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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