ECOM90024
Forecasting in Economics and Business
Assignment 2


Question 1 (5 Marks)

Consider the following ARMA(1,1) process,
! = !"# + ! + !"#
!~$.$.&.(0, ')

a.) Using an appropriate diagram, depict the set of values for the parameters and
for which ! will be invertible AND covariance stationary. (1 Mark)

b.) On the same diagram, depict the set of values of the parameters and for which ! will be a white noise process. (1 Mark)

c.) Assuming invertibility and covariance stationarity, derive the autocovariance ()
and autocorrelation () functions associated with !. (Hint: Using lag operators and
Wold’s Representation Theorem will be helpful here!) (3 Marks)

Question 2 (5 Marks)

You are an analyst working for a real estate investment fund and are tasked with monitoring
and forecasting house prices in the United States. The file csindex.csv contains monthly
observations of the Case-Shiller U.S. National Home Price Index from January 1987 to
December 2022. You are required to compute all your estimations and plots in R.

a.) Generate a plot of the data and provide a brief description of the observed time
series. (1 Mark)

b.) Using the data from January 1987 to December 2018, identify and estimate an
appropriate time series model using the steps outlined in Lecture 6. Make sure to
report all relevant estimation results, plots, statistical tests and information criteria
that you are relying on in determining your preferred model. (2 Marks)

c.) Using your estimation results from part b, compute and plot appropriate point and
interval forecasts for the period spanning January 2019 to January 2022. Do the
forecasts perform well when compared to the actual realisations? Why or why not?
(2 Marks)



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