library(fpp2)
library(tsibble)

Forecasting: Principles and Practices (Chapter 2 - Time serise graphics)

2.1

Use the help function to explore what the series gold, woolyrnq and gas represent.

\((a)\) Use autoplot() to plot each of these in separate plots.

?gold
?woolyrnq
?gas
autoplot(gold)

autoplot(woolyrnq)

autoplot(gas)

\((b)\) What is the frequency of each series? Hint: apply the frequency() function.

paste0("Frequency of gold serise: ", frequency(gold)) 
## [1] "Frequency of gold serise: 1"
paste0("Frequency of woolyrnq serise: ", frequency(woolyrnq))
## [1] "Frequency of woolyrnq serise: 4"
paste0("Frequency of gas serise: ", frequency(gas))
## [1] "Frequency of gas serise: 12"

\((c)\) Use which.max() to spot the outlier in the gold series. Which observation was it?

which.max(gold)
## [1] 770

The observation is 770.

2.3

Download some monthly Australian retail data from the book website. These represent retail sales in various categories for different Australian states, and are stored in a MS-Excel file.

\((a)\) You can read the data into R with the following script:

retaildata <- readxl::read_excel("retail.xlsx", skip=1)
head(names(retaildata))
## [1] "Series ID" "A3349335T" "A3349627V" "A3349338X" "A3349398A" "A3349468W"

The second argument (skip=1) is required because the Excel sheet has two header rows.

\((b)\) Select one of the time series as follows (but replace the column name with your own chosen column):

myts <- ts(retaildata[,"A3349627V"],
  frequency=12, start=c(1982,4))

\((c)\) Explore your chosen retail time series using the following functions:

autoplot(), ggseasonplot(), ggsubseriesplot(), gglagplot(), ggAcf()

Can you spot any seasonality, cyclicity and trend? What do you learn about the series?

autoplot(myts)

The plot shows seasonality and a upward trend.

ggseasonplot(myts) + ggtitle("Seasonal plot: retail sales")

The seasonal plot shows the there is a large jump in sales in December. The graph also shows that the sales decrease in February and increase in March.

ggsubseriesplot(myts) + ggtitle("Seasonal subseries plot: retail sales")

The plot shows higher sales in December, February has low sales compared to other months.

gglagplot(myts, lags = 30)

Here the colours indicate the months. All other lags have positive corelation but the relationship is strongly positive at lags 12 and lag 24.

ggAcf(myts, lag = 48)

The slow decrease in the ACF as the lags increase is due to the trend, while the scalloped shape is due the seasonality.

Forecasting: Principles and Practices (Chapter 6 - Time serise Decomposition)

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)

The plot shows the seasonality and a upward trend.

\((b)\) 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 plastic sales")

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

Yes, the result support the graphical interpretation, above decomposition graph shows the trend, seasonal, and remainder.

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

dcomp <- plastics %>% decompose(type="multiplicative")
adjusted_seasonality <- plastics / dcomp$seasonal

autoplot(plastics, series = 'Data') +
    autolayer(adjusted_seasonality, series = 'Seasonality Adjusted') +
  labs(y = "Sales", x = "Year", 
       title = "Plastic sales", color = 'Serise') +
  scale_color_manual(name="Series", 
                        values = c("Data"="gray50", 
                                   "Seasonality Adjusted"="steelblue"))

\((e)\) 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?

plastics2 <- plastics
plastics2[15] <- plastics2[15] + 500

dcomp2 <- plastics2 %>% decompose(type="multiplicative")
adjusted_seasonality2 <- plastics2 / dcomp2$seasonal

autoplot(plastics, series = 'Data') +
    autolayer(adjusted_seasonality2, series = 'Seasonality Adjusted') +
  labs(y = "Sales", x = "Year", 
       title = "Plastic sales", color = 'Serise') +
  scale_color_manual(name="Series", 
                        values = c("Data"="gray50", 
                                   "Seasonality Adjusted"="steelblue"))

The outlier has major impact on the plot. The sesonality adjusted line structure has changed.

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

plastics3 <- plastics
plastics3[60] <- plastics3[60] + 500

dcomp3 <- plastics3 %>% decompose(type="multiplicative")
adjusted_seasonality3 <- plastics3 / dcomp3$seasonal

autoplot(plastics, series = 'Data') +
    autolayer(adjusted_seasonality3, series = 'Seasonality Adjusted') +
  labs(y = "Sales", x = "Year", 
       title = "Plastic sales") +
  scale_color_manual(name="Series", 
                        values = c("Data"="gray50", 
                                   "Seasonality Adjusted"="steelblue"))

We can see the outlier effect in the plot but at the end. The seasonality-adjusted line looks smooth, with not much variation in the line.