Data 624 HW3

if (!require("fpp2")) install.packages("fpp2")
if (!require("seasonal")) install.packages("seasonal")

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?

autoplot(plastics) + ylab("Monthly Sales")

There is a increasing trend in the timeseries. All sales are at peak in summer

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

fit <- decompose(plastics, type="multiplicative")

trend_indices <- fit$trend
seasonal_indices <- fit$seasonal

autoplot(trend_indices)

The results in of the multiplicative decomposition show that there is an increasing trend till 5 years. After that we can see decreasing it is decresing.

autoplot(seasonal_indices)

seasonal_indices is identical in thoughout all years

C. Do the results support the graphical interpretation from part a?

Yes, Results does support the graphical interpretation. summer months does have sales higher than other seasonal

D. Compute and plot the seasonally adjusted data.

adjusted <- seasadj(fit)
plot(adjusted)

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?

obs_plast <- plastics
obs_plast[17] = obs_plast[17] + 500

fit2 <- decompose(obs_plast, type="multiplicative")

change_obes <- seasadj(fit2)
plot(change_obes)

There is sudden spike in plot

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

obs_plast1 <- plastics
obs_plast1[55] = obs_plast[55] + 500

fit3 <- decompose(obs_plast1, type="multiplicative")

change_obes_end <- seasadj(fit3)
plot(change_obes_end)

It appears that it doesn’t matter where the outlier occurs. we see a identical spike at the end like seen in previous plot

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?

library(readxl)
library(seasonal)

retaildata <- readxl::read_excel("C:/Users/patel/Documents/Data_624/retail.xlsx", skip=1)

myts <- ts(retaildata[,"A3349398A"], frequency=12, start=c(1982,4))
myts %>% seas(x11="") -> myts_x11
autoplot(myts_x11) +
  ggtitle("X11 decomposition")

The X11 decomposition method reveals a smooth upward trend. The remainder plot describes that after 1992 trend and seasonality appear consistent. The unusual features that I had not noticed previously was there is sudden spike at 1986 in remainder plot despite there is consistancy in tread before and after that.