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75 80 85 90 95 00 05 10 MORTG
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75 80 85 90 95 00 05 10 Houst vs. Mortg
Cont em porary Correlat ion: plot of hous t vs . m ort g
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2,400 HOUST 2,000
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2 4 6 8 10 12 M ORTG 14 16 18 15 20 Basic idea of BoxJenkinsApproach Orthogonalize the input x(t)
Fit a univariate model to x(t)
x(t) = [Ax (z)/ Bx (z)]* wnx (t)
(z)]*
(t)
So [Bx /Ax ]* x(t) = wnx (t)
/A ]*
(t)
Apply it to distributed lag model
y(t) = h(z) * x(t) + e(t),
i.e. [Bx /Ax ]*y(t)=h(z)*[Bx /Ax ]*x(t) + [Bx /Ax ]* e(t),
/A ]*y(t)=h(z)*[B /A ]*x(t)
/A ]*
Or w(t) = h(z)* wnx (t) + resid(t)
(t)
W(t) = h0 *wnx (t) + h1 *wnx (t1) + h2 *wnx (t2) …+resid
Correlate dependent variable serially with innovations to x,
where all of the wnx (ti) are orthogonal
The tool for doing this is the crosscorrelation function 16 First worry about stationarity Houst(t) = h(z) * mortg(t) + e(t) The distributed lag h(z) is unknown and
The
we have to figure out how to specify it
we Since houst and mortg are both
Since
evolutionary, we can difference without
changing the reelationship h(z)
changing ∆Houst(t) = h(z) * ∆mortg(t) + ∆e(t)
Houst(t)
mortg(t)
17 dmortg 18 Trace: dmortg is prewhitened
DMORTG
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1975 1980 1985 1990 1995 2000 2005 19 2010 Histogram: dmortg is not normal
40 Ser ies: DMORT G
Sample 1971M04 2013M12
Obser vations 503 00 Mean
Median
Maximum
Minimum
Std. D...
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 Winter '14
 Granger causality, dmortg, Bx /Ax

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