協(xié)整理論及其R語言的實現(xiàn)

1、LogoLogoAdd Your Company Slogan協(xié)整理論及其協(xié)整理論及其R R語言的實現(xiàn)語言的實現(xiàn)邵晨邵晨上海財經(jīng)大學(xué)上海財經(jīng)大學(xué) 統(tǒng)計與管理學(xué)院統(tǒng)計與管理學(xué)院整理整理ppt為什么要協(xié)整?提綱提綱1 1什么是協(xié)整？2 2如何進行協(xié)整檢驗？3 3R語言中相關(guān)函數(shù)4 4案例：中國進出口之間關(guān)系檢驗5 5整理整理ppt偽回歸（虛假回歸）偽回歸（虛假回歸）回歸分析：回歸分析：一個重要的前提假設(shè)：平穩(wěn)性但是，實際上大部分的宏觀經(jīng)濟時間序列和金融時間序列都是非平穩(wěn)的。 整理整理ppt偽回歸（虛假回歸）偽回歸（虛假回歸）案例案例結(jié)果結(jié)果以以1990年至年至2008年年美國美國城鎮(zhèn)居民家城鎮(zhèn)居民

2、家庭人均可支配收入和庭人均可支配收入和中國中國人均消費人均消費性支出為例：性支出為例： data Usincome Chinacoms reg summary(reg) library(zoo) library(lmtest) dwtest(reg)Call:Call:lm(formula = Chinacoms USincome)lm(formula = Chinacoms USincome)Residuals:Residuals: Min 1Q Median 3Q Max Min 1Q Median 3Q Max -640.11 -350.44 -55.96 346.49 1139.42

3、-640.11 -350.44 -55.96 346.49 1139.42 Coefficients:Coefficients: Estimate Std. Error t value Pr(|t|) Estimate Std. Error t value Pr(|t|) (Intercept) -6.886e+03 4.896e+02 -14.06 8.56e-11 (Intercept) -6.886e+03 4.896e+02 -14.06 8.56e-11 * * * *USincome 4.788e-01 1.898e-02 25.23 6.54e-15 USincome 4.788

4、e-01 1.898e-02 25.23 6.54e-15 * * * *-Signif. codes: 0 Signif. codes: 0 * * * * 0.001 0.001 * * * 0.01 0.01 * * 0.05 . 0.1 1 0.05 . 0.1 1 Residual standard error: 477.7 on 17 degrees of freedomResidual standard error: 477.7 on 17 degrees of freedomMultiple R-squared: 0.974, Adjusted R-squared: Multi

5、ple R-squared: 0.974, Adjusted R-squared: 0.9724 0.9724 F-statistic: 636.3 on 1 and 17 DF, p-value: 6.544e-15 F-statistic: 636.3 on 1 and 17 DF, p-value: 6.544e-15 Durbin-Watson test Durbin-Watson testdata: reg data: reg DW = 0.4992, p-value = 4.485e-06DW = 0.4992, p-value = 4.485e-06alternative hyp

6、othesis: true autocorrelation is greater than alternative hypothesis: true autocorrelation is greater than 0 0 顯著的顯著的R R2 2較大的較大的t t值值DWDW統(tǒng)計量很小，存統(tǒng)計量很小，存在嚴(yán)重的自相關(guān)在嚴(yán)重的自相關(guān)整理整理ppt線性回歸模型線性回歸模型lm()函數(shù)：用法： fitted.model reg ts(1:30,start=1980,end=2009, ts(1:30,start=1980,end=2009, frequency=1)frequency=1)季度數(shù)據(jù)：

7、季度數(shù)據(jù)：ts(1:30,start=c(2003,3),end= ts(1:30,start=c(2003,3),end= c(2010,4),frequency=4)c(2010,4),frequency=4)整理整理ppt時間序列舉例時間序列舉例月度數(shù)據(jù)：月度數(shù)據(jù)：ts(1:30,start=c(2008,5), ts(1:30,start=c(2008,5), frequency=12)frequency=12)每日數(shù)據(jù)：每日數(shù)據(jù)： a a print(a,calendar=TRUE) print(a,calendar=TRUE)整理整理ppt單位根檢驗單位根檢驗urca包中的ur.d

8、f()函數(shù):用法：ur.df(y, type = c(none, drift, trend), lags = 1, selectlags = c(Fixed, AIC, BIC) 參數(shù)：y 被檢驗的時間序列type 檢驗類型： “none”, “drift” 或者 trend.lags 內(nèi)生變量的滯后階數(shù)selectlags 滯后階數(shù)確定方法：the Akaike “AIC” 或者 the Bayes “BIC” 信息 準(zhǔn)則，默認(rèn)值是fixed，由lags確定滯后階數(shù)。 整理整理ppt案例分析：中國進出口貿(mào)易之間關(guān)系案例分析：中國進出口貿(mào)易之間關(guān)系數(shù)據(jù)來源：國家統(tǒng)計數(shù)據(jù)庫（ http:/ li

9、brary(urca) library(urca) urt.ex urt.ex summary(urt.ex) summary(urt.ex)# # # Augmented Dickey-Fuller Test Unit Root Test # # Augmented Dickey-Fuller Test Unit Root Test # # # Test regression trend Test regression trend Call:Call:lm(formula = z.diff z.lag.1 + 1 + tt + z.diff.lag)lm(formula = z.diff z

10、.lag.1 + 1 + tt + z.diff.lag)Residuals:Residuals: Min 1Q Median 3Q Max Min 1Q Median 3Q Max -0.17362 -0.05933 0.02236 0.05216 0.12439 -0.17362 -0.05933 0.02236 0.05216 0.12439 Coefficients:Coefficients: Estimate Std. Error t value Pr(|t|) Estimate Std. Error t value Pr(|t|)(Intercept) 0.77701 0.5325

11、3 1.459 0.158(Intercept) 0.77701 0.53253 1.459 0.158z.lag.1 -0.15325 0.11600 -1.321 0.199z.lag.1 -0.15325 0.11600 -1.321 0.199tt 0.02699 0.01723 1.566 0.130tt 0.02699 0.01723 1.566 0.130z.diff.lag 0.20945 0.20765 1.009 0.323z.diff.lag 0.20945 0.20765 1.009 0.323Residual standard error: 0.08564 on 24

12、 degrees of freedomResidual standard error: 0.08564 on 24 degrees of freedomMultiple R-squared: 0.2354, Adjusted R-squared: 0.1398 Multiple R-squared: 0.2354, Adjusted R-squared: 0.1398 F-statistic: 2.462 on 3 and 24 DF, p-value: 0.08697 F-statistic: 2.462 on 3 and 24 DF, p-value: 0.08697 Value of t

13、est-statistic is: Value of test-statistic is: -1.3211 -1.3211 7.0028 3.0289 7.0028 3.0289 Critical values for test statistics: Critical values for test statistics: 1pct 5pct 10pct 1pct 5pct 10pcttau3 tau3 -4.15 -3.50 -3.18-4.15 -3.50 -3.18phi2 7.02 5.13 4.31phi2 7.02 5.13 4.31phi3 9.31 6.73 5.61phi3

14、 9.31 6.73 5.61 urt.im urt.im summary(urt.im) summary(urt.im)Value of test-statistic is: Value of test-statistic is: -2.2266 -2.2266 6.0966 6.0966 3.3771 3.3771 Critical values for test statistics: Critical values for test statistics: 1pct 5pct 10pct 1pct 5pct 10pcttau3 tau3 -4.15 -3.50 -3.18-4.15 -

15、3.50 -3.18phi2 7.02 5.13 4.31phi2 7.02 5.13 4.31phi3 9.31 6.73 5.61phi3 9.31 6.73 5.61整理整理ppt單位根檢驗單位根檢驗對dlnexdlnex單位根檢驗結(jié)果：Value of test-statistic is: -3.2348 5.2379 Critical values for test statistics: 1pct 5pct 10pcttau2 -3.58 -2.93 -2.60phi1 7.06 4.86 3.94對dlnimdlnim單位根檢驗結(jié)果：Value of test-statistic

16、 is: -4.8372 11.7049 Critical values for test statistics: 1pct 5pct 10pcttau2 -3.58 -2.93 -2.60phi1 7.06 4.86 3.94結(jié)論：中國進口和出口的對數(shù)時間序列不平穩(wěn)，但一階差分后平穩(wěn)，結(jié)論：中國進口和出口的對數(shù)時間序列不平穩(wěn)，但一階差分后平穩(wěn)，說明是一階單整序列，即說明是一階單整序列，即lnex,lnim lnex,lnim I(1) I(1)，滿足協(xié)整檢驗條件。，滿足協(xié)整檢驗條件。dlnex - diff(lnex)dlnim exim exim ex ex im im lnim lnim

17、 lnex lnex reg reg summary(reg) summary(reg) library(lmtest) library(lmtest) dw dw |t|) Estimate Std. Error t value Pr(|t|) (Intercept) (Intercept) -0.48270 -0.48270 0.14717 -3.28 0.14717 -3.28 0.00278 0.00278 * * * lnim lnim 1.07457 1.07457 0.02077 51.74 0.02077 51.74 2e-16 2e-16 * * * *-Signif. co

18、des: 0 Signif. codes: 0 * * * * 0.001 0.001 * * * 0.01 0.01 * * 0.05 . 0.05 . 0.1 1 0.1 1 Residual standard error: 0.1401 on 28 degrees of Residual standard error: 0.1401 on 28 degrees of freedomfreedomMultiple R-squared: 0.9897, Adjusted R-Multiple R-squared: 0.9897, Adjusted R-squared: squared: 0.

19、9893 0.9893 F-statistic: 2677 on 1 and 28 DF, p-value: F-statistic: 2677 on 1 and 28 DF, p-value: error urt.resid summary(urt.resid)Value of test-statistic is: -3.6185 Critical values for test statistics: 1pct 5pct 10pcttau1 -2.62 -1.95 -1.61結(jié)論：殘差平穩(wěn)，說明兩個時間序列之間存在協(xié)整關(guān)系。結(jié)論：殘差平穩(wěn)，說明兩個時間序列之間存在協(xié)整關(guān)系。意味著我國的進口

20、和出口之間具有長期均衡關(guān)系，增長或者減少具有協(xié)同效意味著我國的進口和出口之間具有長期均衡關(guān)系，增長或者減少具有協(xié)同效應(yīng)。應(yīng)。整理整理pptEGEG兩步協(xié)整檢驗：第二步（誤差修正模型的建立）兩步協(xié)整檢驗：第二步（誤差修正模型的建立） error error error.lagged error.lagged ecm.reg1 ecm.reg1 summary(ecm.reg1) summary(ecm.reg1) dwtest(ecm.reg1) dwtest(ecm.reg1)Call:Call:lm(formula = dlnex error.lagged + dlnim, data = l

21、m(formula = dlnex error.lagged + dlnim, data = diff.dat)diff.dat)Residuals:Residuals: Min 1Q Median 3Q Max Min 1Q Median 3Q Max -0.17214 -0.05198 0.01546 0.05053 0.14514 -0.17214 -0.05198 0.01546 0.05053 0.14514 Coefficients:Coefficients: Estimate Std. Error t value Pr(|t|) Estimate Std. Error t val

22、ue Pr(|t|) (Intercept) (Intercept) 0.10648 0.10648 0.02358 4.516 0.000131 0.02358 4.516 0.000131 * * * *error.lagged error.lagged -0.29647 -0.29647 0.11430 -2.594 0.015645 0.11430 -2.594 0.015645 * * dlnim dlnim 0.33929 0.33929 0.12470 2.721 0.011681 0.12470 2.721 0.011681 * * -Signif. codes: 0 Signif. codes: 0 * * * * 0.001 0.001 * * * 0.01 0.01 * * 0.05 . 0.1 0.05 . 0.1 1 1 Residual standard error: 0.08024 on 25 degrees of Residual standard error: 0.08024 on 25 degrees of freedomfreedomMultiple R-squared: 0.3008, Adjusted R-squared: Multiple R-squared: 0.3008, Adju