Problem 1

library(fpp2)
## Loading required package: ggplot2
## Loading required package: forecast
## Loading required package: fma
## Loading required package: expsmooth
library(curl)
library(readxl)

gold is the daily price of gold over several years in the 80s. The outlier is February 9, 1987 or the 770th entry of the dataset

x <- gold
autoplot(x)

frequency(x)
## [1] 1
which.max(x)
## [1] 770

woolyrnq is the quarterly production of woolen yarn in Australia.

??woolyrnq
x <- woolyrnq
autoplot(x)

frequency(x)
## [1] 4

gas is the Australian monthly gas production from 1965-1995.

?gas
x <- gas
autoplot(x)

frequency(x)
## [1] 12

Problem 2

curl_download("http://otexts.com/fpp2/extrafiles/tute1.csv", "tute1.csv")
tute1 <- read.csv("tute1.csv", header=TRUE)
ts1 <- ts(tute1[,-1], start=1981, frequency = 4)
autoplot(ts1, facets=TRUE)

autoplot(ts1)

As we can see from this graph, the facets flag is used to tell the autoplot() function that the variables should be graphed separately.

Problem 3

curl_download("https://otexts.com/fpp2/extrafiles/retail.xlsx", "retail.xlsx")
retail <- read_excel("retail.xlsx", skip = 1)
## readxl works best with a newer version of the tibble package.
## You currently have tibble v1.4.2.
## Falling back to column name repair from tibble <= v1.4.2.
## Message displays once per session.
ts2 <- ts(retail[,"A3349872X"], frequency = 12, start = c(1982,4))
autoplot(ts2)

ggseasonplot(ts2)

ggsubseriesplot(ts2)

gglagplot(ts2)

ggAcf(ts2)

The Seasonal and subseries plots clearly show an increased usage of gas in the Australian summer (November and December).

Problem 6

The lag plot, particularly lags 1 and 2 reflect strong seasonality in the data. In addition, there appears to be a long, term cyclical nature to the data, as show by the autocorrelation chart. The scatterplot and subseason plots agree.

tsx <- hsales
autoplot(tsx)

ggseasonplot(tsx)

ggsubseriesplot(tsx)

gglagplot(tsx)

ggAcf(tsx)

The number of accidental deaths in the US is also cyclical, following the properties described above. However, the number of deaths peaks in the Summer, perhaps correlated with an increased number of drivers and a higher number of construction related jobs.

?usdeaths
tsx <- usdeaths
autoplot(tsx)

ggseasonplot(tsx)

ggsubseriesplot(tsx)

gglagplot(tsx)

ggAcf(tsx)

The bricksq data show the Australian quarterly clay brick production, which shows cyclic nature of the business, with production peaking in Q2 and Q3. The 1975 and 1983 recessions are obvious in the data.

?bricksq
tsx <- bricksq
autoplot(tsx)

ggseasonplot(tsx, polar = TRUE)

ggsubseriesplot(tsx)

gglagplot(tsx)

ggAcf(tsx)

Sunspots appear to be cyclical, which si confirmed by the postive lags (numbers 1 and 9) and the autocorrelation plot. The scatter plot appears to show a cyclical growth and decline in the are of sun spots, but the period does not appear to be constant.

?sunspotarea
tsx <- sunspotarea
autoplot(tsx)

gglagplot(tsx)

ggAcf(tsx)

US gasoline production tends to rise in the summer, but is also subject to wider economic trends.

?gasoline
gasoline <- ts(gasoline,frequency = 52)
tsx <- gasoline
autoplot(tsx)

ggseasonplot(tsx)

ggsubseriesplot(tsx)

gglagplot(tsx)

ggAcf(tsx)