Data 624 Homework 1
Steven Gonzalez
2/9/2025
Load Packages
library(fpp3)
library(USgas)Exercise 1
Explore the following four time series: Bricks from
aus_production, Lynx from pelt,
Close from gafa_stock, Demand
from vic_elec.
Use ? (or help()) to find out about the
data in each series. What is the time interval of each series? Use
autoplot() to produce a time plot of each series. For the
last plot, modify the axis labels and title.
?aus_production
aus_production #used to get further familiarized with the data## # A tsibble: 218 x 7 [1Q]
## Quarter Beer Tobacco Bricks Cement Electricity Gas
## <qtr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1956 Q1 284 5225 189 465 3923 5
## 2 1956 Q2 213 5178 204 532 4436 6
## 3 1956 Q3 227 5297 208 561 4806 7
## 4 1956 Q4 308 5681 197 570 4418 6
## 5 1957 Q1 262 5577 187 529 4339 5
## 6 1957 Q2 228 5651 214 604 4811 7
## 7 1957 Q3 236 5317 227 603 5259 7
## 8 1957 Q4 320 6152 222 582 4735 6
## 9 1958 Q1 272 5758 199 554 4608 5
## 10 1958 Q2 233 5641 229 620 5196 7
## # â„ą 208 more rowsAs can be seen from the results above, the Bricks time
series from aus_production has a quarterly time interval.
Below is the time plot illustrating this using
autoplot().
autoplot(aus_production, Bricks)
?pelt
pelt #used to get further familiarized with the data## # A tsibble: 91 x 3 [1Y]
## Year Hare Lynx
## <dbl> <dbl> <dbl>
## 1 1845 19580 30090
## 2 1846 19600 45150
## 3 1847 19610 49150
## 4 1848 11990 39520
## 5 1849 28040 21230
## 6 1850 58000 8420
## 7 1851 74600 5560
## 8 1852 75090 5080
## 9 1853 88480 10170
## 10 1854 61280 19600
## # â„ą 81 more rowsAs can be seen from the results above, the Lynx time
series from pelt has an annual time interval. Below is the
time plot illustrating this using autoplot().
autoplot(pelt, Lynx)
?gafa_stock
gafa_stock #used to get further familiarized with the data## # A tsibble: 5,032 x 8 [!]
## # Key: Symbol [4]
## Symbol Date Open High Low Close Adj_Close Volume
## <chr> <date> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 AAPL 2014-01-02 79.4 79.6 78.9 79.0 67.0 58671200
## 2 AAPL 2014-01-03 79.0 79.1 77.2 77.3 65.5 98116900
## 3 AAPL 2014-01-06 76.8 78.1 76.2 77.7 65.9 103152700
## 4 AAPL 2014-01-07 77.8 78.0 76.8 77.1 65.4 79302300
## 5 AAPL 2014-01-08 77.0 77.9 77.0 77.6 65.8 64632400
## 6 AAPL 2014-01-09 78.1 78.1 76.5 76.6 65.0 69787200
## 7 AAPL 2014-01-10 77.1 77.3 75.9 76.1 64.5 76244000
## 8 AAPL 2014-01-13 75.7 77.5 75.7 76.5 64.9 94623200
## 9 AAPL 2014-01-14 76.9 78.1 76.8 78.1 66.1 83140400
## 10 AAPL 2014-01-15 79.1 80.0 78.8 79.6 67.5 97909700
## # â„ą 5,022 more rowsAs can be seen from the results above, the Close time
series from gafa_stock has a time interval with specific
dates that seem to be business days, which would make sense given that
it is a data set on stock prices. Below is the time plot illustrating
this using autoplot().
autoplot(gafa_stock, Close)
?vic_elec
vic_elec #used to get further familiarized with the data## # 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
## # â„ą 52,598 more rowsAs can be seen from the results above, the Demand time
series from vic_elec has a half-hourly time interval. Below
is the time plot illustrating this using autoplot() with
modified title and axis labels.
autoplot(vic_elec, Demand) +
labs(title = "Half-hourly electricity demand for Victoria, Australia",
y = "Total Electricity Demand (MWh)")
Exercise 2
Use filter() to find what days corresponded to the peak
closing price for each of the four stocks in
gafa_stock.
aapl_peak <- gafa_stock %>%
filter(Symbol == "AAPL") %>%
select(Symbol, Date, Close) %>%
slice_max(Close, n = 1)
aapl_peak## # A tsibble: 1 x 3 [!]
## # Key: Symbol [1]
## Symbol Date Close
## <chr> <date> <dbl>
## 1 AAPL 2018-10-03 232.amzn_peak <- gafa_stock %>%
filter(Symbol == "AMZN") %>%
select(Symbol, Date, Close) %>%
slice_max(Close, n = 1)
amzn_peak## # A tsibble: 1 x 3 [!]
## # Key: Symbol [1]
## Symbol Date Close
## <chr> <date> <dbl>
## 1 AMZN 2018-09-04 2040.fb_peak <- gafa_stock %>%
filter(Symbol == "FB") %>%
select(Symbol, Date, Close) %>%
slice_max(Close, n = 1)
fb_peak## # A tsibble: 1 x 3 [!]
## # Key: Symbol [1]
## Symbol Date Close
## <chr> <date> <dbl>
## 1 FB 2018-07-25 218.goog_peak <- gafa_stock %>%
filter(Symbol == "GOOG") %>%
select(Symbol, Date, Close) %>%
slice_max(Close, n = 1)
goog_peak## # A tsibble: 1 x 3 [!]
## # Key: Symbol [1]
## Symbol Date Close
## <chr> <date> <dbl>
## 1 GOOG 2018-07-26 1268.Exercise 3
Download the file tute1.csv from the book website, open
it in Excel (or some other spreadsheet application), and review its
contents. You should find four columns of information. Columns B through
D each contain a quarterly series, labelled Sales, AdBudget and GDP.
Sales contains the quarterly sales for a small company over the period
1981-2005. AdBudget is the advertising budget and GDP is the gross
domestic product. All series have been adjusted for inflation.
You can read the data into R with the following script:
tute1 <- readr::read_csv("tute1.csv") View(tute1)
Convert the data to time series
mytimeseries <- tute1 |> mutate(Quarter = yearquarter(Quarter)) |> as_tsibble(index = Quarter)
Construct time series plots of each of the three series
mytimeseries |> pivot_longer(-Quarter) |> ggplot(aes(x = Quarter, y = value, colour = name)) + geom_line() + facet_grid(name ~ ., scales = "free_y")
Check what happens when you don’t include facet_grid().
url <- "https://raw.githubusercontent.com/Stevee-G/Data624/refs/heads/main/tute1.csv"
tute1 <- readr::read_csv(url) #Had to modify the command in order to make the RMD reproducible## Rows: 100 Columns: 4
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## dbl (3): Sales, AdBudget, GDP
## date (1): Quarter
##
## â„ą Use `spec()` to retrieve the full column specification for this data.
## â„ą Specify the column types or set `show_col_types = FALSE` to quiet this message.View(tute1)
mytimeseries <- tute1 %>%
mutate(Quarter = yearquarter(Quarter)) %>%
as_tsibble(index = Quarter) #Modified the pipe due to personal preference
mytimeseries %>%
pivot_longer(-Quarter) %>%
ggplot(aes(x = Quarter, y = value, colour = name)) +
geom_line() +
facet_grid(name ~ ., scales = "free_y")
mytimeseries %>%
pivot_longer(-Quarter) %>%
ggplot(aes(x = Quarter, y = value, colour = name)) +
geom_line()
Exercise 4
The USgas package contains data on the demand for
natural gas in the US.
Install the USgas package. Create a tsibble
from us_total with year as the index and state as the key.
Plot the annual natural gas consumption by state for the New England
area (comprising the states of Maine, Vermont, New Hampshire,
Massachusetts, Connecticut and Rhode Island).
#USgas package was installed and loaded in a previous section
?us_total
glimpse(us_total)## Rows: 1,266
## Columns: 3
## $ year <int> 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007…
## $ state <chr> "Alabama", "Alabama", "Alabama", "Alabama", "Alabama", "Alabama"…
## $ y <int> 324158, 329134, 337270, 353614, 332693, 379343, 350345, 382367, …us_total_ts <- us_total %>%
as_tsibble(index = year, key = state)
new_england <- us_total_ts %>%
filter(state == "Maine" |
state == "Vermont" |
state == "New Hampshire" |
state == "Massachusetts" |
state == "Connecticut" |
state == "Rhode Island")
autoplot(new_england, y)
Exercise 5
Download tourism.xlsx from the book website and read it
into R using readxl::read_excel(). Create a tsibble which
is identical to the tourism tsibble from the
tsibble package. Find what combination of
Region and Purpose had the maximum number of
overnight trips on average. Create a new tsibble which combines the
Purposes and Regions, and just has total trips by State.
url1 <- "https://raw.githubusercontent.com/Stevee-G/Data624/refs/heads/main/tourism.csv"
tourism1 <- readr::read_csv(url1) #Had to resort to csv due to an issue with OneDrive making the excel unreadable when importing data from online
glimpse(tourism1)## Rows: 24,320
## Columns: 5
## $ Quarter <date> 1998-01-01, 1998-04-01, 1998-07-01, 1998-10-01, 1999-01-01, 1…
## $ Region <chr> "Adelaide", "Adelaide", "Adelaide", "Adelaide", "Adelaide", "A…
## $ State <chr> "South Australia", "South Australia", "South Australia", "Sout…
## $ Purpose <chr> "Business", "Business", "Business", "Business", "Business", "B…
## $ Trips <dbl> 135.0777, 109.9873, 166.0347, 127.1605, 137.4485, 199.9126, 16…tourism #Take a look at the tourism tsibble in order to compare with tsibble made from the tourism excel sheet## # A tsibble: 24,320 x 5 [1Q]
## # Key: Region, State, Purpose [304]
## Quarter Region State Purpose Trips
## <qtr> <chr> <chr> <chr> <dbl>
## 1 1998 Q1 Adelaide South Australia Business 135.
## 2 1998 Q2 Adelaide South Australia Business 110.
## 3 1998 Q3 Adelaide South Australia Business 166.
## 4 1998 Q4 Adelaide South Australia Business 127.
## 5 1999 Q1 Adelaide South Australia Business 137.
## 6 1999 Q2 Adelaide South Australia Business 200.
## 7 1999 Q3 Adelaide South Australia Business 169.
## 8 1999 Q4 Adelaide South Australia Business 134.
## 9 2000 Q1 Adelaide South Australia Business 154.
## 10 2000 Q2 Adelaide South Australia Business 169.
## # â„ą 24,310 more rows?tourism #Get familiar with tourism tsibble to identify index
tourism1_ts <- tourism1 %>%
mutate(Quarter = yearquarter(Quarter)) %>%
as_tsibble(index = Quarter, key = c(Region, State, Purpose))
tourism1_ts #Glimpse and compare tourism1_ts to tourism tsibble## # A tsibble: 24,320 x 5 [1Q]
## # Key: Region, State, Purpose [304]
## Quarter Region State Purpose Trips
## <qtr> <chr> <chr> <chr> <dbl>
## 1 1998 Q1 Adelaide South Australia Business 135.
## 2 1998 Q2 Adelaide South Australia Business 110.
## 3 1998 Q3 Adelaide South Australia Business 166.
## 4 1998 Q4 Adelaide South Australia Business 127.
## 5 1999 Q1 Adelaide South Australia Business 137.
## 6 1999 Q2 Adelaide South Australia Business 200.
## 7 1999 Q3 Adelaide South Australia Business 169.
## 8 1999 Q4 Adelaide South Australia Business 134.
## 9 2000 Q1 Adelaide South Australia Business 154.
## 10 2000 Q2 Adelaide South Australia Business 169.
## # â„ą 24,310 more rowsBy comparing the tsibbles produced above we can say for certain that
the new tourism1_ts is identical to the original
tourism.
max_avg_trips <- tourism1_ts %>%
group_by(Region, Purpose) %>%
summarise(avg_trips = mean(Trips)) %>%
slice_max(avg_trips, n = 1) %>%
arrange(desc(avg_trips))
max_avg_trips## # A tsibble: 76 x 4 [1Q]
## # Key: Region, Purpose [76]
## # Groups: Region [76]
## Region Purpose Quarter avg_trips
## <chr> <chr> <qtr> <dbl>
## 1 Melbourne Visiting 2017 Q4 985.
## 2 Sydney Business 2001 Q4 948.
## 3 South Coast Holiday 1998 Q1 915.
## 4 North Coast NSW Holiday 2016 Q1 906.
## 5 Brisbane Visiting 2016 Q4 796.
## 6 Gold Coast Holiday 2002 Q1 711.
## 7 Sunshine Coast Holiday 2005 Q1 617.
## 8 Australia's South West Holiday 2016 Q1 612.
## 9 Great Ocean Road Holiday 1998 Q1 548.
## 10 Experience Perth Visiting 2016 Q1 538.
## # â„ą 66 more rowsThrough the code chunk above, we can see that the combination of
Region and Purpose with the maximum number of
overnight trips on average was “Melbourne” and “Visiting”.
total_trips <- tourism1_ts %>%
group_by(State) %>% #By using the group_by function on State, we can collapse all region and purpose data to see what the total trips are by state/territory
summarise(tot_trips = sum(Trips))
total_trips## # A tsibble: 640 x 3 [1Q]
## # Key: State [8]
## State Quarter tot_trips
## <chr> <qtr> <dbl>
## 1 ACT 1998 Q1 551.
## 2 ACT 1998 Q2 416.
## 3 ACT 1998 Q3 436.
## 4 ACT 1998 Q4 450.
## 5 ACT 1999 Q1 379.
## 6 ACT 1999 Q2 558.
## 7 ACT 1999 Q3 449.
## 8 ACT 1999 Q4 595.
## 9 ACT 2000 Q1 600.
## 10 ACT 2000 Q2 557.
## # â„ą 630 more rowsExercise 8
Use the following graphics functions: autoplot(),
gg_season(), gg_subseries(),
gg_lag(), ACF() and explore features from the
following time series: “Total Private” Employed from
us_employment, Bricks from
aus_production, Hare from pelt,
“H02” Cost from PBS, and Barrels
from us_gasoline.
Can you spot any seasonality, cyclicity and trend? What do you learn about the series? What can you say about the seasonal patterns? Can you identify any unusual years?
us_employment## # A tsibble: 143,412 x 4 [1M]
## # Key: Series_ID [148]
## Month Series_ID Title Employed
## <mth> <chr> <chr> <dbl>
## 1 1939 Jan CEU0500000001 Total Private 25338
## 2 1939 Feb CEU0500000001 Total Private 25447
## 3 1939 Mar CEU0500000001 Total Private 25833
## 4 1939 Apr CEU0500000001 Total Private 25801
## 5 1939 May CEU0500000001 Total Private 26113
## 6 1939 Jun CEU0500000001 Total Private 26485
## 7 1939 Jul CEU0500000001 Total Private 26481
## 8 1939 Aug CEU0500000001 Total Private 26848
## 9 1939 Sep CEU0500000001 Total Private 27468
## 10 1939 Oct CEU0500000001 Total Private 27830
## # â„ą 143,402 more rowsprivate_employment <- us_employment %>%
filter(Title == "Total Private")
autoplot(private_employment, Employed)
gg_season(private_employment, y = Employed)
gg_subseries(private_employment, y = Employed)
gg_lag(private_employment, y = Employed)
ACF(private_employment, y = Employed) %>%
autoplot()
As can be seen above, the “Total Private” Employed time
series from us_employment does seem to show some
seasonality where the numbers employed go up through the middle months
of the year just to drop again towards the end of the year but still
higher than they were in the beginning of the year. The series did have
some cyclicity throughout the 80 year stretch that could be due to
fluctuations in the economy, especially the unusual dip recorded in the
few years leading up to 2010. The over all trend of the series is
positive.
aus_production## # A tsibble: 218 x 7 [1Q]
## Quarter Beer Tobacco Bricks Cement Electricity Gas
## <qtr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1956 Q1 284 5225 189 465 3923 5
## 2 1956 Q2 213 5178 204 532 4436 6
## 3 1956 Q3 227 5297 208 561 4806 7
## 4 1956 Q4 308 5681 197 570 4418 6
## 5 1957 Q1 262 5577 187 529 4339 5
## 6 1957 Q2 228 5651 214 604 4811 7
## 7 1957 Q3 236 5317 227 603 5259 7
## 8 1957 Q4 320 6152 222 582 4735 6
## 9 1958 Q1 272 5758 199 554 4608 5
## 10 1958 Q2 233 5641 229 620 5196 7
## # â„ą 208 more rowsautoplot(aus_production, Bricks)
gg_season(aus_production, y = Bricks)
gg_subseries(aus_production, y = Bricks)
gg_lag(aus_production, y = Bricks)
ACF(aus_production, y = Bricks) %>%
autoplot()
As can be seen above, the Bricks time series from
aus_production gives clear signs of seasonality where the
number of bricks produced goes up in quarters two and three to drop
dramatically towards the beginning of the following year. The series was
cyclical every few years and had some especially hard dips around the
years 1975, 1983, 1991, and 1996. The over all trend began positive up
until around 1983 where things began going south. This could probably be
due to consumer demand for bricks decreasing throughout the last few
decades.
pelt## # A tsibble: 91 x 3 [1Y]
## Year Hare Lynx
## <dbl> <dbl> <dbl>
## 1 1845 19580 30090
## 2 1846 19600 45150
## 3 1847 19610 49150
## 4 1848 11990 39520
## 5 1849 28040 21230
## 6 1850 58000 8420
## 7 1851 74600 5560
## 8 1852 75090 5080
## 9 1853 88480 10170
## 10 1854 61280 19600
## # â„ą 81 more rowsautoplot(pelt, Hare)
#gg_season(pelt, y = Hare, period = "year") Couldn't get it to work :(
gg_subseries(pelt, y = Hare)
gg_lag(pelt, y = Hare)
ACF(pelt, y = Hare) %>%
autoplot()
As can be seen above, the Hare time series from
pelt shows very little, f any, signs of seasonality.
Seasonality can only be defined within a year, whether it be quarterly,
monthly, or weekly. This time series does not show to have yearly
patterns but rather a pattern that seems to last around 10 years at a
time. This pattern can be better described as cyclical. With regards to
trend, there seems to be no indication of one, whether positive or
negative. This series is best defined as a pattern of habitual decade
long cycles repeating nonstop.
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
## # â„ą 67,586 more rowsH02 <- PBS %>%
filter(ATC2 == "H02")
autoplot(H02, Cost)
gg_season(H02, y = Cost)
gg_subseries(H02, y = Cost)
#gg_lag(H02, y = Cost) Couldn't get it to work :(
ACF(H02, y = Cost) %>%
autoplot()
As can be seen above, the “H02” Cost time series from
PBS is seasonal for some
Concession/Type combinations but not for all.
Right off the bat we can see in the gg_season and
gg_subseries plots that general/co_payments combination is
not seasonal, while the rest are. Concessional/co-payments seems to rise
throughout the middle months, concessional/safety net seems to dip
during the middle months, and general/safety net seems to rise slightly
during the final months of the year. Given the above plots, we can’t say
for sure whether there is a cycle since the fluctuations seen can be
explained by the seasonality mentioned earlier. There are noticeable
trends with concessional/co_payments and concessional/safety net moving
in the positive throughout the years while general_co-payments and
general/safety net remain about the same.
us_gasoline## # A tsibble: 1,355 x 2 [1W]
## Week Barrels
## <week> <dbl>
## 1 1991 W06 6.62
## 2 1991 W07 6.43
## 3 1991 W08 6.58
## 4 1991 W09 7.22
## 5 1991 W10 6.88
## 6 1991 W11 6.95
## 7 1991 W12 7.33
## 8 1991 W13 6.78
## 9 1991 W14 7.50
## 10 1991 W15 6.92
## # â„ą 1,345 more rowsautoplot(us_gasoline, Barrels)
gg_season(us_gasoline, y = Barrels)
gg_subseries(us_gasoline, y = Barrels)
gg_lag(us_gasoline, y = Barrels)
ACF(us_gasoline, y = Barrels) %>%
autoplot()
As can be seen above, the Barrels time series from
us_gasoline does seem to show slight seasonality with the
barrels sold between the months of March and October bumping up and
going back down shortly after. There don’t seem to be any prominent
cycles except for the dip observed around the years 2007 to 2013 which
was most likely caused by the economic
recession of 2008. The overall trend, however, is positive and it
seems that US gasoline consumption managed to recover from the
downturn.
Works Cited
History.com Editors. (2019, October 11). Great Recession. HISTORY; A&E Television Networks. https://www.history.com/topics/21st-century/recession