2.1 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.
Answers:
aus_production has a quarterly time interval. Bricks from
aus_production is plotted below
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
## # ℹ 208 more rows
autoplot(aus_production, Bricks)
pelt has a annual/yearly time interval. Lynx from pelt is plotted
below.
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
## # ℹ 81 more rows
autoplot(pelt, Lynx)
gafa_stock has a daily time interval.Close from gafa_stock is
plotted below.
gafa_stock
## # 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
## # ℹ 5,022 more rows
autoplot(gafa_stock, Close)
vice_elec has a half hourly time interval.Demand from vic_elec is
plotted below.
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
autoplot(vic_elec, Demand)+
ggtitle("Half-hourly electricity demand for Victoria, Australia") +
xlab("Date ") +
ylab("Demand")
2.3: Download the tute1.csv and analyze its contents
Read the data
Convert the data into a time series
Construct time series plots of each of the three series
Answers:
Facet grid places the y axis scaling for each facet in more detail
making it easy to understand the trend. Removing this function will
bring the three time series to a common y axis scale and difficult to
comprehend.
# read the data into R file by uploading teh file into github account
tute1 <- read_csv("https://raw.githubusercontent.com/datanerddhanya/DATA-624/refs/heads/main/tute1.csv",show_col_types = FALSE)
#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 with facet grid
mytimeseries |>
pivot_longer(-Quarter) |>
ggplot(aes(x = Quarter, y = value, colour = name)) +
geom_line() +
facet_grid(name ~ ., scales = "free_y")+
labs(title = "Sales vs GDP vs Budget over time( with facet grid)")
# Construct time series plots of each of the three series without facet grid
mytimeseries |>
pivot_longer(-Quarter) |>
ggplot(aes(x = Quarter, y = value, colour = name)) +
geom_line() +
labs(title = "Sales vs GDP vs Budget over time( without facet grid)")
2.4 The USgas package .
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).
# Create a tsibble from us_total with year as the index and state as the key.
ustotal_series <- as_tsibble(us_total,key = state,index = year)
# view ustotal_series
ustotal_series
## # 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
# 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).
ustotal_series |>
filter( state %in% c("Maine", "Vermont", "New Hampshire", "Massachusetts", "Connecticut","Rhode Island")) |>
ggplot(aes(x = year, y = y, colour = state)) +
geom_line() +
geom_point() +
labs(title = "US Annual Total Natural Gas Consumption by state for the New England area",
x = "Year",
y = "Total natural gas consumption in a million cubic feet") +
theme_minimal() +
scale_x_continuous(breaks = seq(min(ustotal_series$year), max(ustotal_series$year), by = 3)) +
scale_y_continuous(labels = scales::comma)
2.5 Use tourism dataset
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.
Answers:
Sydney region with a purpose of visiting in 2017 Q4 had the maximum
number of overnight trips on average.
# read the data into R file by uploading the file into github account
# Download the Excel file from the URL
GET("https://raw.githubusercontent.com/datanerddhanya/DATA-624/main/tourism.xlsx",
write_disk(tf <- tempfile(fileext = ".xlsx")))
## Response [https://raw.githubusercontent.com/datanerddhanya/DATA-624/main/tourism.xlsx]
## Date: 2025-02-08 03:19
## Status: 200
## Content-Type: application/octet-stream
## Size: 679 kB
## <ON DISK> C:\Users\ajay2\AppData\Local\Temp\RtmpEPOFbB\file66e435e719d0.xlsx
# Read the downloaded Excel file
tourism_file<- read_excel(tf, col_names = TRUE)
# Converting data type from "Quarter" to Date and "Trips" to numeric
# Creating a tsibble identical to the tourism one
tourism <- tourism_file |>
mutate(Quarter = yearquarter(Quarter),Trips = as.numeric(Trips))
# Creating a tsibble identical to the tourism one
tourismtstibble <- as_tsibble(tourism, key = c(Region, State, Purpose), index = Quarter)
# combination of Region and Purpose had the maximum number of overnight trips on average.
tourism_avg_trips<- tourismtstibble |>
group_by(Region,Purpose) |>
summarize(average_trips = mean(Trips, na.rm = TRUE)) |>
arrange(desc(average_trips))
# display the top five combination
head(tourism_avg_trips)
## # A tsibble: 6 x 4 [1Q]
## # Key: Region, Purpose [4]
## # Groups: Region [3]
## Region Purpose Quarter average_trips
## <chr> <chr> <qtr> <dbl>
## 1 Melbourne Visiting 2017 Q4 985.
## 2 Sydney Business 2001 Q4 948.
## 3 Sydney Visiting 2016 Q4 921.
## 4 Sydney Visiting 2017 Q4 920.
## 5 Sydney Visiting 2017 Q1 916.
## 6 South Coast Holiday 1998 Q1 915.
# Create a new tsibble which combines the Purposes and Regions, and just has total trips by State.
tourism_total_trips <- tourismtstibble %>%
group_by(State) %>%
summarise(total_trips = sum(Trips)) %>%
arrange(desc(total_trips))
view (tourism_total_trips)
2.8 Graphic functions
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?
Answers:
“Total Private” Employed from us_employment
In this dataset, I can make the following observations:
1.The data shows a strong upward trend through the years.The
employment is going up over the years.Exception is from 2008 to 2010 as
there is a sudden drop due to the financial bubble. we can see no strong
seasonality or cyclic behavior in general.
2. Through the seasonal plot we can observe that there is low
seasonality behavior across the months jan to june there is a increase
and then it is stable for the year.
3. In the sub season plot, there is a strong positive trend for each
month through the years. The mean remains the same in each month.
4. As evident in the lag plot, there is strong positive correlation
in lag 1 to lag 9 sub plots. it proves that there is seasonality.
5. The ACF shows a trend as the autocorrelations for small lags tend
to be large and positive because observations nearby in time are also
nearby in value. So the ACF of a trended time series tends to have
positive values that slowly decrease as the lags increase.
us_employment |> filter(Title=='Total Private') |>
autoplot(Employed)+
ggtitle("US monthly employment for “Total Private” Employed using autoplot()") +
xlab( "Month") +
ylab("Employed count") +
scale_y_continuous(labels = scales::comma)
us_employment |> filter(Title=='Total Private') |>
gg_season(Employed)+
ggtitle("US monthly employment for “Total Private” Employed using gg_season()") +
xlab( "Month") +
ylab("Employed count") +
scale_y_continuous(labels = scales::comma)
us_employment |> filter(Title=='Total Private') |>
gg_subseries(Employed)+
ggtitle("US monthly employment for “Total Private” Employed using gg_subseries()") +
xlab( "Month") +
ylab("Employed count") +
scale_y_continuous(labels = scales::comma)
us_employment |> filter(Title=='Total Private') |>
gg_lag(Employed)+
ggtitle("US monthly employment for “Total Private” Employed using gg_lag()") +
xlab( "Month") +
ylab("Employed count") +
scale_y_continuous(labels = scales::comma)
us_employment |> filter(Title=='Total Private') |>
ACF(Employed)|>
autoplot()
Bricks from aus_production dataset
In the aus_production dataset, I can make the following
observations:
1. The Brick production shows a upward trend from 1956 to 1980,
thereafter there is a downward trend. So we can refer this trend as
“changing direction”, as it goes from an increasing trend to a
decreasing trend.There is seasonality as it seems to drop every
alternate year in Q1.There is no cyclic behavior as there is no rise or
fall pattern over a long term.
2. Using the seasonal sub series plot we can observe that there is a
seasonality behavior as the production is the least in Q1 across all
years . It increases in Q2 and Q3 and then decreases in Q4 across the
years.
3. As evident in the lag plot, there is positive and highest
correlation for Lag1 followed by lag4, thus reflecting the strong
seasonality in the data.
4. ACF shows a trended time series as it has positive values that
slowly decrease as the lags increase, while the “scalloped” shape is due
to the seasonality.
The highest drop in brick production was in 1986 probably due to
Australia economy.
autoplot(aus_production, Bricks)+
ggtitle("Quarterly production of Brick commodity in Australia using autoplot()") +
xlab("Quarter ") +
ylab("Brick production in millions of bricks")
gg_season(aus_production, Bricks)+
ggtitle("Quarterly production of Brick commodity in Australia using gg_season()") +
xlab("Quarter ") +
ylab("Brick production in millions of bricks")
gg_subseries(aus_production, Bricks)+
ggtitle("Quarterly production of Brick commodity in Australia using gg_subseries()") +
xlab("Quarter ") +
ylab("Brick production in millions of bricks")
gg_lag(aus_production, Bricks, geom ="point")+
ggtitle("Quarterly production of Brick commodity in Australia using gg_lag()") +
xlab("Quarter ") +
ylab("Brick production in millions of bricks")
ACF(aus_production, Bricks)|>
autoplot()
Hare from pelt
In the pelt dataset, I can make the following observations:
1.The Hare pelt trading record shows no clear trend. However, we can
see strong cyclic behavior. We can see sharp increases and decreases of
hare pelt traded in a repeating pattern..
2. As evident in the lag plot, there is no correlation in any lags.
it proves that there is not seasonality. The ACF shows that the cyclic
pattern is repeated every 5 years.
autoplot(pelt, Hare)+
ggtitle("Hudson Bay Company: Annual Snowshoe Hare pelts traded using autoplot()") +
xlab( "Year ") +
ylab("Snowshoe Hare pelts traded")
gg_lag(pelt, Hare, geom="point")+
ggtitle("Hudson Bay Company: Annual Snowshoe Hare pelts traded using gg_lag()") +
xlab( "Year ") +
ylab("Snowshoe Hare pelts traded")
ACF(pelt,Hare)|>
autoplot()
“H02” Cost from PBS
In the PBS dataset, I can make the following observations:
1.The data shows a upward trend in general for ATC2:H02 concessional
types. There is no trend observed for ATC2:H02 General types. we can see
strong cyclic behavior as there is sharp increases and decreases in a
repeating pattern..
2. Through the seasonal plot we can observe that there is a
seasonality behavior. For safety net type, It is least from Feb to May
and then increases till Jan. This is correct as the Safety net subsidies
are provided to individuals only after their script expenditure exceeds
the threshold cost. On the contrary the concessional co-payment types
are high from Feb to May, and thereafter it reduces as Co-payments are
made until an individual’s script expenditure hits a threshold . There
is no seasonliaty observed in General co-payments.
Barrels from us_gasoline
In the us_gasoline dataset, I can make the following
observations:
1. The Barrel supply shows a upward trend from 1990 to 2004,
thereafter there is a downward trend, then increase and decrease. So we
can refer this trend as “changing direction”, as it goes from an
increasing trend to a decreasing trend. No seasonality or cyclic
behavior can be observed from the time plot.
2. In the seasonal plots, it is not clear if there is any
seasonality.
3. In the lag plot, there is a positive correlation for all the lags
1-8 sub plots. This shows that there is seasonality.
4. the ACF plot, indicates a higher lagged correlation, that of 26
weeks. ACF of a trended time series tends to have positive values that
slowly decrease as the lags increase.
autoplot(us_gasoline,Barrels) +
ggtitle("US gasoline supply in Barrels using autoplot()") +
xlab( "Week") +
ylab("Barrels") +
scale_y_continuous(labels = scales::comma)
gg_season(us_gasoline,Barrels) +
ggtitle("US gasoline supply in Barrels using gg_season()") +
xlab( "Week") +
ylab("Barrels") +
scale_y_continuous(labels = scales::comma)
gg_subseries(us_gasoline,Barrels) +
ggtitle("US gasoline supply in Barrels using gg_subseries()") +
xlab( "Week") +
ylab("Barrels") +
scale_y_continuous(labels = scales::comma)
gg_lag(us_gasoline,Barrels, geom ="point") +
ggtitle("US gasoline supply in Barrels using autoplot()") +
xlab( "Week") +
ylab("Barrels") +
scale_y_continuous(labels = scales::comma)
us_gasoline |>
ACF(Barrels,lag_max=110)|>
autoplot()
