2.10 Exercise

library(tidyr)
library(knitr)
library(utils)
library(ggplot2)
library(readxl)
library(forecast)
## Registered S3 method overwritten by 'quantmod':
##   method            from
##   as.zoo.data.frame zoo
library(fpp2)
## ── Attaching packages ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── fpp2 2.4 ──
## ✓ fma       2.4     ✓ expsmooth 2.3
##

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

  1. Use autoplot() to plot each of these in separate plots.
autoplot(gold) +
  ggtitle("Daily morning gold prices") +
  xlab("1 January 1985 to 31 March 1989") +
  ylab("US Dollars")

autoplot(woolyrnq) +
  ggtitle("Quarterly production of woollen yarn in Australia") +
  xlab("Mar 1965 to Sep 1994") +
  ylab("Tonnes")

autoplot(gas) +
  ggtitle("Australian monthly gas production") +
  xlab("1956 to 1995") +
  ylab("production")

  1. What is the frequency of each series? Hint: apply the frequency() function.
frequency(gold)
## [1] 1
frequency(gas)
## [1] 12
frequency(woolyrnq)
## [1] 4
  1. Use which.max() to spot the outlier in the gold series. Which observation was it?
which.max(gold)
## [1] 770
which.max(gas)
## [1] 475
which.max(woolyrnq)
## [1] 21

2.2 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.

file1 = "https://raw.githubusercontent.com/vsinha-cuny/data624/master/hw1/tute1.csv"
tute1 = read.csv(file = file1, header = T)

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

autoplot(mytimeseries, facets=FALSE)

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

library(openxlsx)
file2 = "https://raw.githubusercontent.com/vsinha-cuny/data624/master/hw1/retail.xlsx"
retaildata <- read.xlsx(file2, sheet=1, startRow=2)
myts <- ts(retaildata[,"A3349873A"], frequency=12, start=c(1982,4))
autoplot(myts) +
    ggtitle("Australian retail data")

Seasonality: There is a large jump in sales starting in October and lasting till end of December.

ggseasonplot(myts)

ggsubseriesplot(myts)

The subseries plot shows the mean values of the time series. In this case we see that the values are in an upward trend from October to December.

gglagplot(myts, lags=12)

From the lagplot we see that there is a strong correlation for all lag values. It is strongest for lag=12.

ggAcf(myts)

The ACF plot shows strong autocorrelation. The seasonality is reflected in the strongest ACF being observed at lag=12.

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

autoplot(hsales) +
    ggtitle("Monthly sales of new one-family houses sold in the USA since 1973")

ggseasonplot(hsales)

ggsubseriesplot(hsales)

gglagplot(hsales, lags=12)

ggAcf(hsales)

autoplot(usdeaths) +
    ggtitle("Monthly accidental deaths in USA")

ggseasonplot(usdeaths)

ggsubseriesplot(usdeaths)

gglagplot(usdeaths, lags=12)

ggAcf(usdeaths)

autoplot(bricksq) +
    ggtitle("Australian quarterly clay brick production: 1956–1994")

ggseasonplot(bricksq)

ggsubseriesplot(bricksq)

gglagplot(bricksq, lags=12)

ggAcf(bricksq)

autoplot(sunspotarea) +
    ggtitle("Annual average sunspot area (1875-2015)")

# ggseasonplot(sunspotarea)
# 
# ggsubseriesplot(sunspotarea)
# 
# gglagplot(sunspotarea, lags=12)
# 
# ggAcf(sunspotarea)
autoplot(gasoline) +
    ggtitle("US finished motor gasoline product supplied")

ggseasonplot(gasoline)

# ggsubseriesplot(gasoline)

gglagplot(gasoline, lags=12)

ggAcf(gasoline)