Problem 6.2

The plastics data set consists of the monthly sales (in thousands) of product A for a plastics manufacturer for five years.

a. Plot the time series of sales of product A. Can you identify seasonal fluctuations and/or a trend-cycle? There appears to be seasonaility and an upward trend cycle

plastics <- plastics
autoplot(plastics)

b. Use a classical multiplicative decomposition to calculate the trend-cycle and seasonal indices.

multiplicative_decomposition <- decompose(plastics, type = "multiplicative")
autoplot(multiplicative_decomposition)

c. Do the results support the graphical interpretation from part a? Yes the results from the muliplicative decomposition do match the graphical interpretation from part a, we can see that there is an upward trend and there is a strong seasonality component.

d. Compute and plot the seasonally adjusted data.

autoplot(plastics, series="Data") +
  autolayer(trendcycle(multiplicative_decomposition), series="Trend") +
  autolayer(seasadj(multiplicative_decomposition), series="Seasonally Adjusted") +
  xlab("Year") + ylab("Monthly Sales in Thousands") +
  ggtitle("Plastic Product Sales") +
  scale_colour_manual(values=c("gray","blue","red"), breaks=c("Data","Seasonally Adjusted","Trend"))

e. Change one observation to be an outlier (e.g., add 500 to one observation), and recompute the seasonally adjusted data. What is the effect of the outlier?

outlier_plastics <- plastics
outlier_plastics[20] <- outlier_plastics[20] + 500
multiplicative_decomposition_new <- decompose(outlier_plastics, type = "multiplicative")

autoplot(outlier_plastics, series = "Data") +
  autolayer(trendcycle(multiplicative_decomposition_new), series = "Trend") +
  autolayer(seasadj(multiplicative_decomposition_new), series = "Seasonally Adjusted") +
  xlab("Year") + ylab("Monthly Sales in Thousands") +
  ggtitle("Plastic Product Sales") +
  scale_color_manual(values=c("gray", "blue", "red"), breaks=c("Data", "Seasonally Adjusted", "Trend"))

The outlier slighty affects the trend but dramatically effects the seasonally adjusted data.

Does it make any difference if the outlier is near the end rather than in the middle of the time series? The outlier seems to have a slighly stronger impact on the trend component when it is at the end of the series

outlier_plastics <- plastics
outlier_plastics[50] <- outlier_plastics[50] + 500
multiplicative_decomposition_new <- decompose(outlier_plastics, type = "multiplicative")

autoplot(outlier_plastics, series = "Data") +
  autolayer(trendcycle(multiplicative_decomposition_new), series = "Trend") +
  autolayer(seasadj(multiplicative_decomposition_new), series = "Seasonally Adjusted") +
  xlab("Year") + ylab("Monthly Sales in Thousands") +
  ggtitle("Plastic Product Sales") +
  scale_color_manual(values=c("gray", "blue", "red"), breaks=c("Data", "Seasonally Adjusted", "Trend"))

Problem 6.3

Recall your retail time series data (from Exercise 3 in Section 2.10). Decompose the series using X11. Does it reveal any outliers, or unusual features that you had not noticed previously?

There appears to be some spikes in the remainder graphs that may be an indicator of the prescence of outliers

retaildata <- read_excel("retail.xlsx", skip = 1)
retail <- ts(retaildata[, "A3349337W"], frequency = 12, start = c(1982, 4))
x11_retail <- seas(retail, x11="")
autoplot(x11_retail) +
  ggtitle("X11 Decomposition of Retail Sales Data")