library(fpp3)

Exercise 2.1

Explore the following four time series: Bricks from aus_production, Lynx from pelt, Close from gafa_stock, Demand from vic_elec.

data(aus_production, pelt, gafa_stock, vic_elec)
  • Use ? (or help()) to find out about the data in each series.
?aus_production
?pelt
?gafa_stock
?vic_elec
  • What is the time interval of each series?
  1. aus_production: quarterly
  2. pelt: annually
  3. gafa_stock: daily
  4. vic_elec: half-hourly
  • Use autoplot() to produce a time plot of each series.
(p1 <- autoplot(aus_production, Bricks))
## Warning: Removed 20 rows containing missing values (`geom_line()`).

(p2 <- autoplot(pelt, Lynx))

(p3 <- autoplot(gafa_stock, Close))

(p4 <- autoplot(vic_elec, Demand))

  • For the last plot, modify the axis labels and title.
p4 +
  labs(title = 'Electricity Demand Over Time for Victoria, Australia',
       y = 'Total Demand (MWh)',
       x = 'Time (Half-Hourly)')

Exercise 2.2

Use filter() to find what days corresponded to the peak closing price for each of the four stocks in gafa_stock.

gafa_stock |>
  group_by(Symbol) |>
  filter(Close == max(Close)) |>
  knitr::kable()
Symbol Date Open High Low Close Adj_Close Volume
AAPL 2018-10-03 230.05 233.470 229.78 232.07 230.2755 28654800
AMZN 2018-09-04 2026.50 2050.500 2013.00 2039.51 2039.5100 5721100
FB 2018-07-25 215.72 218.620 214.27 217.50 217.5000 58954200
GOOG 2018-07-26 1251.00 1269.771 1249.02 1268.33 1268.3300 2405600

Exercise 2.3

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.

  1. You can read the data into R with the following script:
tute1 <- readr::read_csv("https://raw.githubusercontent.com/ShanaFarber/cuny-sps/master/DATA_624/Homeworks/Data/tute1.csv")
  1. Convert the data to time series
mytimeseries <- tute1 |>
  mutate(Quarter = yearquarter(Quarter)) |>
  as_tsibble(index = Quarter)
  1. 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().

mytimeseries |>
  pivot_longer(-Quarter) |>
  ggplot(aes(x = Quarter, y = value, colour = name)) +
  geom_line()

When you do not use facet grid(), each variable is plotted together on the same grid with the same scale. Plotting these variables together does not add any value to our analysis, and we can more easily see the individual trends for each variable when they are plotted on their own.

Exercise 2.4

The USgas package contains data on the demand for natural gas in the US.

  1. Install the USgas package.
#install.packages('USgas')
library(USgas)
  1. Create a tsibble from us_total with year as the index and state as the key.
(us_total_ts <- as_tsibble(us_total, index=year, key=state))
## # A tsibble: 1,266 x 3 [1Y]
## # Key:       state [53]
##     year state        y
##    <int> <chr>    <int>
##  1  1997 Alabama 324158
##  2  1998 Alabama 329134
##  3  1999 Alabama 337270
##  4  2000 Alabama 353614
##  5  2001 Alabama 332693
##  6  2002 Alabama 379343
##  7  2003 Alabama 350345
##  8  2004 Alabama 382367
##  9  2005 Alabama 353156
## 10  2006 Alabama 391093
## # ℹ 1,256 more rows
  1. 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).
new_england <- c('Maine', 'Vermont', 'New Hampshire', 'Massachusetts', 'Connecticut', 'Rhode Island')
us_total_ts |>
  filter(state %in% new_england) |>
  autoplot() +
  labs(title = "Natural Gas Consumption for New England States (1997-2019)",
       x = 'Year',
       y = 'Gas Consumption (Million Cubic Feet)') +
  scale_y_continuous(label = scales::comma)
## Plot variable not specified, automatically selected `.vars = y`

Exercise 2.5

  1. Download tourism.xlsx from the book website and read it into R using readxl::read_excel().
tourism_data <- read.csv('https://raw.githubusercontent.com/ShanaFarber/cuny-sps/master/DATA_624/Homeworks/Data/tourism.csv')
head(tourism_data)
##      Quarter   Region           State  Purpose    Trips
## 1 1998-01-01 Adelaide South Australia Business 135.0777
## 2 1998-04-01 Adelaide South Australia Business 109.9873
## 3 1998-07-01 Adelaide South Australia Business 166.0347
## 4 1998-10-01 Adelaide South Australia Business 127.1605
## 5 1999-01-01 Adelaide South Australia Business 137.4485
## 6 1999-04-01 Adelaide South Australia Business 199.9126
  1. Create a tsibble which is identical to the tourism tsibble from the tsibble package.
data(tourism)
head(tourism)
## # A tsibble: 6 x 5 [1Q]
## # Key:       Region, State, Purpose [1]
##   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.
keys = c('Region', 'State', 'Purpose')
tourism_ts <- tourism_data |>
  mutate(Quarter = yearquarter(Quarter)) |>
  as_tsibble(index=Quarter, key=all_of(keys))

identical(tourism, tourism_ts)
## [1] TRUE
  1. Find what combination of Region and Purpose had the maximum number of overnight trips on average.
tourism_data |>
  group_by(Region, Purpose) |>
  summarize(avg_trips = mean(Trips)) |>
  arrange(desc(avg_trips)) |>
  head(1) |>
  knitr::kable()
## `summarise()` has grouped output by 'Region'. You can override using the
## `.groups` argument.
Region Purpose avg_trips
Sydney Visiting 747.27
  1. Create a new tsibble which combines the Purposes and Regions, and just has total trips by State.
trips_by_state_ts <- tourism_data |>
  group_by(Quarter, State) |>
  summarize(total_trips = sum(Trips)) |>
  mutate(Quarter = yearquarter(Quarter)) |>
  as_tsibble(index=Quarter, key=State)
## `summarise()` has grouped output by 'Quarter'. You can override using the
## `.groups` argument.
head(trips_by_state_ts)
## # A tsibble: 6 x 3 [1Q]
## # Key:       State [1]
## # Groups:    @ Quarter [6]
##   Quarter State total_trips
##     <qtr> <chr>       <dbl>
## 1 1998 Q1 ACT          551.
## 2 1998 Q2 ACT          416.
## 3 1998 Q3 ACT          436.
## 4 1998 Q4 ACT          450.
## 5 1999 Q1 ACT          379.
## 6 1999 Q2 ACT          558.

Exercise 2.8

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?

Employed

us_employment |>
  filter(Title == 'Total Private') |>
  autoplot(Employed) +
  labs(title = 'Autoplot')

us_employment |>
  filter(Title == 'Total Private') |>
  gg_season(Employed) +
  labs(title = 'Seasonal Decomposition')

us_employment |>
  filter(Title == 'Total Private') |>
  gg_subseries(Employed) +
  labs(title = 'Subseries Plot')

us_employment |>
  filter(Title == 'Total Private') |>
  gg_lag(Employed) +
  labs(title = 'Lag Plot')

us_employment |>
  filter(Title == 'Total Private') |>
  ACF(Employed) |>
  autoplot() +
  labs(title = 'Autocorrelation')

From the plots, we can see that there is an apparent upward trend in employment and some seasonality. There appears to be a slight increase in the earlier months of the year, from January until about June, and then a leveling out of employment. There is a positive correlation across all lag plots.There are several dips in employment in the 70s, 80s, 90s, and early 2000s.

Bricks

aus_production |>
  autoplot(Bricks) +
  labs(title = 'Autoplot')
## Warning: Removed 20 rows containing missing values (`geom_line()`).

aus_production |>
  gg_season(Bricks) +
  labs(title = 'Seasonal Decomposition')
## Warning: Removed 20 rows containing missing values (`geom_line()`).

aus_production |>
  gg_subseries(Bricks) +
  labs(title = 'Subseries Plot')
## Warning: Removed 5 rows containing missing values (`geom_line()`).

aus_production |>
  gg_lag(Bricks, geom='point') +
  labs(title = 'Lag Plot')
## Warning: Removed 20 rows containing missing values (gg_lag).

aus_production |>
  ACF(Bricks) |>
  autoplot() +
  labs(title = 'Autocorrelation')

The Australian brick production data appears quite cyclical. It starts out with a clear upward trend until about the early to mid 70s and from then on there are severe dips and then increases. Seasonally, brick production seems to increase from the first to the third quarter and then decrease. The largest dips in production are in the mid 70s and early 80s.

Hare

pelt |>
  autoplot(Hare) +
  labs(title = 'Autoplot')

pelt |>
  gg_lag(Hare, geom='point') +
  labs(title = 'Lag Plot')

pelt |>
  ACF(Hare) |>
  autoplot() +
  labs(title = 'Autocorrelation')

The hare data is very cyclic. Plotting the autocorrelation shows about a 5 year cycle (5 years decreasing and then five years increasing). The largest increases were in the 1860s and 1880s.

Cost

PBS |>
  filter(ATC2 == 'H02') |>
  autoplot(Cost) +
  labs(title = 'Autoplot')

PBS |>
  filter(ATC2 == 'H02') |>
  gg_season(Cost) +
  labs(title = 'Seasonal Decomposition')

Concessional co-payments seem to be at their highest in the middle of the year, from around March to August. Concessional safety net and general safety net both experience the opposite, where they are at their lowest in these months.

Barrels

us_gasoline |>
  autoplot(Barrels) +
  labs(title = 'Autoplot')

us_gasoline |>
  gg_season(Barrels) +
  labs(title = 'Seasonal Decomposition')

us_gasoline |>
  gg_subseries(Barrels) +
  labs(title = 'Subseries Plot')

There seems to be pretty much an upward trend. As far as seasonality goes, there does not seem to be such a clear trend, although there does seem to be some elevation in the weeks between June and September.