Exercise 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?

library(fpp2)
library(ggplot2)

hsales - Monthly sales of new one-family houses sold in the USA since 1973.

autoplot(hsales)

ggseasonplot(hsales)

ggseasonplot(hsales, polar = TRUE)

ggsubseriesplot(hsales)

gglagplot(hsales)

ggAcf(hsales)

• This is one of the datasets that was described in the book. The authors state that, “The monthly housing sales show strong seasonality within each year, as well as some strong cyclic behaviour with a period of about 6–10 years. There is no apparent trend in the data over this period.” While I would agree with the comments on trend and cyclicity, I don’t see any strong evidents for a seasonality of anything other than yearly.
• Judging from the graphs, perhaps the most overwhelming consistency in the data is that the numbers peak in March and deep in December.

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usdeaths - Monthly accidental deaths in USA (from 1973 to 1979).

autoplot(usdeaths)

ggseasonplot(usdeaths)

ggseasonplot(usdeaths, polar = TRUE)

ggsubseriesplot(usdeaths)

gglagplot(usdeaths)

ggAcf(usdeaths)

• There appears to be no trend and no apparent cycle here, but the graphs do show somewhat strong monthly seasonality.
  
• Interistingly the data consistently shows decline and lowest levels between January and February. Whereas the increase and peak numbers are between June and July.

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bricksq - Australian quarterly clay brick production: 1956–1994.

autoplot(bricksq)

ggseasonplot(bricksq)

ggseasonplot(bricksq, polar = TRUE)

ggsubseriesplot(bricksq)

gglagplot(bricksq)

ggAcf(bricksq)

• The graphs show that there is a positive trend and some 7-8 year cycle to the data. However, there appears to be no evident seasonality.
• Remarkably there is a very clear and almost an identical pattern repeated in the ggsubseriesplot() plot. However it’s not clear if this can translate to some seasonality or rather some cycle.

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sunspotarea - Annual averages of the daily sunspot areas (in units of millionths of a hemisphere) for the full sun.

autoplot(sunspotarea)

#ggseasonplot(sunspotarea)
#ggseasonplot(sunspotarea, polar = TRUE)
#ggsubseriesplot(sunspotarea)
gglagplot(sunspotarea)

ggAcf(sunspotarea)

• This data is probably a good example where there is no clear seasonality nor any trend. In fact, the ggseasonplot and ggsubseriesplot fail with some error. However, there appears to be a consistent cycle of about 12 years.
• The cycle is in fact so regular, I wonder if it hints to some natural phenomena which is yet to be explained. It is as if there is some pulsating activity that takes about 12 years to manifest itself with peaks and troughs.

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

autoplot(gasoline)

#ggseasonplot(gasoline)
#ggseasonplot(gasoline, polar = TRUE)
#ggsubseriesplot(gasoline)
gglagplot(gasoline)

ggAcf(gasoline)

• There appears to be a positive long term trend. There might be a long range cycle, but its not evident yet, given the amount of data so far. Also, there is no clear seasonality as well.
• The increasing trend is not surprising given that it is a limited natural resource, which is also subject to overall inflation in the market.

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