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Question - Assume that we believe that ¥; = fo + 8:X1 + ue where the error term t, is II (indepenctent and identically distributed)

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Question - Assume that we believe that ¥; = fo + 8:X1 + ue where the error term t, is II

(indepenctent and identically distributed).

a) What does it mean that a variable X; is nonstationary? a .
b) What can we say about Y; and the relationship with X, if our belief is correct?
c) How would we estimate the relationship given that X; is nonstationary? Be precise about t
ateps that you would take. .
¢ Question 2 (15p). We want to forecast Y based on past yearly values of itself. .

&) How would you decide what past valucs to use in a regression? How many lags would you incluc
What methods are there to help you to decide? Explain intuitively what they do and how th
relate to cach other. Step by step how would you go sbout selecting a prefered model using th«
methods.

b) Assume that you find that the two last years Y;2 and Y;_,-should be chosen to forecast Yz. If |
last period is T, how would you go about forecasting Yr+i,Yr+2 and Yrig, giving a step by s:
explanation with formulas?

¢) You are asked for a 95% confidence interval for ¥r4,. How would you go about calculating th

+ Question 3 (20p). Given data for three variables Y;, X; and We, you estimate with both X, and W
Ye = Bo + By Xe + BW + uy
and with just X; as an explanatory variable
Y, = ay + 01X1 + vy
In doing this, you obtain very different regression results for the effect of X; as seen in Table 2 be!
a) How can we understand the difference in the estimates when W, is included or not? Deriv
gencral relationship between the population equations that explain the difference between J; :
ay
b) If you estimated W, = to + 1Xe + w, what would the estimate 4 be? Justify your derivatic
c) What can you say about the correlation cocfficient between X, and W,, given the summ
statistics ag geen in Table 1 below and ni?
, Table 1: Summary statistics
. _—_
term nabs mvan sd min max
xX 50 0.1148273 1.0182288 -1.555764 2.484699
; WwW 50 0.0311620  0.7884120 -1.677899 1.446711
s Y 50 11160649 0.9245036 -1.176618 3.605180
eee
Q 4.