1. 先對所有變數 (x1, x2, y1, y2) 進行 ADF 單根檢定
應可發現 (x1, y1) 為非定態變數; (x2,y2) 則皆是定態變數。
2. 執行 Engle-Granger 兩步驟 共整合檢定(針對非定態變數); 或跑一般 OLS(針對定態變數)。
2.1 分別對 (y1, x1) 以及 (y2, x2) 跑迴歸
2.2 對(y1, x1) 跑迴歸結果之 "殘差" 進行ADF 單根檢定, 應該可發現, 對殘差之檢定, 無法拒絕此 "殘差" 為非定態變之虛無假設。故 (y1, x1) 兩變數具有假性迴歸。
2.3 對(y2, x2) 跑迴歸結果, 應可發現, z2 之係數十分顯著; 由於 (y2, x2) 皆為定態變數, 故 (y1, x1) 兩變數具有真的迴歸之關係。
= gretl 的結果=
(對 y1, x1) 之估計 & 檢定結果:
步驟 1: 對變數 Y1 進行單根檢定(unit root test)
Dickey-Fuller test for Y1
樣本大小 99
單根檢定之虛無假設 H0: a = 1
不含常數項 without constant
模型: (1-L)y = (a-1)*y(-1) + e
1 階自我相關係數 for e : -0.108
(a - 1) 的估計值: -0.00314608
檢定統計值: tau_nc(1) = -0.351632
p-value 0.5559
步驟 2: 對變數 X1 進行單根檢定(unit root test)
Dickey-Fuller test for X1
樣本大小 99
單根檢定之虛無假設 H0: a = 1
不含常數項 without constant
模型: (1-L)y = (a-1)*y(-1) + e
1 階自我相關係數 for e : -0.130
(a - 1) 的估計值: 0.00118882
檢定統計值: tau_nc(1) = 0.155341
p-value 0.729
步驟 3: 跑共整合迴歸 (cointegrating regression)
Cointegrating regression -
OLS, 使用中之子樣本範圍: 1-100
應變數 (Dependent variable): Y1
coefficient std. error t-ratio p-value
--------------------------------------------------------
X1 0.623360 0.0166792 37.37 3.51e-60 ***
Mean dependent var −4.071828 S.D. dependent var 1.438872
Sum squared resid 123.3012 S.E. of regression 1.116005
R-squared 0.933814 Adjusted R-squared 0.933814
Log-likelihood −152.3669 Akaike criterion 306.7337
Schwarz criterion 309.3389 Hannan-Quinn 307.7881
rho 0.970356 Durbin-Watson 0.090980
步驟 4: 對變數 uhat 進行單根檢定(unit root test)
Dickey-Fuller test for uhat
樣本大小 99
單根檢定之虛無假設 H0: a = 1
模型: (1-L)y = (a-1)*y(-1) + e
1 階自我相關係數 for e : -0.126
(a - 1) 的估計值: -0.0296438
檢定統計值: tau_nc(2) = -0.960882
p-value 0.7191
========= Engle-Granger 共整合檢定 結果判讀 =========
如果以上的檢定, 同時出現以下的情況, 則很明顯的有共整合關係 :
(a) 個別變數的單根檢定皆無法被拒絕,
且
(b) 殘差 (uhat) 的單根檢定被拒絕 (殘差係來自於共整合迴歸)
==(對 y2, x2) 之估計 & 檢定結果: ==
步驟 1: 對變數 Y2 進行單根檢定(unit root test)
Dickey-Fuller test for Y2
樣本大小 99
單根檢定之虛無假設 H0: a = 1
不含常數項 without constant
模型: (1-L)y = (a-1)*y(-1) + e
1 階自我相關係數 for e : -0.384
(a - 1) 的估計值: -0.231787
檢定統計值: tau_nc(1) = -3.51481
p-value 0.0005774
步驟 2: 對變數 X2 進行單根檢定(unit root test)
Dickey-Fuller test for X2
樣本大小 99
單根檢定之虛無假設 H0: a = 1
不含常數項 without constant
模型: (1-L)y = (a-1)*y(-1) + e
1 階自我相關係數 for e : -0.383
(a - 1) 的估計值: -0.202937
檢定統計值: tau_nc(1) = -3.24867
p-value 0.001392
步驟 3: 跑共整合迴歸 (cointegrating regression)
Cointegrating regression -
OLS, 使用中之子樣本範圍: 1-100
應變數 (Dependent variable): Y2
coefficient std. error t-ratio p-value
--------------------------------------------------------
X2 −0.486724 0.0114611 −42.47 2.35e-65 ***
Mean dependent var 0.753879 S.D. dependent var 0.590071
Sum squared resid 4.751183 S.E. of regression 0.219070
R-squared 0.947963 Adjusted R-squared 0.947963
Log-likelihood 10.44498 Akaike criterion −18.88995
Schwarz criterion −16.28478 Hannan-Quinn −17.83559
rho 0.250510 Durbin-Watson 1.498952
步驟 4: 對變數 uhat 進行單根檢定(unit root test)
Dickey-Fuller test for uhat
樣本大小 99
單根檢定之虛無假設 H0: a = 1
模型: (1-L)y = (a-1)*y(-1) + e
1 階自我相關係數 for e : 0.013
(a - 1) 的估計值: -0.74949
檢定統計值: tau_nc(2) = -7.66372
p-value 4.47e-10
========= Engle-Granger 共整合檢定 結果判讀 =========
如果以上的檢定, 同時出現以下的情況, 則很明顯的有共整合關係 :
(a) 個別變數的單根檢定皆無法被拒絕,
且
(b) 殘差 (uhat) 的單根檢定被拒絕 (殘差係來自於共整合迴歸)
重要事項 Import Notes
重要事項 Import Notes
修習國際金融專題學生,
請務必參見 課程網頁維護重要事項 Import Notes
Registered students MUST see the Import Notes
修習國際金融專題學生,
請務必參見 課程網頁維護重要事項 Import Notes
Registered students MUST see the Import Notes
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PO 文注意事項 (Notes about your posts required for this course)
每位同學必需建立與維護 2 個網頁: (updated on 2010.9.19)
Every registered student MUST post and maintain TWO pages at this site.
1. 你的期末報告想要仿照的原始 paper 重點摘要頁, 見 [範例]
A summary of the paper you choose to follow in your term-project. (see a suggestive [summary example ]).
2. 你的學習紀錄頁, 見 [範例]
A "learning weblog" of your progress during this course (see [example]). This example is demonstrative rather than required to conform to.
3. 記得每一頁要在頁尾處輸入你的「標籤」, 包含學號後5碼, 名字或暱稱, 和 其它你自訂的關鍵字, 例 ADF、共整合、PPP、等
When you edit your pages, be sure to write appropriate "Tags" (as many as you wish) (around the bottom of editing screen) for your posted pages to let me identify your required contributions. The tags should at least include your last 5-digit student ID and keywords about the page.
4. 請同學在你所選的 paper 加上標籤:「已選」
If you have already decided a paper to follow and post a page for it. Please be sure to attach that page a specific tag named "selected or 已選." It is of course possible that two or more students may choose the same paper to follow as their term-project. BUT only one of them can be authorized to follow the specific paper. The decision will be based on a first-come-first-serve rule. That is, the one who posts the summary page of a paper gets the first priority to follow that paper posted with a tag named"selected" paper .
5. 在你的 學習紀錄頁加上標籤:「學習記事」
Don't forget to stick a tag "weblog" with your "learning weblog" page in addition to your last 5-digit student ID.
== Posted on 2009.10.05 ==
請同學在你所選的 paper 加上標籤:「已選」
在你的 學習紀錄頁加上標籤:「學習記事」
Every registered student MUST post and maintain TWO pages at this site.
1. 你的期末報告想要仿照的原始 paper 重點摘要頁, 見 [範例]
A summary of the paper you choose to follow in your term-project. (see a suggestive [summary example ]).
2. 你的學習紀錄頁, 見 [範例]
A "learning weblog" of your progress during this course (see [example]). This example is demonstrative rather than required to conform to.
3. 記得每一頁要在頁尾處輸入你的「標籤」, 包含學號後5碼, 名字或暱稱, 和 其它你自訂的關鍵字, 例 ADF、共整合、PPP、等
When you edit your pages, be sure to write appropriate "Tags" (as many as you wish) (around the bottom of editing screen) for your posted pages to let me identify your required contributions. The tags should at least include your last 5-digit student ID and keywords about the page.
4. 請同學在你所選的 paper 加上標籤:「已選」
If you have already decided a paper to follow and post a page for it. Please be sure to attach that page a specific tag named "selected or 已選." It is of course possible that two or more students may choose the same paper to follow as their term-project. BUT only one of them can be authorized to follow the specific paper. The decision will be based on a first-come-first-serve rule. That is, the one who posts the summary page of a paper gets the first priority to follow that paper posted with a tag named"selected" paper .
5. 在你的 學習紀錄頁加上標籤:「學習記事」
Don't forget to stick a tag "weblog" with your "learning weblog" page in addition to your last 5-digit student ID.
== Posted on 2009.10.05 ==
請同學在你所選的 paper 加上標籤:「已選」
在你的 學習紀錄頁加上標籤:「學習記事」
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