1. Use the help function to explore what the series gold, woolyrnq and gas represent.

str(gold) 
##  Time-Series [1:1108] from 1 to 1108: 306 300 303 297 304 ...
str(woolyrnq) 
##  Time-Series [1:119] from 1965 to 1994: 6172 6709 6633 6660 6786 ...
str(gas) 
##  Time-Series [1:476] from 1956 to 1996: 1709 1646 1794 1878 2173 ...

a. Use autoplot() to plot each of these in separate plots.

autoplot(gold) 

autoplot(woolyrnq) 

autoplot(gas)

b. What is the frequency of each series? Hint: apply the frequency() function

cat("Gold Frequency is: ", frequency(gold)) 
## Gold Frequency is:  1
cat("woolyrnq Frequency is: ", frequency(woolyrnq)) 
## woolyrnq Frequency is:  4
cat("gas Frequency is: ", frequency(gas)) 
## gas Frequency is:  12

c. Use which.max() to spot the outlier in the gold series. Which observation was it?

cat("When is the maximum value for gold? ",which.max(gold)) 
## When is the maximum value for gold?  770
cat("What is the maximum value for gold? ",gold[which.max(gold)]) 
## What is the maximum value for gold?  593.7

2. Tute1 file

Download the file 1.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 <-
read.csv("tute1.csv", header=TRUE) #View(tute1)

b. Convert the data to time series

mytimeseries <- ts(tute1[,-1], start=1981, frequency=4)

(The [,-1] removes the first column which contains the quarters as we don’t need them now.)

c. Construct time series plots of each of the three series

autoplot(mytimeseries, facets=TRUE)

Check what happens when you don’t include facets=TRUE.

autoplot(mytimeseries)

3. Retail file

Download some monthly Australian retail data from the book website. These represent retail sales in various categories for different Australian states, and are stored in a MS-Excel file.

a. You can read the data into R with the following script:

retaildata <- readxl::read_excel("retail.xlsx", skip=1)

The second argument (skip=1) is required because the Excel sheet has two header rows.

b. Time Series Graph data

Select one of the time series as follows (but replace the column name with your own chosen column):

myts <- ts(retaildata[,"A3349640L"],
frequency=12, start=c(1982,4))

c. Time Series Graphs

Explore your chosen retail time series using the following functions: autoplot(), ggseasonplot(), ggsubseriesplot(), gglagplot(), ggAcf()

Can you spot any seasonality, cyclicity and trend? What do you learn about the series?

Data generated on Turnover; Victoria;Cafes, restaurants and catering services

autoplot(myts) 

ggseasonplot(myts)

# too many observations to clearly read the non polar graph
ggseasonplot(myts, polar=TRUE)

ggsubseriesplot(myts) 

gglagplot(myts) 

ggAcf(myts)

  • Between ~1997 and 2000 there is a sharp uptick in values.
    • Before this date the seasonality exists but at a much smaller rate.
    • Further example of a raise in values from around 1997 and up.
  • Everything takes a dip in Feb and rises from Nov into Dec
    • Appears to be a very small dip around Jun; potential onset of Winter
    • there is a dip in the mean around the same section
  • correlations are significantly different from zero
  • Does not appear to have any defined shape of seasonality just a drop over lag

6. Use the following graphics functions:

autoplot(), ggseasonplot(), ggsubseriesplot(), gglagplot(), ggAcf() and explore features from the following time series: hsales, usdeaths, bricksq, sunspotarea, gasoline.

Can you spot any seasonality, cyclicity and trend?
What do you learn about the series?

House Sales

autoplot(hsales)

ggseasonplot(hsales)

ggseasonplot(hsales, polar = TRUE)

ggsubseriesplot(hsales)

gglagplot(hsales)

ggAcf(hsales)

  • There is clear seasonality in home sales starting in March
    • The house buying season starts in Spring aroudn March and tapers off until we get the lowest point around the holidays
  • Not sure if we are also seeing cycles or just market factors, (gas shortage 1975, recession 1982-83, etc.)

US Deaths

autoplot(usdeaths)

ggseasonplot(usdeaths)

ggseasonplot(usdeaths, polar = TRUE)

ggsubseriesplot(usdeaths)

gglagplot(usdeaths)

ggAcf(usdeaths)

  • The data suggests a potential 5 year cycle
  • Seasonal pattern of Summer months are more prone to deaths
    • Slight uptick around the holidays
    • Feb being the lowest

Quarterly clay brick production

autoplot(bricksq)

ggseasonplot(bricksq)

# too many observations to clearly read the non polar graph
ggseasonplot(bricksq, polar=TRUE)

ggsubseriesplot(bricksq)

gglagplot(bricksq)

ggAcf(bricksq)

  • Upward trend in production from earliest date to most recent date of data.
  • Seasonal pattern in Q2 and Q3 where production is higher in the warmer months
  • As the lag grows the ACF drop suggesting the use of the earlier models.

Annual Average Sunspot Area (1875-2011)

autoplot(sunspotarea)

#ggseasonplot(sunspotarea)
#ggsubseriesplot(sunspotarea)
gglagplot(sunspotarea)

ggAcf(sunspotarea)

  • This data shows a clear example of no seasonality or trends.
  • There does exist a good example of a ~12 year cycle.

Gasoline

Weekly data beginning 2 February 1991, ending 20 January 2017. Units are “million barrels per day”.

autoplot(gasoline)

ggseasonplot(gasoline)

# too many observations to clearly read the non polar graph
ggseasonplot(gasoline, polar = TRUE)

#ggsubseriesplot(gasoline)
gglagplot(gasoline)

ggAcf(gasoline)

  • There is a rising trend in gasoline production from 1990 to around 2008 where it starts to fall off.
    • Could the recession of 2008 have played such a major effect
  • The data does not allow us to see any seasonality clearly as there is not enough observations.
    • Looking at the autoplot there does seem to be something seasonal but further data work would be required.
  • No significent cycle