Submit exercises 2.1, 2.2, 2.3, 2.4, 2.5 and 2.8 from the Hyndman online Forecasting book. (https://oteinsom/fpp3/)

library(fpp3)

Question 2.1

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

a.Use ? (or help()) to find out about the data in each series. b.What is the time interval of each series? c.Use autoplot() to produce a time plot of each series. d.For the last plot, modify the axis labels and title.

Part 1: Bricks from aus_production a.

invisible(?aus_production)

Bricks: Clay brick production in millions of bricks.

  1. The time intervals are annual durations.

c.and d.

autoplot(aus_production, Bricks)+
  labs(title = "Quarterly Brick Production in Australia",
       y = "Bricks (millions)",
       x = "Time (Year and Quarter 1)")
## Warning: Removed 20 rows containing missing values (`geom_line()`).

d.

Part 2:Lynx from pelt a.

invisible(?pelt)

Lynx: The number of Canadian Lynx pelts traded.

b.The time intervals are annual durations.

  1. and d.
autoplot(pelt, Lynx)+
  labs(title = "Canadian Lynx Pelts Traded",
       x = "Time (Year)")

Part3:Close from gafa_stock a.

invisible(?gafa_stock)

Close: The closing price for the stock.

b.The time intervals are day durations.

  1. and d.
autoplot(gafa_stock, Close)+
  labs(title = "Closing Price of GAFA stock from 2014-2018",
       y = "Close ($USD)",
       x = "Time (Day)")

Part4: Demand from vic_elec a.

invisible(?vic_elec)

Demand: Total electricity demand in MWh.

b.The time intervals are half-hour durations. c. and d.

autoplot(vic_elec, Demand)+
  labs(title = "Electricity Demand for Victoria, Australia",
       y = "Demand (MWh)",
       x = "Time (30mins)")

Question 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))%>%
  select(Symbol,Date)
## # A tsibble: 4 x 2 [!]
## # Key:       Symbol [4]
## # Groups:    Symbol [4]
##   Symbol Date      
##   <chr>  <date>    
## 1 AAPL   2018-10-03
## 2 AMZN   2018-09-04
## 3 FB     2018-07-25
## 4 GOOG   2018-07-26

Question 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("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.
#View(tute1)

b.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")

  1. Check what happens when you don’t include facet_grid().
mytimeseries %>%
  pivot_longer(-Quarter) %>%
  ggplot(aes(x = Quarter, y = value, colour = name)) +
  geom_line()

Without the facet_grid() function, the categorical data is on the same scale. This makes it a lot harder to see trends in the time series between the 3 values.

Question 2.4

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

a.Install the USgas package.

library(USgas)
## Warning: package 'USgas' was built under R version 4.2.3
invisible(?us_total)

b.Create a tsibble from us_total with year as the index and state as the key.

timeseries <- us_total %>%
  as_tsibble(key = state ,index = year)

c.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).

timeseries %>% 
  filter(state %in% c("Maine", "Vermont", "New Hampshire", "Massachusetts",
                      "Connecticut", "Rhode Island")) %>%
  ggplot(aes(x = year, y = y, color=state)) +
  labs(y= " Total Gas (Million cubic feet)")+
  geom_line() +
  facet_grid(state ~ ., scales="free_y")



Question 2.5

a.Download tourism.xlsx from the book website and read it into R using readxl::read_excel().

tourism <- readxl::read_excel("tourism.xlsx")

b.Create a tsibble which is identical to the tourism tsibble from the tsibble package.

invisible(??tourism)
tourism_tsibble <- tourism %>%
  mutate(Quarter = yearquarter(Quarter)) %>%
  as_tsibble(key = c(Region, State, Purpose),
             index = Quarter)

c.Find what combination of Region and Purpose had the maximum number of overnight trips on average.

(max_ave_trips <- tourism %>%
  group_by(Region, Purpose) %>%
  summarize(AverageOvernightTrips = mean(Trips)) %>%
  arrange(desc(AverageOvernightTrips)))
## # A tibble: 304 × 3
## # Groups:   Region [76]
##    Region          Purpose  AverageOvernightTrips
##    <chr>           <chr>                    <dbl>
##  1 Sydney          Visiting                  747.
##  2 Melbourne       Visiting                  619.
##  3 Sydney          Business                  602.
##  4 North Coast NSW Holiday                   588.
##  5 Sydney          Holiday                   550.
##  6 Gold Coast      Holiday                   528.
##  7 Melbourne       Holiday                   507.
##  8 South Coast     Holiday                   495.
##  9 Brisbane        Visiting                  493.
## 10 Melbourne       Business                  478.
## # ℹ 294 more rows

d.Create a new tsibble which combines the Purposes and Regions, and just has total trips by State.

(newtourism_tsibble  <- tourism_tsibble %>%
  group_by(State) %>%
  summarize(TotalTrips = sum(Trips)) %>%
  tsibble(index = Quarter,
             key = State))
## # A tsibble: 640 x 3 [1Q]
## # Key:       State [8]
##    State Quarter TotalTrips
##    <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.
## # ℹ 630 more rows

Question 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?

# Load the required time series datasets
data("us_employment", "aus_production", "pelt", "PBS", "us_gasoline")
  1. “Total Private” Employed from us_employment
us_employment %>% filter(Title == "Total Private") %>% autoplot(Employed)

us_employment %>% filter(Title == "Total Private") %>% gg_season(Employed)

us_employment %>% filter(Title == "Total Private") %>% gg_subseries(Employed)

us_employment %>% filter(Title == "Total Private") %>% gg_lag(Employed)

us_employment %>% filter(Title == "Total Private") %>% ACF(Employed)%>%autoplot()



The data exhibits a robust upward trend with noticeable seasonality. There is no indication of any cyclic behavior in the series. The employment levels consistently rise over time. The seasonal patterns remain stable throughout the year, though there is a slight upward curve in June, which diminishes after December. An identified anomalous year appears to be 2008/2010.



2.Bricks from aus_production

autoplot(aus_production, Bricks)

gg_season(aus_production, Bricks) 

gg_subseries(aus_production, Bricks) 

gg_lag(aus_production, Bricks) 

ACF(aus_production,Bricks)%>% autoplot()



The data displays strong seasonality within each year and exhibits pronounced cyclic behavior with a period of 40 years. No discernible trend is evident over this period. Brick production shows an increase from quarter 1 to 3 and decreases in quarter 4. A notable decline in brick production is observed around 1983.



  1. Hare from pelt
autoplot(pelt, Hare)

#gg_season(pelt, Hare)
gg_subseries(pelt, Hare) 

gg_lag(pelt, Hare) 

ACF(pelt, Hare)%>% autoplot()



The data exhibits cyclical behavior. There is no discernible trend or defined seasonality. The ACF plot illustrates a cyclic pattern occurring every ten years.

4.“H02” Cost from PBS

PBS %>% filter(ATC2 == "H02") %>% autoplot(Cost)

PBS %>% filter(ATC2 == "H02") %>% gg_season(Cost)

PBS %>% filter(ATC2 == "H02") %>% gg_subseries(Cost)

#PBS %>% filter(ATC2 == "H02") %>% gg_lag(Cost)
PBS %>% filter(ATC2 == "H02") %>% ACF(Cost)%>%autoplot()



The data demonstrates strong seasonality within each year, as well as pronounced cyclic behavior, with no discernible trend.



5.Barrels from us_gasoline

autoplot(us_gasoline, Barrels)

gg_season(us_gasoline, Barrels)

gg_subseries(us_gasoline, Barrels) 

gg_lag(us_gasoline, Barrels) 

ACF(us_gasoline, Barrels)%>% autoplot()



Lacks any trend, seasonality, or cyclic behavior. Random fluctuations are present, appearing to be unpredictable, with no distinct patterns that would facilitate the development of a forecasting model.