Homework 1
Lewris Mota Sanchez
2024-09-05
Imports
library(fpp3)## Registered S3 method overwritten by 'tsibble':
## method from
## as_tibble.grouped_df dplyr## ── Attaching packages ──────────────────────────────────────────── fpp3 1.0.0 ──## ✔ tibble 3.2.1 ✔ tsibble 1.1.5
## ✔ dplyr 1.1.4 ✔ tsibbledata 0.4.1
## ✔ tidyr 1.3.1 ✔ feasts 0.3.2
## ✔ lubridate 1.9.3 ✔ fable 0.3.4
## ✔ ggplot2 3.5.1 ✔ fabletools 0.4.2## ── 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()library(USgas)Excercise 2.1
Explore the following four time series: Bricks from aus_production, Lynx from pelt, Close from gafa_stock, Demand from vic_elec.
Quarterly production of selected commodities in Australia.
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 rowsWhat is the time interval? Quarterly
Brick Time Series
autoplot(aus_production ,.vars = Bricks)## Warning: Removed 20 rows containing missing values or values outside the scale range
## (`geom_line()`).
Pelt trading records
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 rowsWhat is the time interval?
Yearly
Lynx furs trade Time Series
autoplot(pelt,.vars = Lynx)
Gafa Stock Prices
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 rowsWhat is the time interval?
Daily frequency from year 2014 to 2018
Gafa Stock Time Series
autoplot(gafa_stock,.vars = Close)
Electricity demand for Victoria, Australia
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 rowsWhat is the time interval? Half-hourly
autoplot(vic_elec,.vars = Demand)+ xlab("Half-hourly electricity demand") + ylab("Total electricity demand in MWh")
Excercise 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 |> filter(Close,max(Close) > 0)
gafa_stock %>% group_by(Symbol) %>% filter(Close == max(Close))## # A tsibble: 4 x 8 [!]
## # Key: Symbol [4]
## # Groups: Symbol [4]
## Symbol Date Open High Low Close Adj_Close Volume
## <chr> <date> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 AAPL 2018-10-03 230. 233. 230. 232. 230. 28654800
## 2 AMZN 2018-09-04 2026. 2050. 2013 2040. 2040. 5721100
## 3 FB 2018-07-25 216. 219. 214. 218. 218. 58954200
## 4 GOOG 2018-07-26 1251 1270. 1249. 1268. 1268. 2405600The results are as follows:
- Google (GOOG) peak closing price was 1268.33$.
- Amazon (AMZN) peak closing price was 2039.51$.
- Facebook (FB) peak closing price was 217.50$.
- Apple (AAPL) peak closing price was 232.07$.
Excercise 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.
read the data into R:
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)- 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():
mytimeseries |>
pivot_longer(-Quarter) |>
ggplot(aes(x = Quarter, y = value, colour = name)) +
geom_line() 
By using facet_grid(), you can separate data into distinct panels based on one or more variables, making it easier to compare distributions across different categories or levels. Without it, all data is overlaid in a single panel, which can obscure important differences or patterns, especially in complex datasets.
Excercise 2.4
The USgas package contains data on the
demand for natural gas in the US.
- USgas package installed
head(us_total)## year state y
## 1 1997 Alabama 324158
## 2 1998 Alabama 329134
## 3 1999 Alabama 337270
## 4 2000 Alabama 353614
## 5 2001 Alabama 332693
## 6 2002 Alabama 379343- Create a tsibble from
us_totalwith year as the index and state as the key.
gasData <- us_total |> as_tsibble(key=state,index=year)
gasData## # 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).
gasData |>
filter(state %in% c("Maine","Vermont","New Hampshire","Massachusetts","Connecticut","Rhode Island")) |>
autoplot(.var=y) + facet_grid(state ~ ., scales = "free_y")+xlab("Year") +
ylab("monthly natural gas consumption (million cubic feet)") 
Excercise 2.5
Download tourism.xlsx and read it into R
using readxl::read_excel().
- Create a tsibble which is identical to the
tourismtsibble from thetsibblepackage. Tsibble tourism package
tourism## # 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.
## # ℹ 24,310 more rowsTourism Data
tourismData <- readxl::read_excel("tourism.xlsx") |> mutate(Quarter = yearquarter(Quarter)) |>
as_tsibble(key=c("Region","State","Purpose"),index=Quarter)
tourismData## # 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.
## # ℹ 24,310 more rowsidentical(tourism,tourism)## [1] TRUETourism Data
- Find what combination of
RegionandPurposehad the maximum number of overnight trips on average.
tourismData |> as_tibble() |> group_by(Region,Purpose) |> summarise(averageTrips=mean(Trips)) |> ungroup() |>
filter(averageTrips == max(averageTrips))## `summarise()` has grouped output by 'Region'. You can override using the
## `.groups` argument.## # A tibble: 1 × 3
## Region Purpose averageTrips
## <chr> <chr> <dbl>
## 1 Sydney Visiting 747.- Create a new tsibble which combines the Purposes and Regions, and just has total trips by State.
tourismData |> group_by(State) |> summarise(totalTrips=sum(Trips)) |> ungroup()## # 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 rowsExcercise 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?
USA Employment
totalPrivateEmployment <-us_employment |> filter(Title == "Total Private")
totalPrivateEmployment## # A tsibble: 969 x 4 [1M]
## # Key: Series_ID [1]
## 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
## # ℹ 959 more rowstotalPrivateEmployment |> autoplot() ## Plot variable not specified, automatically selected `.vars = Employed`
Season
totalPrivateEmployment |> gg_season(Employed) 
Subseries
totalPrivateEmployment |> gg_subseries(Employed) 
Lag
totalPrivateEmployment |> gg_lag(Employed) 
Auto Correlation
totalPrivateEmployment |> ACF(Employed) |> autoplot()
Answer
The employment data in the USA demonstrates a clear overall upward trend over time, with strong evidence of seasonality. Two key seasonal patterns are observed: an increase in employment during the summer months and a decrease, or trough, by early January. This repetitive pattern of employment fluctuations remains highly correlated with previous data points, suggesting a predictable trend over the years. However, there are exceptions to this predictability, such as the significant decline in employment between 2008 and 2010, which corresponds to the global financial crisis. Despite such disruptions, the long-term trend shows consistent growth with seasonal variation.
Aus Production
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 rowsaus_production |> autoplot(.var=Bricks) ## Warning: Removed 20 rows containing missing values or values outside the scale range
## (`geom_line()`).
Season
aus_production |> gg_season(Bricks) ## Warning: Removed 20 rows containing missing values or values outside the scale range
## (`geom_line()`).
Subseries
aus_production |> gg_subseries(Bricks) ## Warning: Removed 5 rows containing missing values or values outside the scale range
## (`geom_line()`).
Lag
aus_production |> gg_lag(Bricks, geom = "point") ## Warning: Removed 20 rows containing missing values (gg_lag).
Auto Correlation
aus_production |> ACF(Bricks) |> autoplot()
Answer
The bricks production data initially shows an upward trend until Q1 of 1980, after which a downtrend becomes evident. The data also exhibits cyclicality, with seasonal patterns that can be observed in the autocorrelation plot. Over the years, Q2 and Q3 have consistently experienced the largest increases in production, followed by a decline leading up to Q1 of the following year, when production begins to rise again, albeit more moderately. Between 1980 and 1983, there is a notable sharp decrease in brick production across all quarters, marking a significant trough during this period. Despite these fluctuations, the data follows both a trend and seasonal cycles.
Pelt
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 rowspelt |> autoplot(.var=Hare)
Season No season
Subseries
pelt |> gg_subseries(Hare) 
Lag
pelt |> gg_lag(Hare, geom = "point") 
Auto Correlation
pelt |> ACF(Hare) |> autoplot()
Answer
The data does not reveal seasonality trends, as it wasn’t divided into shorter periods like days, weeks, months, or quarters. However, while there’s no indication of an overarching trend, clear cyclicality is present. The ACF plot suggests that cycles occur every 10 years, with peaks every decade and troughs happening 5 years after each peak, following a consistent 10-year pattern.
PBS
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
## # ℹ 67,586 more rowsH02Data <- PBS |> filter(ATC2 == "H02")
H02Data## # A tsibble: 816 x 9 [1M]
## # Key: Concession, Type, ATC1, ATC2 [4]
## 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-paym… H Systemic… H02 CORTICOS… 63261 317384
## 2 1991 Aug Concessional Co-paym… H Systemic… H02 CORTICOS… 53528 269891
## 3 1991 Sep Concessional Co-paym… H Systemic… H02 CORTICOS… 52822 269703
## 4 1991 Oct Concessional Co-paym… H Systemic… H02 CORTICOS… 54016 280418
## 5 1991 Nov Concessional Co-paym… H Systemic… H02 CORTICOS… 49281 268070
## 6 1991 Dec Concessional Co-paym… H Systemic… H02 CORTICOS… 51798 277139
## 7 1992 Jan Concessional Co-paym… H Systemic… H02 CORTICOS… 42436 221772
## 8 1992 Feb Concessional Co-paym… H Systemic… H02 CORTICOS… 52913 272345
## 9 1992 Mar Concessional Co-paym… H Systemic… H02 CORTICOS… 62908 325700
## 10 1992 Apr Concessional Co-paym… H Systemic… H02 CORTICOS… 68499 349271
## # ℹ 806 more rowsH02Data |> autoplot(.var=Cost) + scale_y_continuous(labels = scales::comma) 
Season
H02Data |> gg_season(Cost) + scale_y_continuous(labels = scales::comma) 
subseries
H02Data |> gg_subseries(Cost) + scale_y_continuous(labels = scales::comma) 
Auto Correlation
H02Data |> ACF(Cost) |> autoplot()
US Gasoline
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
## # ℹ 1,345 more rowsus_gasoline |> autoplot()## Plot variable not specified, automatically selected `.vars = Barrels`
Season
us_gasoline |> gg_season()## Plot variable not specified, automatically selected `y = Barrels`
Subseries
us_gasoline |> gg_subseries() ## Plot variable not specified, automatically selected `y = Barrels`
Lag
us_gasoline |> gg_lag(Barrels, geom = "point") 
Auto Correlation
us_gasoline |> ACF(Barrels) |> autoplot()