Homework 01

library(fpp3)

## ── Attaching packages ──────────────────────────────────────────── fpp3 1.0.3 ──

## ✔ tibble      3.3.1     ✔ tsibble     1.2.0
## ✔ dplyr       1.2.1     ✔ tsibbledata 0.4.1
## ✔ tidyr       1.3.2     ✔ ggtime      1.0.0
## ✔ lubridate   1.9.5     ✔ feasts      0.5.0
## ✔ ggplot2     4.0.3     ✔ fable       0.5.0

## ── Conflicts ───────────────────────────────────────────────── fpp3_conflicts ──
## ✖ lubridate::date()    masks base::date()
## ✖ dplyr::filter()      masks stats::filter()
## ✖ tsibble::intersect() masks base::intersect()
## ✖ tsibble::interval()  masks lubridate::interval()
## ✖ dplyr::lag()         masks stats::lag()
## ✖ tsibble::setdiff()   masks base::setdiff()
## ✖ tsibble::union()     masks base::union()

Exercise 2.1

Exploring 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

## starting httpd help server ... done

?pelt
?gafa_stock
?vic_elec

What is the time interval of each series?

aus_production: quarterly pelt: annually gafa_stock: daily 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 or values outside the scale range
## (`geom_line()`).

(p2 <- autoplot(pelt, Lynx))

(p3 <- autoplot(gafa_stock, Close))

(p4 <- autoplot(vic_elec, Demand))

Regarding the last plot, modifying both 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

Using filter() to find out days corresponding to the peak closing price for 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

Obtained the file called tute1.csv from the course website, open it in MS Excel and review its contents. Locating four variable columns. Columns B through D containing quarterly series, named as Sales, AdBudget and GDP. Sales features the quarterly sales for a small company over the period 1981-2005. AdBudget stands for the advertising budget and finally GDP represents 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("https://raw.githubusercontent.com/sturrm/class_files/refs/heads/main/tute1.csv")

## Rows: 100 Columns: 4
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## dbl  (3): Sales, AdBudget, GDP
## date (1): Quarter
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

Converting the data to time series.

mytimeseries <- tute1 |>
  mutate(Quarter = yearquarter(Quarter)) |>
  as_tsibble(index = Quarter)

Generating 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")

Checking status without including facet_grid().

Without facet grid(), each variable is shown alongside within the same grid and the same scale. Displaying these variables hand-in-hand does not create any value to this analysis, the individual trends reveal themselves nicely for each variable when they are shown on their own.

Exercise 2.4

The USgas package prsents data regarding the usage of natural gas for the US.

Installing the USgas package.

library(USgas)

Generating 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

3> Showing the annual natural gas usage 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

Obtaining tourism.xlsx file from the course website and reading it into R using readxl::read_excel()

tourism_data <- read.csv('https://raw.githubusercontent.com/sturrm/class_files/refs/heads/main/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

Creating carbon copy of a tsibble just like the one in 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

Finding combination of Region and Purpose in the context of the maximum number for average overnight trips.

tourism_data |>
  group_by(Region, Purpose) |>
  summarize(avg_trips = mean(Trips)) |>
  arrange(desc(avg_trips)) |>
  head(1) |>
  knitr::kable()

## `summarise()` has regrouped the output.
## ℹ Summaries were computed grouped by Region and Purpose.
## ℹ Output is grouped by Region.
## ℹ Use `summarise(.groups = "drop_last")` to silence this message.
## ℹ Use `summarise(.by = c(Region, Purpose))` for per-operation grouping
##   (`?dplyr::dplyr_by`) instead.

Region	Purpose	avg_trips
Sydney	Visiting	747.27

Generating another tsibble combining both Purposes and Regions with total trips listed 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 regrouped the output.
## ℹ Summaries were computed grouped by Quarter and State.
## ℹ Output is grouped by Quarter.
## ℹ Use `summarise(.groups = "drop_last")` to silence this message.
## ℹ Use `summarise(.by = c(Quarter, State))` for per-operation grouping
##   (`?dplyr::dplyr_by`) instead.

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

Utlizing the following graph functions: autoplot(), gg_season(), gg_subseries(), gg_lag(), ACF() and exploring themes 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?

Employment

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

Bricks

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

## Warning: Removed 20 rows containing missing values or values outside the scale range
## (`geom_line()`).

Hare

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

Cost

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

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')

An upward trend can be spotted herein. In terms of seasonality apsect, any visible trend is not clearly manifested, still an uptick can be spotted for the weeks stating June and ending September.