ETW3420 Principles of Forecasting and Applications
Principles of Forecasting and Applications
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Topic 6 Exercises – Part 1
Question 1
The figure below shows (from left to right) the ACFs for 36 random numbers, 360 random
numbers and 1,000 random numbers.
(a) Explain the differences among these figures. Do they indicate that the data are white
5 10 15 20
5 10 15 20
5 10 15 20
(b) Why are the critical values at different distances from the mean of zero? Why are the
autocorrelations different in each figure when they each refer to white noise?
Question 2
A classic example of a non-stationary series is the daily closing IBM stock price series (data
set ibmclose). Use R to plot the daily closing prices for IBM stock and the ACF and PACF.
Explain how each plot shows that the series is non-stationary and should be differenced.
ggtsdisplay(ibmclose)
Question 3
For the following series, find an appropriate Box-Cox transformation and order of differencing
in order to obtain stationary data.
(a) usnetelec
(b) enplanements
(c) visitors
autoplot(usnetelec)
autoplot(enplanements)
autoplot(visitors)
Question 4
For the enplanements data, write down the differences you chose above using backshift
operator notation.
Question 5 (Self-Practice)
The “retail.xls” file contains data on the retail sales in various categories for different
Australian states. For this question, we will consider the retail turnover for Wales
(A3349873A).
As per question 3, using this data set, find an appropriate Box-Cox transformation and order
of differencing in order to obtain stationary data.
#Import data and convert into ts
myts <- readxl::read_excel("retail.xlsx", skip=1)[,"A3349873A"] %>%
ts(frequency=12, start=c(1982,4))
#Plot data
ggtsdisplay(myts)
Question 1
Question 2
Question 3
Question 4
Question 5 (Self-Practice)
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