Homework Assignment 3

6.2

?plastics
plastics
##    Jan  Feb  Mar  Apr  May  Jun  Jul  Aug  Sep  Oct  Nov  Dec
## 1  742  697  776  898 1030 1107 1165 1216 1208 1131  971  783
## 2  741  700  774  932 1099 1223 1290 1349 1341 1296 1066  901
## 3  896  793  885 1055 1204 1326 1303 1436 1473 1453 1170 1023
## 4  951  861  938 1109 1274 1422 1486 1555 1604 1600 1403 1209
## 5 1030 1032 1126 1285 1468 1637 1611 1608 1528 1420 1119 1013

a.

plot(plastics, ylab="Sales (Thousands)", xlab="Year", main="Plastics Yearly Sales Time Plot")

The graph shows us that there is a seasonal trend, with an overall upward trend to the data. There is a clear drop in sales at the beginning of each year. ####b.

model<- plot(decompose(plastics, type="multiplicative"))

model
## NULL
calc <- decompose(plastics)
calc$figure
##  [1] -273.203993 -339.933160 -263.099826 -104.943576   56.504340
##  [6]  193.316840  183.441840  254.952257  265.316840  221.139757
## [11]   -4.953993 -188.537326

c.

yes, we can see from the trend graph that there is an increase in sales overtime. From the seasonal graph, we can see the seasonality in each of the 5 years. In the random graph, we can see some randomness in the residuals.

d.

autoplot(plastics, series="Data") +
  autolayer(trendcycle(calc), series="Trend") +
  autolayer(seasadj(calc), series="Seasonally Adjusted") +
  xlab("Year") + ylab("Monthly Sales amount") +
  ggtitle("Sales of plastic product (in thousand)") +
  scale_colour_manual(values=c("gray","blue","red"),
                     breaks=c("Data","Seasonally Adjusted","Trend"))
## Warning: Removed 12 rows containing missing values (geom_path).

e.

plastics[30]=plastics[30]+500
model<-decompose(plastics, type="multiplicative")

tr<-model$trend
seas<- model$seasonal

plot(seasadj(model))

The outlier caused a significant change in the graph when it was added. ####f.

plastics[60]=plastics[60]+500
model<-decompose(plastics, type="multiplicative")

tr<-model$trend
seas<- model$seasonal

plot(seasadj(model))

The graph has less variance if the outlier is added to the end of the data. But it does cause a significant spike at the end of the series when added.

6.3

retaildata <- readxl::read_excel('retail.xlsx', skip = 1)
## readxl works best with a newer version of the tibble package.
## You currently have tibble v1.4.2.
## Falling back to column name repair from tibble <= v1.4.2.
## Message displays once per session.
myts <- ts(retaildata[,'A3349399C'], frequency = 12, start = c(1982,4))
autoplot(myts)

x11_retail <- seas(myts, x11 = "")
autoplot(x11_retail)

In the remainders plot, I can see some outliers around the year 2001 that I had not noticed prior to plotting this. I can also spot a variance in the seasonality around that time. The trend plot is as I had expected, with an increase over time.