Problem Set 2
Robert Kohn
UNSW School of Business
University of New South Wales
ECON 5248
April 5, 2023
Please hand in this problem by 6 pm on 19th 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 = ℓt−1 + bt−1 + st−m + εt
ℓt = ℓt−1 + bt−1 + αεt
bt = bt−1 + βεt
st = st−m + γεt
(b)
yt = ℓt−1 + φvt−1 + st−m + εt
ℓt = ℓt−1 + ϕbt−1 + αεt
bt = ϕbt−1 + βεt
st = st−m + γεt
1
(c)
yt = (ℓt−1 + bt−1 + st−m) (1 + εt)
ℓt = ℓt−1 + bt−1 + α (ℓt−1 + bt−1 + st−m) εt
bt = bt−1 + β (ℓt−1 + bt−1 + st−m) εt
st = st−m + γ (ℓt−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.