計(jì)量經(jīng)濟(jì)學(xué)實(shí)驗(yàn)報(bào)告(實(shí)驗(yàn)項(xiàng)目：時(shí)間序列計(jì)量經(jīng)濟(jì)學(xué)模型)(2)

1、實(shí)驗(yàn)項(xiàng)目：時(shí)間序列計(jì)量經(jīng)濟(jì)學(xué)模型一實(shí)驗(yàn)?zāi)康耐ㄟ^上機(jī)實(shí)驗(yàn)掌握計(jì)量經(jīng)濟(jì)學(xué)軟件EViews，運(yùn)用EViews軟件進(jìn)行時(shí)間序列計(jì)量經(jīng)濟(jì)學(xué)模型的分析，掌握時(shí)間序列計(jì)量經(jīng)濟(jì)學(xué)模型，包括建立模型，了解其單整性、平穩(wěn)性。二預(yù)備知識(shí)單位根檢驗(yàn)、單整性檢驗(yàn)、ADF檢驗(yàn)、最小二乘估計(jì)原理。三實(shí)驗(yàn)內(nèi)容F表給出了 1978 2006年中國居民消費(fèi)價(jià)格指數(shù)CPI.(1990年=100)年份CPI年份CPI年份CPI197846.21198882.31998202.59197947.071989971999199.72198050.6219901002000200.55198151.91991103.422001201.9

2、4198252.951992110.032002200.321983541993126.22003202.73198455.471994156.652004210.63198560.651995183.412005214.42198664.571996198.662006217.65198769.31997204.21做出時(shí)間序列CPI的樣本相關(guān)圖，并通過圖形判斷該序列時(shí)間序列的平穩(wěn)性。對(duì)CPI序列進(jìn)行單位根檢驗(yàn)，以進(jìn)一步明確它們的平穩(wěn)性。檢驗(yàn)CPI的單整性。四實(shí)驗(yàn)步驟(一)啟動(dòng)軟件包Eviews 的啟動(dòng)步驟：雙擊Eviews快捷方式，進(jìn)入EViews窗口；或點(diǎn)擊開始/程序/ Eviews 6

3、，進(jìn)入EViews窗口。（二）創(chuàng)建工作文件。1建立工作文件并錄入數(shù)據(jù)，如圖1所示?？?Series： CP! Workfile: UN TITLE D:UntFtled京 |圖12平穩(wěn)性檢驗(yàn)2.1平穩(wěn)性的圖示判斷給出一個(gè)隨機(jī)時(shí)間序列，首先可以通過該序列的事件路徑圖來粗略地判斷它是否是平穩(wěn)的。使用語句 T=TREND+197產(chǎn)生時(shí)間點(diǎn)的序列 T，畫出CPI跟時(shí)間T的關(guān)系圖，即時(shí)序 圖，如圖2所示。 Series; CPI Workfile: UNTTTLED；!Urrtitfed 口【回爭W&fljppt|Object| Properties Print Name F亡皀z皀 | Sam

4、ple| Genr| She皀t| Gnph| Stats| IcJent|CPI由圖2,我們可以直觀地看到CPI關(guān)于時(shí)間T有明顯遞增的趨勢，不同時(shí)間段的均值不同，有持續(xù)上升，即CPI序列不平穩(wěn)。當(dāng)然，這種直觀的圖示也常長生誤導(dǎo)，因此需要進(jìn)行進(jìn)一步的判斷。2.2樣本自相關(guān)圖判斷點(diǎn)擊主界面 Quick'Series Statistics'Correlogram.，在彈出的對(duì)話框中輸入CPI，點(diǎn)擊0K就會(huì)彈出Correlogram Specification對(duì)話框，選擇 Level，并輸入要輸出的階數(shù)（一般為12），點(diǎn)擊OK即可得到CPI的樣本相關(guān)函數(shù)圖，如圖3所示。Correlo

5、gram SpecrficationCorrelogram ofLevel1st differenceOK |2nd differenceLags to indude1 cancelDate: OS/13/12 Time: 14:113Sample: 197B 2006Included obser-ations: 29AC PAG Q-Stat Prot>Autocorrelation Partial Correlation11匚1< LII| II| 1I匚1| rII匚II匚1匚II| II1110.9310 93127.8430.00020 847-0.153517200,0

6、0030755-0.08971 440O.QOQ40.662-0.05487 2050.00050.566-0.08099.1870.00060.462-0.113107 530.00070.352-0.108112600.00080.239-0.099115050.00090.120-0 137115.700.00010-0 004-0 139115.70O.QOQ11-0.120-0.063116420.00012-0.221-0.003119010.000圖3一個(gè)時(shí)間序列的樣本自相關(guān)函數(shù)定義為：n上、(Xt -X)(Xt .k -X)k =1,2,3,.t m2' (Xt -X)

7、t m易知，隨著k的增加，樣本自相關(guān)函數(shù)下降且趨于零。但從下降速度來看，平穩(wěn)序列要比非平穩(wěn)序列快得多。從上述樣本相關(guān)函數(shù)圖，可以看到CPI的樣本相關(guān)函數(shù)是緩慢的遞減趨 于零的，并沒有像偏自相關(guān)函數(shù)那樣的迅速減為零。所以，通過CPI的樣本相關(guān)圖，可初步判定該CPI時(shí)間序列非平穩(wěn)。當(dāng)然這中判斷方法也是有一定的主觀性的，下面我們進(jìn)行客觀性的判斷，進(jìn)一步明確CPI序列的平穩(wěn)性。2.3單位跟檢驗(yàn)（ADF檢驗(yàn)）采用ADF檢驗(yàn)對(duì) CPI序列進(jìn)行平穩(wěn)性的單位根檢驗(yàn)。點(diǎn)擊主界面Quick'SeriesStatistics' Unit Root Test.，在彈出的 Series 對(duì)話框中輸入 C

8、PI，點(diǎn)擊 OK 就會(huì)出現(xiàn)Un it Root Test對(duì)話框，如圖 4所示。Unit Root TestTest typeAugmented Dicke y-FdlerL 的 length Automate se ection:|sdi腳ar? Inft Criterion |Maxim jm lags: pUser speafied :11Test for unit root inLevel廣 1st diffierence廠 2nd differenceIndud亡 in test equatian Intercept' Trend and interceptf' Non

9、 亡OK I CancelUnit Root Test對(duì)話框的設(shè)置。其中Test for unit root in欄中，Level是水平序列，1st是一階差分序列，2nd是二階差分序列；In elude in test equation 欄中，In tercept 是常數(shù)項(xiàng)，對(duì)應(yīng) ADF檢驗(yàn)中的第二個(gè)模型，Trend and in tercept是趨勢項(xiàng)加常數(shù)項(xiàng)，對(duì)應(yīng)ADF檢驗(yàn)中的第三個(gè)模型，None是沒有趨勢項(xiàng)跟常數(shù)項(xiàng)，對(duì)應(yīng)ADF檢驗(yàn)中的第一個(gè)模型；右側(cè)的Lag length是滯后階數(shù)的確定，系統(tǒng)默認(rèn)是用SC值確定，且默認(rèn)最大滯后階數(shù)為6階。本題中，對(duì)于 CPI序列的單位根檢驗(yàn)是選擇Leve

10、l項(xiàng)，ADF檢驗(yàn)結(jié)果如下。對(duì)于模型3:VariableCoeFicientStd. Errort-StatisticProb.CPK-1)-0.2392740.Q92967-2.5737460.0212D(CPI( 1)1 2B37390.2010396.4104040.0000D(CPI(-2)-0.7802050.341234-2.2864210.0372D(CPI(-3)0.7735290.3792252.0529490,0579D(CPl(-4)-0.5530160.339560*1.6206280.1242D(CPl(-5)0.5222950.2220242 3524300.0327

11、C07251753 2420450.2236700.8260TREND(1978)1.3849660.80236B2.3492540 0329R-squared0.817179Mean dependent var7.115217Adjusted R-squared0.731863S.D. dependentvar8.605129S.E. of regression4.455904kaike info criterion6.094545Sum squared resid297.8252Schwarz criterion6.439500Log likelihood-52.08727Hannan-Q

12、uinn criter.6193975F-statistic9.578226Durbin-Watson stat1.920843ProbfF-statisti c)0.000146訥皀矗 | Pck | Object Prop亡巾凸 | Pint|NBm|FEZE Sample Gen” She已t| Gnph Stats IdentAugmented Dickey-Fuller Unrt Root Test on CPIO Series; CPI Warkfile; UNTTTLED：!Untitled-a- 回'iewj Proc | Object | Properties Pri

13、nt (Name (Freeze Sample Genr| Sheet | Graph StatsIdent |Augmented Dickey-Fuller Unrt Root Test on CPINull Hypothesis: CPI has a unit rootExogenous: Constant. LinearTrendLag Length: 5 (Automatic based on SIC, MAXLAG=6)t-StaVsticProb*Augmented Dickey*Fuller test statistic-2.5737460.2939Test critical v

14、alues:1% level 5% level 10% level-4.416345-3.622033-3.248592'MacKinnon(1996) one-sided pvalues.Augmented Dickey-Fuller Test Equation Dependent Variable' D(CPI)Method: Least SquaresDate: 06/13/12 Time: 14:20Sample (adjusted): 1984 2006Included obseations: 23 after adjustments Series: CPT Work

15、file: UNTTTLEDtiUrrtitled圖5可以看到偽概率 P =0.2939 ，在5%的水平下是接受有單位根的原假設(shè)的。模型3的估計(jì)結(jié)果為：t -3CPI t =0.7251.885 t -0.239 CPI1.289 CPI t 4 一 0.780 CPI 0.779 CPI 0.553 ：CPI j 0.522 CPI 心其中，趨勢項(xiàng)參數(shù):的估計(jì)值的t統(tǒng)計(jì)量為t = 2.349254 ，查ADF分布臨界值表得，模 型3樣本個(gè)數(shù)為25個(gè)（最接近的個(gè)數(shù)）時(shí)£加.025 = 3.25，即接受0 =0的原假設(shè)，于是可與 進(jìn)行模型2的估計(jì)。對(duì)于模型2:口 Senes:匚円 Wo

16、rkfile： UNTTTLED:UntitledVi皀矗 | Objxt| Prop皀rtiEE |Sample GenrJSheEt G召ph|5tats Iident|Augmented Dickey-Fuller Unit Root Test on CPINull Hypothesis: CPI has a unit rootExogenous: ConstantLag Length: 2 (Automatic based on SIC, L1AXLAG=6)t-StatisticProb*Augmented Dickey*Fuiier test statistic-0.4725590

17、.S815Test critical values:1% level5% level10% level071145 了 -2.981038 -2.6299Q6* MacKinnon(1996) one-sided p<alues.Augmented Dickey-Fuller Test Equation Dependent Variable D(CPI Method: Least SquaresDate: 06/13/12 Ums: 14:115Sample (adjusted): 19B1 2006Included observations: 26 after adjustmentsr

18、 Series; CPT Warkfile: UNTTTLEDjiUrrtitled訥世理 | Pot | Objgut | Prop皀rtiEW | Pint|N日m皀 | F亡皀z皀 | Sample | Genr | She皀t| Gnph | Stats 11日皀nt |Augmented Dickey-Fuller Unit Root Test on CPI 匕UHWM,岳口! 7乂2 0>1 口Date: 05/13/12 Time: 14:15Sample (adjusted): 1961 2006Included observations: 26 alter adjust

19、mentsVariableCoefficientStd. Errort-StatisticProb.CPI(-1)-0.0075100.015893*0.4725590,6412D(CPI(-1)1.12759701787566.3080170.0000D(CPI-2)-0.524934Q181473-2 8926340.0084C34837332.3570231.4776680.1537R-squared0.581683Mean dependent var6.424231Adjusted R-sqjared0.633276S.D dependentvar8304869S.E. of regr

20、ession4.994839Akaike info criterion6 195326Sum squared resid54B.a651Schwarz criterion6.386879Log likelihood-76.53923Hannan-Quinn criter.6.2510&2F-statistic1570448Durbin-Watson stat1 746395ProbfF-statisti c)0.000011可以看到偽概率 P =0.8815，在5%的水平下是接受有單位根的原假設(shè)的。模型2的估計(jì)結(jié)果為：.：CPI t = 3.484 0.0075 CPI t1.128

21、. ：CPI t一 0.525 . ：CPI tj其中，常數(shù)項(xiàng)參數(shù):-的估計(jì)值的t統(tǒng)計(jì)量為t =1.477668 ，查ADF分布臨界值表得，模 型2樣本個(gè)數(shù)為25個(gè)（最接近的個(gè)數(shù)）時(shí)o.o25 = 2.97，即接受a =0的原假設(shè)，于是可與 進(jìn)行模型1的估計(jì)。對(duì)于模型1 : Series: CPT Workfie： UNTITLED;:Untitd丫的| Proc Objxt| Prop皀rtis | Pint|Nmm|FZE | Sample | Genr | She皀t| Gmph | Stats | IcJent|Null Hypothesis: CPI has a unit rootE

22、xogenous: NoneLag Length: 2 Automatic based on SIC, MAXLAG=6)t-StatisticProb*Augmented Dickey*Fuller test statistic1.3821490.9541Test critical values:1% level &% level 10% level-2.656915-1 954414-1.609329'MacKinnon(1996) one-sided pvalues.Augmented Dickey-Fuller Test Equation Dependent Varia

23、ble D(CPI)Method: Least SquaresDate: 06/13/12 Time: 14:21Sample (adjusted): 1981 2006Included obseations: 26 after adjustments Series: CPI Workfile: UNTTTLED:iUrrtitled| 口 回衛(wèi)訥皀呻 | Pck | Object PropertiEE |Freeze Sample Genr | She已t| Gnph | Stats 11血毗 |Augmented Dickey-Fuller Unit Root Test on CPIinu

24、yn lenieuunei iavi-ftJOTivnDependent Variable D(CPI)Method: Least SquaresDate: 06/13/12 Time: 1421Sample (adjusted): 19B1 2006Included observations: 26 after adjustmentsVanableCoefficientStd Errort* Stati sticProbCPK-1)0.0122180.0088401.3821490 1802D(CPI(-1)1.191B32Q.1777956.7034040.0000D(CPI(-2)-0.

25、5489910.105333-2.9621940 0070R-squared0.650090Mean dependent var6.424231Adjusted R-squared0.619663S.D. dependent var6.304869SE of regression5.121736kaike info criterion6.213031Sum squared： resid603.3400Schwarz criterion6.350196Log likelihood-7776940Hannan-Quinn criter.6254833DurbinWatson stat1 73625

26、2 - 一一圖7可以看到偽概率 P =0.9541 ，在5%的水平下是接受有單位根的原假設(shè)的。 模型1的估計(jì)結(jié)果為：CPI t =0.0122 CPI 21.1918 CPI 2 0.549 CPIt -2綜上所述，根據(jù) ADF檢驗(yàn)知，CPI序列存在單位根，即序列非平穩(wěn)。3單整性檢驗(yàn)所謂序列的單整性， 就是原序列經(jīng)過d階差分后變成了平穩(wěn)序列，就稱原序列為d階單整序列。于是對(duì)序列的單整性檢驗(yàn)又轉(zhuǎn)化為平穩(wěn)性檢驗(yàn)，即可用ADF檢驗(yàn)，其不同的就僅僅是需要對(duì)原序列進(jìn)行差分。然后，對(duì)CPI進(jìn)行單整性檢驗(yàn)，跟上述的平穩(wěn)的ADF檢驗(yàn)步驟類似，只是在 Unit RootTest對(duì)話框的設(shè)置中選擇 1st選項(xiàng)，就

27、是一階差分，這小題的檢驗(yàn)結(jié)果如下所示。對(duì)于模型3:Null Hypothesis: D(CPi) has a unit root Exogenous: Constant. LinearTrendLag Length: 1 (Automatic based on SIC, MAXLAG=6)t-StatisticProb.*Augmented Dickey*Fuller test statistic-3.1339070.1186Test critical values:1% level5% level10% level-4.356068 -3 595026-3.233456* MacKinnon

28、(1996) one-sided p values.Augmented Dickey-Fuller Test EquationDependent Variable D(CPL2)Method: Least SquaresDate: 06/13/12 Time: 14:24Sample (adjusted): 12006Included observations: 26 after adjustmentsDate: OS/13/12 Time: U:24Sample (adjusted): 1961 2006Included observations: 26 alter adjustmentsV

29、ariableCoefficientStd. Errort-StatisticProb.D(CPI(-1)*0.4069440.129645-3.1369070.0048D(CPI(-1)h2)0.5447200 1779363,0613320.0057C2.6504932.3797691.1137610 2774TREND(1978)-0.0067660.132002-0.0512580.9595R-squared0.394152Mean dependent var-0.012303Adjusted R-sqjared0.311536S.D dependentvar6 049997S.E.

30、of regression5.019825Akaike info criterion6.205306Sum squared resid5543702Schwarz criterion6.39&869Log likelihood-76.65897Hannan-Quinn criter.6 251042F-statistic477090BDurbin-Watson stat1755816ProbfF-statisti c)0.010399可以看到偽概率 P =0.1186 ，在5%的水平下是接受有單位根的原假設(shè)的。 模型3的估計(jì)結(jié)果為：-2 2二 CPI t = 2.650-0.0068

31、t - 0.407 LCPI t 丄 0.545 二 CPI t其中，趨勢項(xiàng)參數(shù) '的估計(jì)值的t統(tǒng)計(jì)量為t - -0.051258 ，查ADF分布臨界值表得，模 型3樣本個(gè)數(shù)為25個(gè)（最接近的個(gè)數(shù)）時(shí)1甌025 = 3.25，即接受0 =0的原假設(shè)，于是可與 進(jìn)行模型2的估計(jì)。對(duì)于模型2 : Series: CPT Workfile: UNTTTLEDjiUrrtitledView|Pat|Object|Properties| PrintN日m皀Freeze Sample Genr | She皀t| Gph | Stats | IcJent|Augmented Dickey-Fulle

32、r Unit Root Test on D(CPI)Null Hypothesis: D(CPI) has a unit root Exogenous: ConstantLag Length: 1 Automatic based on SIC, MAXLAG=6)t-StaVsticProb*Augmented Dickey*Fuller test statistic-3.2168490.0304Test aitical values:1% level5% level10%le7el-3.711457-2.981038-2.629906* MacKinnon(1996) one-sided pvalues.Augmented Dicke