped.
  • Enables the underlying seasonal pattern to be seen more clearly, and also allows any substantial departures from the seasonal pattern to be easily identified.
  • In R: gg_season()

Seasonal subseries plots

a10 |>
  gg_subseries(total_cost) +
  labs(y = "$ million", title = "Subseries plot: antidiabetic drug sales")

Seasonal subseries plots

  • Data for each season collected together in time plot as separate time series.
  • Enables the underlying seasonal pattern to be seen clearly, and changes in seasonality over time to be visualized.
  • In R: gg_subseries()

Quarterly Australian Beer Production

beer <- aus_production |>
  select(Quarter, Beer) |>
  filter(year(Quarter) >= 1992)
beer |> autoplot(Beer)

Quarterly Australian Beer Production

beer |> gg_season(Beer, labels="right")

Quarterly Australian Beer Production

beer |> gg_subseries(Beer)

Multiple seasonal periods

vic_elec
# A tsibble: 52,608 x 5 [30m] <Australia/Melbourne>
   Time                Demand Temperature Date       Holiday
   <dttm>               <dbl>       <dbl> <date>     <lgl>  
 1 2012-01-01 00:00:00  4383.        21.4 2012-01-01 TRUE   
 2 2012-01-01 00:30:00  4263.        21.0 2012-01-01 TRUE   
 3 2012-01-01 01:00:00  4049.        20.7 2012-01-01 TRUE   
 4 2012-01-01 01:30:00  3878.        20.6 2012-01-01 TRUE   
 5 2012-01-01 02:00:00  4036.        20.4 2012-01-01 TRUE   
 6 2012-01-01 02:30:00  3866.        20.2 2012-01-01 TRUE   
 7 2012-01-01 03:00:00  3694.        20.1 2012-01-01 TRUE   
 8 2012-01-01 03:30:00  3562.        19.6 2012-01-01 TRUE   
 9 2012-01-01 04:00:00  3433.        19.1 2012-01-01 TRUE   
10 2012-01-01 04:30:00  3359.        19.0 2012-01-01 TRUE   
# ℹ 52,598 more rows

Multiple seasonal periods

vic_elec |> gg_season(Demand)

Multiple seasonal periods

vic_elec |> gg_season(Demand, period = "week")

Multiple seasonal periods

vic_elec |> gg_season(Demand, period = "day")

Australian holidays

holidays <- tourism |>
  filter(Purpose == "Holiday") |>
  group_by(State) |>
  summarise(Trips = sum(Trips))
# A tsibble: 640 x 3 [1Q]
# Key:       State [8]
   State Quarter Trips
   <chr>   <qtr> <dbl>
 1 ACT   1998 Q1  196.
 2 ACT   1998 Q2  127.
 3 ACT   1998 Q3  111.
 4 ACT   1998 Q4  170.
 5 ACT   1999 Q1  108.
 6 ACT   1999 Q2  125.
 7 ACT   1999 Q3  178.
 8 ACT   1999 Q4  218.
 9 ACT   2000 Q1  158.
10 ACT   2000 Q2  155.
# ℹ 630 more rows

Australian holidays

holidays |> autoplot(Trips) +
  labs(y = "thousands of trips", title = "Australian domestic holiday nights")

Seasonal plots

holidays |> gg_season(Trips) +
  labs(y = "thousands of trips", title = "Australian domestic holiday nights")

Seasonal subseries plots

holidays |>
  gg_subseries(Trips) +
  labs(y = "thousands of trips", title = "Australian domestic holiday nights")

Lag plots and autocorrelation

Example: Beer production

new_production <- aus_production |>
  filter(year(Quarter) >= 1992)
new_production
# A tsibble: 74 x 7 [1Q]
   Quarter  Beer Tobacco Bricks Cement Electricity   Gas
     <qtr> <dbl>   <dbl>  <dbl>  <dbl>       <dbl> <dbl>
 1 1992 Q1   443    5777    383   1289       38332   117
 2 1992 Q2   410    5853    404   1501       39774   151
 3 1992 Q3   420    6416    446   1539       42246   175
 4 1992 Q4   532    5825    420   1568       38498   129
 5 1993 Q1   433    5724    394   1450       39460   116
 6 1993 Q2   421    6036    462   1668       41356   149
 7 1993 Q3   410    6570    475   1648       42949   163
 8 1993 Q4   512    5675    443   1863       40974   138
 9 1994 Q1   449    5311    421   1468       40162   127
10 1994 Q2   381    5717    475   1755       41199   159
# ℹ 64 more rows

Example: Beer production

new_production |> gg_lag(Beer)

Example: Beer production

new_production |> gg_lag(Beer, geom='point')

Lagged scatterplots

  • Each graph shows \(y_t\) plotted against \(y_{t-k}\) for different values of \(k\).
  • The autocorrelations are the correlations associated with these scatterplots.
  • ACF (autocorrelation function):
    • \(r_1=\text{Correlation}(y_{t}, y_{t-1})\)
    • \(r_2=\text{Correlation}(y_{t}, y_{t-2})\)
    • \(r_3=\text{Correlation}(y_{t}, y_{t-3})\)
    • etc.

Autocorrelation

Covariance and correlation: measure extent of linear relationship between two variables (\(y\) and \(X\)).

Autocovariance and autocorrelation: measure linear relationship between lagged values of a time series \(y\).

We measure the relationship between:

  • \(y_{t}\) and \(y_{t-1}\)
  • \(y_{t}\) and \(y_{t-2}\)
  • \(y_{t}\) and \(y_{t-3}\)
  • etc.

Autocorrelation

We denote the sample autocovariance at lag \(k\) by \(c_k\) and the sample autocorrelation at lag \(k\) by \(r_k\). Then define

  • \(r_1\) indicates how successive values of \(y\) relate to each other
  • \(r_2\) indicates how \(y\) values two periods apart relate to each other
  • \(r_k\) is the same as the sample correlation between \(y_t\) and \(y_{t-k}\).

Autocorrelation

Results for first 9 lags for beer data:

new_production |> ACF(Beer, lag_max = 9)
# A tsibble: 9 x 2 [1Q]
       lag     acf
  <cf_lag>   <dbl>
1       1Q -0.102 
2       2Q -0.657 
3       3Q -0.0603
4       4Q  0.869 
5       5Q -0.0892
6       6Q -0.635 
7       7Q -0.0542
8       8Q  0.832 
9       9Q -0.108

Autocorrelation

Results for first 9 lags for beer data:

new_production |> ACF(Beer, lag_max = 9) |> autoplot()
  • Together, the autocorrelations at lags 1, 2, , make up the or ACF.
  • The plot is known as a correlogram

Autocorrelation

new_production |> ACF(Beer) |> autoplot()
  • \(r_{4}\) higher than for the other lags. This is due to the seasonal pattern in the data: the peaks tend to be 4 quarters apart and the troughs tend to be 2 quarters apart.
  • \(r_2\) is more negative than for the other lags because troughs tend to be 2 quarters behind peaks.

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.

Autocorrelation functions

US retail trade employment

retail <- us_employment |>
  filter(Title == "Retail Trade", year(Month) >= 1980)
retail |> autoplot(Employed)

US retail trade employment

retail |>
  ACF(Employed, lag_max = 48) |>
  autoplot()

Google stock price

google_2015 <- gafa_stock |>
  filter(Symbol == "GOOG", year(Date) == 2015) |>
  select(Date, Close)
google_2015
# A tsibble: 252 x 2 [!]
   Date       Close
   <date>     <dbl>
 1 2015-01-02  522.
 2 2015-01-05  511.
 3 2015-01-06  499.
 4 2015-01-07  498.
 5 2015-01-08  500.
 6 2015-01-09  493.
 7 2015-01-12  490.
 8 2015-01-13  493.
 9 2015-01-14  498.
10 2015-01-15  499.
# ℹ 242 more rows

Google stock price

google_2015 |> autoplot(Close)

Google stock price

google_2015 |>
  ACF(Close, lag_max=100)
# A tsibble: 100 x 2 [1]
        lag   acf
   <cf_lag> <dbl>
 1        1 0.982
 2        2 0.959
 3        3 0.937
 4        4 0.918
 5        5 0.901
 6        6 0.883
 7        7 0.865
 8        8 0.849
 9        9 0.834
10       10 0.818
# ℹ 90 more rows

Google stock price

google_2015 |>
  ACF(Close, lag_max = 100) |>
  autoplot()

Which is which?

White noise

Example: White noise

set.seed(30)
wn <- tsibble(t = 1:50, y = rnorm(50), index = t)
wn |> autoplot(y)

Note

White noise data is uncorrelated across time with zero mean and constant variance.

(Technically, we require independence as well.)

Example: White noise

wn |> ACF(y)
\(r_{1}\) \(r_{2}\) \(r_{3}\) \(r_{4}\) \(r_{5}\) \(r_{6}\) \(r_{7}\) \(r_{8}\) \(r_{9}\) \(r_{10}\)
0.014 -0.163 0.163 -0.259 -0.198 0.064 -0.139 -0.032 0.199 -0.024
  • Sample autocorrelations for white noise series.
  • Expect each autocorrelation to be close to zero.
  • Blue lines show 95% critical values.

Sampling distribution of autocorrelations

Sampling distribution of \(r_k\) for white noise data is asymptotically N(0,\(1/T\)).

  • 95% of all \(r_k\) for white noise must lie within \(\pm 1.96/\sqrt{T}\).
  • If this is not the case, the series is probably not WN.
  • Common to plot lines at \(\pm 1.96/\sqrt{T}\) when plotting ACF. These are the .

Example: Pigs slaughtered

pigs <- aus_livestock |>
  filter(State == "Victoria", Animal == "Pigs", year(Month) >= 2014)
pigs |> autoplot(Count/1e3) +
  labs(y = "Thousands", title = "Number of pigs slaughtered in Victoria")

Example: Pigs slaughtered

pigs |> ACF(Count) |> autoplot()

Example: Pigs slaughtered

Monthly total number of pigs slaughtered in the state of Victoria, Australia, from January 2014 through December 2018 (Source: Australian Bureau of Statistics.)

  • Difficult to detect pattern in time plot.
  • ACF shows significant autocorrelation for lag 2 and 12.
  • Indicate some slight seasonality.

Important

These show the series is not a white noise series.

Your turn

You can compute the daily changes in the Google stock price in 2018 using

dgoog <- gafa_stock |>
  filter(Symbol == "GOOG", year(Date) >= 2018) |>
  mutate(diff = difference(Close))

Does diff look like white noise?