國立中正大學(xué)國際經(jīng)濟(jì)研究所在職專班

1、國立中正大學(xué)國際經(jīng)濟(jì)研究所在職專班時間序列分析作業(yè)報告姓名： 侯承育 595510005姓名： 鄧昌禮 595510019中 華 民 國 九十六 年 八 月 十二 日一、請以ex-chow.wf1的y1變數(shù)進(jìn)行，估計含截距項的AR(3)模型，計算並寫出SSRR；再將樣本資料分割為4,200和201,300兩個樣本，同樣以含截距項的AR(3)估計，並計算(或找出)並寫出其子樣本之殘差平方和，分別為SSR1和SSR2，最後請計算並寫出Chow轉(zhuǎn)變點檢定之F值，並說明檢定結(jié)果。以y1變數(shù)利用AR(3)模型來估計，在Eviews的主選單上點選【Objects】"【New Object】&qu

2、ot;【Equation】後設(shè)定y1變數(shù)之估計方程設(shè)名稱為EQ_Y1，模型為【y1 c y1(-1) y1(-2) y1(-3)】經(jīng)過Eviews估計後得到下列之結(jié)果：Dependent Variable: Y1Method: Least SquaresDate: 08/11/07 Time: 20:00Sample (adjusted): 4 300Included observations: 297 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.  C0.0403740.0188032.147

3、2520.0326Y1(-1)0.4464500.0564017.9155980.0000Y1(-2)0.2441330.0605474.0321130.0001Y1(-3)0.2547940.0563504.5216790.0000R-squared0.816073    Mean dependent var0.707626Adjusted R-squared0.814189    S.D. dependent var0.125519S.E. of regression0.054106  &#

4、160; Akaike info criterion-2.982373Sum squared resid0.857740    Schwarz criterion-2.932626Log likelihood446.8824    F-statistic433.3400Durbin-Watson stat2.079934    Prob(F-statistic)0.000000y1=0.040+0.446yt-1+0.244yt-2+0.255yt-3+tR2=0.

5、816SC=-2.93而所謂SSR(regression osum of squares)代表回歸模型中的已解釋變異。SSR愈大代表模型樣本資料的解釋能力愈好。而此所得之SSR=0.856。再將樣本資料分割為4,200和201,300兩個樣本，同樣以含截距項的AR(3)估計，分別找出兩個子樣本的殘差平方和(SSR1及SSR2)，我們?nèi)岳肊views來估計，所得知結(jié)果分別如下所示：樣本為4,200：Dependent Variable: Y1Method: Least SquaresDate: 08/11/07 Time: 20:21Sample: 4 200Included observat

6、ions: 197VariableCoefficientStd. Errort-StatisticProb.  C0.4728480.0664477.1161970.0000Y1(-1)0.1682580.0733142.2950470.0228Y1(-2)0.1351250.0744881.8140530.0712Y1(-3)-0.0592290.073923-0.8012260.4240R-squared0.051680    Mean dependent var0.625216Adjusted R-squared0.036939

7、    S.D. dependent var0.048375S.E. of regression0.047473    Akaike info criterion-3.237229Sum squared resid0.434956    Schwarz criterion-3.170565Log likelihood322.8670    F-statistic3.505934Durbin-Watson stat1.958233

8、0;   Prob(F-statistic)0.016423所估計之方程是資料及SSR1為：y1=0.473+0.168yt-1+0.135yt-2-0.059yt-3+tR2=0.052SC=-3.17而此所得之SSR1=0.435。樣本為201,300：Dependent Variable: Y1Method: Least SquaresDate: 08/11/07 Time: 20:27Sample: 201 300Included observations: 100VariableCoefficientStd. Errort-StatisticProb.&

9、#160; C0.7136890.1170546.0970820.0000Y1(-1)0.1421780.1004681.4151590.1603Y1(-2)-0.0945930.091447-1.0344000.3035Y1(-3)0.1326050.0864861.5332610.1285R-squared0.042763    Mean dependent var0.869973Adjusted R-squared0.012850    S.D. dependent var0.048330S.E.

10、of regression0.048019    Akaike info criterion-3.195274Sum squared resid0.221356    Schwarz criterion-3.091067Log likelihood163.7637    F-statistic1.429562Durbin-Watson stat1.980355    Prob(F-statistic)0.238933所估計之方程是資料及

11、SSR2為：y1=0.714+0.142yt-1-0.095yt-2+0.133yt-3+tR2=0.043SC=-3.09而此所得之SSR2=0.221最後進(jìn)行Chow檢定，執(zhí)行【View】"【Stability tests】"【Chow breakpoint test】可得到下面結(jié)果：Chow Breakpoint Test: 201 F-statistic22.17414    Probability0.000000Log likelihood ratio79.49637    

12、Probability0.000000由Chow檢定中可知其F統(tǒng)計量為22.174，且相對應(yīng)之p值都小於0.01，所以顯著拒絕虛無假設(shè)，表示在t=201附近應(yīng)該會有結(jié)構(gòu)性轉(zhuǎn)變出現(xiàn)。而以全部樣本所計算之SSR為0.856，另外以4,200及201,300所計算之SSR1及SSR2二、請依範(fàn)例4.1中對y1最後估計模型之診斷步驟，完成對y2變數(shù)最後所估計出模型之診斷。首先在Eviews中利用y2的資料執(zhí)行【view】"【Graph】"【Line】，可得到下面的圖形，由圖型中可以大略看出，在y2的資料中於t=200的附近可能會產(chǎn)生結(jié)構(gòu)性轉(zhuǎn)變。第二步驟是用ACF和PACF輔助判斷變

13、數(shù)的DGP，在y2視窗中執(zhí)行【view】"【Correlogram】"【Level】，及可以得到ACF及PACF的圖形，可以發(fā)現(xiàn)y2的ACF是呈現(xiàn)遞減的現(xiàn)象及PACF在第三期後完全切斷，所以可以知道y2變數(shù)的DGP可能是AR(3)。 第三個步驟要估計出基本模型，y2變數(shù)的DGP可能是AR(3)，用此當(dāng)作基本模型來估計。在Eviews的主選單上點選【Objects】"【New Object】，故可以估計出y2的基本模型，如下表示：y2=0.156+0.492yt-1+0.142yt-2+0.238yt-3+tR2=0.629SC=1.73第四步驟要進(jìn)行Chow轉(zhuǎn)變點

14、檢定，在EQ_y2的選單中執(zhí)行【View】"【Stability tests】"【Chow breakpoint test】，可得到以下資料。由Chow檢定中可知其F統(tǒng)計量為14.836，且相對應(yīng)之p值都小於0.01，所以顯著拒絕虛無假設(shè)，表示在t=200附近應(yīng)該會有結(jié)構(gòu)性轉(zhuǎn)變出現(xiàn)。Chow Breakpoint Test: 200 F-statistic14.83580    Probability0.000000Log likelihood ratio55.46819    Pro

15、bability0.000000接下來第五步驟是要假設(shè)虛擬變數(shù)，且重新估計模型，並去除不顯著的變數(shù)，假設(shè)虛擬變數(shù)的方式是在Eviews指令行下指令設(shè)定，並且再執(zhí)行【Estimate】加入虛擬變數(shù)重新估計模型，指令與重新估計後之結(jié)果如下：smpl 1 200genr d2=0smpl 201 300genr d2=1smpl 1 300Dependent Variable: Y2Method: Least SquaresDate: 08/08/07 Time: 22:03Sample (adjusted): 4 300Included observations: 297 after adjust

16、mentsVariableCoefficientStd. Errort-StatisticProb.  C0.4412030.0746245.9123440.0000Y2(-1)0.2209900.0706343.1286920.0019Y2(-2)-0.0166990.072111-0.2315750.8170Y2(-3)0.0966370.0702841.3749510.1702D20.5890890.2536232.3226990.0209D2*Y2(-1)0.2654180.1276912.0786000.0385D2*Y2(-2)0.0828420.1366940

17、.6060390.5450D2*Y2(-3)-0.1177110.124665-0.9442170.3458R-squared0.693970    Mean dependent var1.154963Adjusted R-squared0.686557    S.D. dependent var0.918833S.E. of regression0.514418    Akaike info criterion1.535005Sum squared resid76.4768

18、2    Schwarz criterion1.634499Log likelihood-219.9482    F-statistic93.62148Durbin-Watson stat1.985158    Prob(F-statistic)0.000000得到該結(jié)果後再逐一去除不顯著的變數(shù)，以5%的顯著水準(zhǔn)為標(biāo)準(zhǔn)，使所有的P值都小於0.05，在反覆進(jìn)行削除不顯著之變數(shù)後，最後所得到的結(jié)果如下：Dependent Variable: Y2Method: Least Squ

19、aresDate: 08/08/07 Time: 22:14Sample (adjusted): 2 300Included observations: 299 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.  C0.4946730.0561898.8037180.0000Y2(-1)0.2133630.0683013.1238550.0020D20.5701630.2098112.7175050.0070D2*Y2(-1)0.3021110.1126762.6812420.0077R-squared0.691157    Mean dependent var1.150653Adjusted R-squared0.68801