DATA 624 Homework 1
Philip Tanofsky
9/12/2021
# Import required R libraries
library(fpp3)Exercise 2.1
Use the help function to explore what the series gafa_stock, PBS, vic_elec and pelt represent.
gafa_stock: Historical stock prices from 2014-2018 for Google, Amazon, Facebook and Apple. All prices are in $USD. Contains data on irregular trading days.
PBS: Monthly tsibble with two values, Scripts for total number of scripts and Cost for cost of the scripts in $AUD
vic_elec: Half-hourly tsibble with three values, Demand for total electricity demand in MW, Temperature for the temperature of Melbourne (BOM site 086071) and Holiday for the indicator for if that day is a public holiday.
pelt: Hudson Bay Company trading records for Snowshoe Hare and Canadian Lynx furs from 1845 to 1935. This data contains trade records for all areas of the company.
head(gafa_stock)## # A tsibble: 6 x 8 [!]
## # Key: Symbol [1]
## 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 69787200head(PBS)## # A tsibble: 6 x 9 [1M]
## # Key: Concession, Type, ATC1, ATC2 [1]
## 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-pa… A Alimentary … A01 STOMATOLO… 18228 67877
## 2 1991 Aug Concessional Co-pa… A Alimentary … A01 STOMATOLO… 15327 57011
## 3 1991 Sep Concessional Co-pa… A Alimentary … A01 STOMATOLO… 14775 55020
## 4 1991 Oct Concessional Co-pa… A Alimentary … A01 STOMATOLO… 15380 57222
## 5 1991 Nov Concessional Co-pa… A Alimentary … A01 STOMATOLO… 14371 52120
## 6 1991 Dec Concessional Co-pa… A Alimentary … A01 STOMATOLO… 15028 54299head(vic_elec)## # A tsibble: 6 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 TRUEhead(pelt)## # A tsibble: 6 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 8420A.
Use autoplot() to plot some of the series in these data sets.
autoplot(gafa_stock, Close) +
labs(title = "Closing Stock Price",
subtitle = "Google, Amazon, Facebook, Apple",
y = "Price")
pbs_a10 <- PBS %>%
filter(ATC2 == "A10" & Concession == "Concessional" & Type == "Co-payments") %>%
mutate(Cost = Cost/1e6) %>%
select(Month, Cost)
autoplot(pbs_a10, Cost) +
labs(title = "Total cost of Medicare Australia prescriptions by Month",
subtitle = "Data defined as ATC2 is A10, Concessional and Co-payments",
y = "Cost in millions")
autoplot(vic_elec, Demand) +
labs(title = "Electricity Demand",
subtitle = "Victoria, Australia",
y = "Megawatts")
autoplot(pelt, Hare) +
labs(title = "Trading records of furs from 1845 to 1935",
subtitle = "Hudson Bay Company",
y = "Pelts Traded")
B.
What is the time interval of each series?
gafa_stock: One day, excluding days the stock market is closed (time interval of [!] indicates irregularity)
PBS: One month
vic_elec: 30 minutes
pelt: One year
Exercise 2.2
Use filter() to find what days corresponded to the peak closing price for each of the four stocks in gafa_stock.
result <- gafa_stock %>%
group_by(Symbol) %>%
filter(Close == max(Close)) %>%
arrange(desc(Close))
result## # 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 AMZN 2018-09-04 2026. 2050. 2013 2040. 2040. 5721100
## 2 GOOG 2018-07-26 1251 1270. 1249. 1268. 1268. 2405600
## 3 AAPL 2018-10-03 230. 233. 230. 232. 230. 28654800
## 4 FB 2018-07-25 216. 219. 214. 218. 218. 58954200Exercise 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.
A.
You can read the data into R with the following script:
tute1 <- readr::read_csv("tute1.csv")
View(tute1)B.
Convert the data to time series
mytimeseries <- tute1 %>%
mutate(Quarter = yearmonth(Quarter)) %>%
as_tsibble(index = Quarter)
head(mytimeseries)## # A tsibble: 6 x 4 [3M]
## Quarter Sales AdBudget GDP
## <mth> <dbl> <dbl> <dbl>
## 1 1981 Mar 1020. 659. 252.
## 2 1981 Jun 889. 589 291.
## 3 1981 Sep 795 512. 291.
## 4 1981 Dec 1004. 614. 292.
## 5 1982 Mar 1058. 647. 279.
## 6 1982 Jun 944. 602 254C.
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().
As seen below, without facet_grid(), the three time series are all graphed on the same graph instead of 3 individual graphs. I would argue this provides a more contextualized graph of the relationship between the three separate time series. With a shared y-axis, the relationships between the three time series are more evident than the separated graphs.
mytimeseries %>%
pivot_longer(-Quarter) %>%
ggplot(aes(x = Quarter, y = value, colour = name)) +
geom_line()
Exercise 2.4
The USgas package contains data on the demand for natural gas in the US.
A.
Install the USgas package.
library(USgas)B.
Create a tsibble from us_total with year as the index and state as the key.
ts <- us_total
ts <- ts %>%
as_tsibble(index = year, key = state)
head(ts)## # A tsibble: 6 x 3 [1Y]
## # Key: state [1]
## 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 379343C.
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).
ne_ts <- ts %>%
filter(state == 'Maine' |
state == 'Vermont' |
state == 'New Hampshire' |
state == 'Massachusetts' |
state == 'Connecticut' |
state == 'Rhode Island') %>%
mutate(y = y/1e3)
head(ne_ts)## # A tsibble: 6 x 3 [1Y]
## # Key: state [1]
## year state y
## <int> <chr> <dbl>
## 1 1997 Connecticut 145.
## 2 1998 Connecticut 131.
## 3 1999 Connecticut 152.
## 4 2000 Connecticut 160.
## 5 2001 Connecticut 146.
## 6 2002 Connecticut 178.autoplot(ne_ts, y) +
labs(title = "Annual natural gas consumption by state",
subtitle = "New England area",
y = "Consumption in thousands")
Exercise 2.5
A.
Download tourism.xlsx from the book website and read it into R using readxl::read_excel().
tourism_data <- readxl::read_excel("tourism.xlsx")
head(tourism_data)## # A tibble: 6 × 5
## Quarter Region State Purpose Trips
## <chr> <chr> <chr> <chr> <dbl>
## 1 1998-01-01 Adelaide South Australia Business 135.
## 2 1998-04-01 Adelaide South Australia Business 110.
## 3 1998-07-01 Adelaide South Australia Business 166.
## 4 1998-10-01 Adelaide South Australia Business 127.
## 5 1999-01-01 Adelaide South Australia Business 137.
## 6 1999-04-01 Adelaide South Australia Business 200.B.
Create a tsibble which is identical to the tourism tsibble from the tsibble package.
First, display tourism as sample.
# Output tourism tsibble
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.Initial thoughts, five columns are the same. Steps: 1: Convert column Quarter into the index. 2: Define Region, State and Purpose as keys.
# Convert tourism_data to tsibble
tourism_ts <- tourism_data %>%
mutate(Quarter = yearquarter(Quarter)) %>%
as_tsibble(index = Quarter, key = c(Region, State, Purpose))
head(tourism_ts)## # 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.C.
Find what combination of Region and Purpose had the maximum number of overnight trips on average.
tourism_by_reg_pur_ts <- tourism_data %>%
group_by(Region, Purpose) %>%
summarise(Trip_Avg = mean(Trips)) %>%
filter(Trip_Avg == max(Trip_Avg)) %>%
arrange(desc(Trip_Avg))
head(tourism_by_reg_pur_ts)## # A tibble: 6 × 3
## # Groups: Region [6]
## Region Purpose Trip_Avg
## <chr> <chr> <dbl>
## 1 Sydney Visiting 747.
## 2 Melbourne Visiting 619.
## 3 North Coast NSW Holiday 588.
## 4 Gold Coast Holiday 528.
## 5 South Coast Holiday 495.
## 6 Brisbane Visiting 493.Answer: Combination of region Sydney and purpose Visiting has the maximum number of overnight trips on average per quarter surveyed with a count of 747.
D.
Create a new tsibble which combines the Purposes and Regions, and just has total trips by State.
trips_by_state <- tourism_ts %>%
group_by(State) %>%
summarise(Trips = sum(Trips)) %>%
mutate(Quarter = yearquarter(Quarter)) %>%
as_tsibble(index = Quarter, key = State)
head(trips_by_state)## # A tsibble: 6 x 3 [1Q]
## # Key: State [1]
## State Quarter Trips
## <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.Exercise 2.8
Monthly Australian retail data is provided in aus_retail. Select one of the time series as follows (but choose your own seed value):
#set.seed(12345678)
set.seed(8675309)
myseries <- aus_retail %>%
filter(`Series ID` == sample(aus_retail$`Series ID`,1))
head(myseries)## # A tsibble: 6 x 5 [1M]
## # Key: State, Industry [1]
## State Industry `Series ID` Month Turnover
## <chr> <chr> <chr> <mth> <dbl>
## 1 Queensland Takeaway food services A3349718A 1982 Apr 26.7
## 2 Queensland Takeaway food services A3349718A 1982 May 27.3
## 3 Queensland Takeaway food services A3349718A 1982 Jun 26.2
## 4 Queensland Takeaway food services A3349718A 1982 Jul 25.2
## 5 Queensland Takeaway food services A3349718A 1982 Aug 25.6
## 6 Queensland Takeaway food services A3349718A 1982 Sep 26.7dim(myseries)## [1] 441 5Explore your chosen retail time series using the following functions:
autoplot(), gg_season(), gg_subseries(), gg_lag(), ACF() %>% autoplot()
autoplot(myseries, Turnover) +
labs(title = "Turnover in Queensland Takeaway food services",
subtitle = "Series ID: A3349767W",
y = "Turnover")
autoplot() indicates a increasing trend.
gg_season(myseries, Turnover) +
labs(title = "Turnover in Queensland Takeaway food services",
subtitle = "Series ID: A3349767W",
y = "Turnover")
gg_season() indicates a seasonal pattern particularly in the more recent years.
gg_subseries(myseries, Turnover) +
labs(title = "Turnover in Queensland Takeaway food services",
subtitle = "Series ID: A3349767W",
y = "Turnover")
gg_subseries() reiterates the finding from gg_season(). The blue average line represents the seasonal, yearly nature of the turnover.
gg_lag(myseries, geom ="point") +
labs(x = "lag(Turnover, k)")
I’ll admit the gg_lag() is not telling me much besides a strongly positive relationship. My impression is that the graph is speaking more to the overall increase of turnover.
myseries %>% ACF(Turnover) %>% autoplot()
Can you spot any seasonality, cyclicity and trend? What do you learn about the series?
I would say an increasing trend is present in the data and the data does follow a seasonal pattern over the course of a given year. The ACF() graph almost captures the scallop graphical pattern as identified in the textbook, but not quite. Given the step-down pattern present after lag 12, 24, I do define this data as seasonal on a yearly basis. I would not say a cyclic nature exists for the data.
In wanting to say Yes to a cyclic nature, perhaps an argument could be made for a general 7-year stock-market cycle starting in 1998 through 2014, but I think that’s a stretch. I’m not an expert on the Australian economy, but if the Australian economy follows the US economy based on global impacts, then I could believe the dot com bust of late 90s and the 2008 subprime mortgage market crash are being reflected here. But I wouldn’t say that’s a cycle. I wouldn’t say this data captures a true stock-market cycle given the data provided.