1 Question - 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?

Answer:

The autoplot shows a significantinscreasing trend.

autoplot(plastics) +
  xlab("Year") + ylab("Sales") +
  ggtitle("Autoplot: Monthly Sales of Plastic Product A") +
  theme_hc()

The ggsubseriesplot presents a significant normal seasonal fluctuations.

ggsubseriesplot(plastics) +
  xlab("Year") + ylab("Sales") +
  ggtitle("ggsubseriesplot: Monthly Sales of Plastic Product A") +
  theme_hc()

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

plastics %>% decompose(type="multiplicative") %>% 
  autoplot() + xlab("Year") +
  ggtitle("Classical Multiplicative Decomposition of Monthly Sales of Plastic Product A") +
  theme_hc()

(c.) Do the results support the graphical interpretation from part a?

Answer: Yes. The result of classical multiplicative decomposition supports the graphical interpretation from part A.

(d.) Compute and plot the seasonally adjusted data.

fit <- plastics %>% decompose(type="multiplicative")
autoplot(plastics, series="Original Data") +
  autolayer(trendcycle(fit), series="Trend") +
  autolayer(seasadj(fit), series="Seasonally Adjusted Data") +
  xlab("Year") + ylab("Sales") +
  ggtitle("Monthly Sales of Plastic Product A (Seasonally Adjusted)") +
  scale_color_manual(values=c("gray", "blue", "red"), 
                     breaks=c("Original Data", "Seasonally Adjusted Data", "Trend")) +
  theme_hc()

(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?

Anwer:

From the autoplot after multiplicative decomposition, it is obversed that both the trend and seasonal effect got affected after introducting an outline in middle of the TS.

plastics_ol1 <- plastics
plastics_ol1[31] <- 500

fit_ol1 <- plastics_ol1 %>% decompose(type="multiplicative")
grid.arrange(
  plastics_ol1 %>% decompose(type="multiplicative") %>%
    autoplot() + xlab("Year") +
  ggtitle("Classical Multiplicative Decomposition \n(Outliner in Middle)") +
    theme_hc(),
  plastics %>% decompose(type="multiplicative") %>%
    autoplot() + xlab("Year") +
  ggtitle("Classical Multiplicative Decomposition") +
    theme_hc(),
  ncol = 2)

However after seasonality adjustment, the adjusted data still greatly affected by the outliner in the middle of the TS.

grid.arrange(
  autoplot(plastics_ol1, series="Original Data") +
    autolayer(trendcycle(fit_ol1), series="Trend") +
    autolayer(seasadj(fit_ol1), series="Seasonally Adjusted Data") +
    xlab("Year") + ylab("Sales") +
    ggtitle("Monthly Sales(Outliner in Middle)") +
    scale_color_manual(values=c("gray", "blue", "red"), 
                     breaks=c("Original Data", "Seasonally Adjusted Data", "Trend")) +
    theme_hc()+
    ylim(500, 1750),
  autoplot(plastics, series="Original Data") +
    autolayer(trendcycle(fit), series="Trend") +
    autolayer(seasadj(fit), series="Seasonally Adjusted Data") +
    xlab("Year") + ylab("Sales") +
    ggtitle("Monthly Sales") +
    scale_color_manual(values=c("gray", "blue", "red"), 
                     breaks=c("Original Data", "Seasonally Adjusted Data", "Trend")) +
    theme_hc() +
    ylim(500, 1750),
  ncol = 2)

(f.) Does it make any difference if the outlier is near the end rather than in the middle of the time series?

Answer: The outlier near the end has less effect on both the trend and seasonal fluctuation than that in the middle of the TS.

plastics_ol2 <- plastics
plastics_ol2[58] <- 500

fit_ol2 <- plastics_ol2 %>% decompose(type="multiplicative")
grid.arrange(
  plastics_ol2 %>% decompose(type="multiplicative") %>%
    autoplot() + xlab("Year") +
  ggtitle("Classical Multiplicative Decomposition \n(Outliner at the end)") +
    theme_hc(),
  plastics %>% decompose(type="multiplicative") %>%
    autoplot() + xlab("Year") +
  ggtitle("Classical Multiplicative Decomposition") +
    theme_hc(),
  ncol = 2)

grid.arrange(
  autoplot(plastics_ol2, series="Original Data") +
    autolayer(trendcycle(fit_ol2), series="Trend") +
    autolayer(seasadj(fit_ol2), series="Seasonally Adjusted Data") +
    xlab("Year") + ylab("Sales") +
    ggtitle("Monthly Sales(Outliner in Middle)") +
    scale_color_manual(values=c("gray", "blue", "red"), 
                     breaks=c("Original Data", "Seasonally Adjusted Data", "Trend")) +
    theme_hc()+
    ylim(500, 1750),
  autoplot(plastics, series="Original Data") +
    autolayer(trendcycle(fit), series="Trend") +
    autolayer(seasadj(fit), series="Seasonally Adjusted Data") +
    xlab("Year") + ylab("Sales") +
    ggtitle("Monthly Sales") +
    scale_color_manual(values=c("gray", "blue", "red"), 
                     breaks=c("Original Data", "Seasonally Adjusted Data", "Trend")) +
    theme_hc() +
    ylim(500, 1750),
  ncol = 2)

2 Question - 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?

Answer:

From the X11 decomposition remainder graph, it is observed there are multiple up or down spikes, which are possible outliners.

data <- import("https://raw.githubusercontent.com/shirley-wong/Data-624/main/HW1/retail.xlsx", skip=1) 


myts <- ts(data[,"A3349398A"], frequency=12, start=c(1982,4))
autoplot(myts) +
  ggtitle("Monthly Food Retailing in Australia") +
  xlab("Year") + 
  ylab("Sales") +
  theme_hc()

#x11 decomposition
fit <- myts %>% seas(x11="")
autoplot(fit, series="Data") +
  xlab("Year") + ylab("Sales") +
  ggtitle("X11 Decomposition of Monthly Food Retailing in Australia")