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**Unformatted text preview: **1,1111 1 11 1111 1-1 Brock University
Faculty of Social Sciences
Department of Economics Economics 3P92: Forecasting
Fall 2011 Midterm 2 ﬁnestion 1 [10 marks]: You are sure that a series you want to forecast is trending, and that a
linear trend is adequate, but you are not sure whether seasonality is important. To be safe, you ﬁt a
forecasting model with both trend and seasonal dummies, ‘97
yt = 1811110161 + z ”Ti-Di: + U: W ’71;
1:1 The hypothesis of no seasonality, in which case you could drop the seasonal dummies, corresponds
to equal seasonal coefﬁcients across seasons, which is a set of s — 1 linear restrictions: 72172 731- ad’s—l : 73 How would you perform an F test of the hypothesis? What assumptions are you implicitly making about the regressiﬁdisturbance terjrpn? A I:
er W V‘Le J“ 5‘ C @uestion 2 [10 marks]: Describe how you would ﬁt a purely seasonal model for the following
monthly series In particular, what dummy variab1e(s ) would you use to capture the r’elemntﬁlecm. mung a) A sporting goods store ﬁnds that detrended monthly sales are about the same for each month___ in
a. given 3- month season For example, sales are nsimilar 1n the winter months of January, February, arc ; in e spring months of April, May,.l and so on. 5:; i ii
6W“, cry 1'
b) A campus bookstore ﬁnds that detrendeds see are similar for all ﬁrst all second, all and all
fourth months of each semester For example, sales are similar" 1 J and e tern r, the
ﬁrst months of the first, second and third trimesters, res ectively. ' (111.1 *2,
meEx Wealth @uestion 3 [10 marks]: You fit a purely seasonal model for a monthly series on employee hours
using a full set of monthly dummy variables. Discuss how the estimated dummies 71,72, . .would
change if you changed the first dummy variable D1: {1, 0,0,. ..} (with all the other dummies staying the same) to 3 L310
a)D1:{2,0,0,...}
b) D1= {— 10, 0,. .}
(Question 4 {10 marks}: Rewrite the following expressions in lag operator form: f 3
a) y:+y:_1 +...+y1“N = a+ut+u¢_1+...+ut_N b) y; = “1—2 + ”1—4 + U: Question 5 [Bonus 10 marks]: While interviewing at a top investment bank, your interviewer
notices that you took a forecasting course. She decides to test your knowledge of the auto CQVNEEEE j. structure of covariance static ary series and lie four auto covariance functions Jim is a constant): sh_ 7 __ ”fur a) ﬂak) = a ._.—7 -- L’r// <73 -
b) “({t, k) = oak c) ﬂak) = a/k Which auto covariance function(s) are consistent with covariance stationary, and which are not?
Why?
Question 6 [10 marks]: Describe the difierence between autocorrelations and partial autocorrela—
tions. pﬁgofm 153} go ”If Question 7 {40 marks]: A researcher obtained montlgl/cg/ri’c—urgfﬁ IBM and Monthly simple
returns for the Vaiue—Weighted index of US markets. The a 3. covers 1926.1 to 1997112. One version of the Capital AsseLPrisiag CAPM) stipulates that the return of an asset is
not predictable and should ion. erify this claim using nothing but the sample autocorrelations (see Exhibit A and the LB tests (see Exhibit B: for the simple and log returns of
IBM and the market 111 ex. Explain your conclusion. Now focus on the simple returns for the index (see Exhibit A). Using the sample partial autocorrelations
try to come up with two tentative AR models for the returns. Justify your answer. Estimation of an AR(3) and an AR(5) (see Exhibit C). Analyze your results using the BoxAJenkins
method. Be sure to pay attention to the interpretation of the parameters, in particular with regard to
serial dependence of the returns. Which of these two AR representation ﬁts best. Explain. V-t: 6%: >44 {CG + )3, L117 a‘yt’liaﬁfwz‘EC/ft
Va : Lie at stab, p, {alt/{G7, Li
9
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- Fall '11
- JeanFrancisLamarche
- Economics