Problem Set 7
Robert Kohn
UNSW School of Business
University of New South Wales
ECON 5248
April 7, 2022
This problem set should be handed in for marking if you did not hand
in Problem set 5. Please hand in this problem by 6 pm on 17th of April.
Although you can discuss issues with fellow students, the work you hand in
should be your own.
Q1. Choose a series from us employment, the total employment in different
industries in the United States.
Please fit the following ETS models to the data and select the best
fitting model, explaining the criterion or criteria you used to define
”best”.
(a)
yt = t 1 + bt 1 + st m + εt
t = t 1 + bt 1 + αεt
bt = bt 1 + βεt
st = st m + γεt
(b)
yt = t 1 + φvt 1 + st m + εt
t = t 1 + bt 1 + αεt
bt = bt 1 + βεt
st = st m + γεt
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(c)
yt = ( t 1 + bt 1 + st m) (1 + εt)
t = t 1 + bt 1 + α ( t 1 + bt 1 + st m) εt
bt = bt 1 + β ( t 1 + bt 1 + st m) εt
st = st m + γ ( t 1 + bt 1 + st m) εt
(d) Consider also the model in (a), but with a log transformation.
Q2. Obtain the STL decomposition for the data set in Q1, either for the
original data or for the log transformed data, whichever is most appro-
priate from Q1.
(a) Are the residuals from the STL model white noise
(b) Compare the STL estimates of trend and seasonal from STL with
those of your best model from Q1.
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