Lab_Six_Recap_Takehome_One

# Mortgage rate hous t 2800 2400 2000 1600 1200 800 400

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Unformatted text preview: 2,000 1,600 1,200 800 400 75 80 85 90 95 00 05 10 MORTG 20 16 12 8 4 14 0 75 80 85 90 95 00 05 10 Houst vs. Mortg Cont em porary Correlat ion: plot of hous t vs . m ort g 2,800 2,400 HOUST 2,000 1,600 1,200 800 400 2 4 6 8 10 12 M ORTG 14 16 18 15 20 Basic idea of Box-JenkinsApproach 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 (t-1) + h2 *wnx (t-2) …+resid Correlate dependent variable serially with innovations to x, where all of the wnx (t-i) are orthogonal The tool for doing this is the cross-correlation 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 3 2 1 0 -1 -2 -3 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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