Time Series Analysis: Vector Error Correction Model …motegi/figs_ch6_VECM_kobe_v1.pdfFigure 1:...
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Transcript of Time Series Analysis: Vector Error Correction Model …motegi/figs_ch6_VECM_kobe_v1.pdfFigure 1:...
Time Series Analysis:
Vector Error Correction Model (VECM)
Kaiji Motegi∗
Fall 2016, Kobe University
1 Descriptions of Figure 1
Let ϵy1, . . . , ϵy100, ϵx1, . . . , ϵx100i.i.d.∼ N(0, 1). Consider a simple VECM:[
∆yt
∆xt
]=
[αy
αx
][1,−0.8]
[yt−1
xt−1
]+
[uyt
uxt
],
where uyt = ϵyt + 0.8ϵxt and uxt = ϵxt.
Panel 1: (αy, αx) = (−1, 0). {yt, xt} are cointegrated.
Panel 2: (αy, αx) = (0, 1). {yt, xt} are cointegrated.
Panel 3: (αy, αx) = (−1, 1). {yt, xt} are cointegrated.
Panel 4: (αy, αx) = (−1,−0.5). {yt, xt} are cointegrated.
Panel 5: (αy, αx) = (0, 0). {yt, xt} are not cointegrated.
Panel 6: (αy, αx) = (0.01,−0.01). {yt, xt} are not cointegrated.
∗Lecturer, Graduate School of Economics, Kobe University. E-mail: [email protected] Website:http://www2.kobe-u.ac.jp/˜motegi/
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0 50 100-15
-10
-5
0
5
y x
1. (αy, αx) = (−1, 0)
0 50 100-10
0
10
20
30
y x
2. (αy, αx) = (0, 1)
0 50 100-10
0
10
20
y x
3. (αy, αx) = (−1, 1)
0 50 100-30
-20
-10
0
10
y x
4. (αy, αx) = (−1,−0.5)
0 50 100-20
-10
0
10
20
y x
5. (αy, αx) = (0, 0)
0 50 100-40
-20
0
20
40
y x
6. (αy, αx) = (0.01,−0.01)
Figure 1: Vector Error Correction Model (VECM)
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