HHernandez_DATA624_HW03
humbertohp
February 17, 2020
Exercise 6.2
The plastics data set consists of the monthly sales (in thousands) of product A for a plastics manufacturer for five years.
- Plot the time series of sales of product A. Can you identify seasonal fluctuations and/or a trend-cycle?
- Use a classical multiplicative decomposition to calculate the trend-cycle and seasonal indices.
- Do the results support the graphical interpretation from part a?
- Compute and plot the seasonally adjusted data.
- 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?
- Does it make any difference if the outlier is near the end rather than in the middle of the time series?
## Jan Feb Mar Apr May Jun
## 1 742 697 776 898 1030 1107## [1] 12
a) There seems to be an upward trend and a seasonal fluctuation of low sales at the beggining of each month
# b)
plastics %>% decompose(type="multiplicative") %>%
autoplot() + xlab("Month") +
ggtitle("Classical multiplicative decomposition
of Product sales")
## Jan Feb Mar Apr May Jun Jul
## 1 NA NA NA NA NA NA 976.9583
## 2 1000.4583 1011.2083 1022.2917 1034.7083 1045.5417 1054.4167 1065.7917
## 3 1117.3750 1121.5417 1130.6667 1142.7083 1153.5833 1163.0000 1170.3750
## 4 1208.7083 1221.2917 1231.7083 1243.2917 1259.1250 1276.5833 1287.6250
## 5 1374.7917 1382.2083 1381.2500 1370.5833 1351.2500 1331.2500 NA
## Aug Sep Oct Nov Dec
## 1 977.0417 977.0833 978.4167 982.7083 990.4167
## 2 1076.1250 1084.6250 1094.3750 1103.8750 1112.5417
## 3 1175.5000 1180.5417 1185.0000 1190.1667 1197.0833
## 4 1298.0417 1313.0000 1328.1667 1343.5833 1360.6250
## 5 NA NA NA NA NAb), c) Yes, the classical multiplicative decomposition supports the graphical interpretation from a), upward trend-cycle and monthly seasonal fluctuation
# d)
plastics %>% decompose(type="multiplicative") -> decomp_plast
autoplot(plastics, series="Data") +
autolayer(seasadj(decomp_plast), series="Seasonally Adjusted") +
xlab("Year") + ylab("Sales") +
ggtitle("Monthly sales (in thousands) of product A")
# e)
plastics2 <- plastics
plastics2[40] <- plastics2[40] + 500
plastics2 %>% decompose(type="multiplicative") -> decomp_plast2
autoplot(plastics2, series="Data") +
autolayer(seasadj(decomp_plast2), series="Seasonally Adjusted (Recomputed)") +
xlab("Year") + ylab("Sales") +
ggtitle("Monthly sales (in thousands) of product A")
e) The outlier affects the seasonality adjusted data considerably, it follows the outlier completely
# f)
plastics3 <- plastics
plastics3[55] <- plastics2[55] + 500
plastics3 %>% decompose(type="multiplicative") -> decomp_plast3
autoplot(plastics3, series="Data") +
autolayer(seasadj(decomp_plast3), series="Seasonally Adjusted (Recomputed)") +
xlab("Year") + ylab("Sales") +
ggtitle("Monthly sales (in thousands) of product A")
f) The outlier at the end of the series still affects the seasonality adjusted data, but not as much as it did when it was in the middle, it does not overlap precisely to the magnitude of the outlier
Exercise 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?
retaildata <- readxl::read_excel("retail.xlsx", skip=1)
myts <- ts(retaildata[,"A3349873A"], frequency=12, start=c(1982,4))
autoplot(myts) +
ggtitle("Monthly Retail Sales")
library(seasonal)
myts_x11 <- seas(myts, x11 = "")
autoplot(myts_x11) +
ggtitle("Monthly Retail Sales (X11)")