我國(guó)能源消費(fèi)量的計(jì)量分析

1、我國(guó)能源消費(fèi)量的計(jì)量分析一、經(jīng)濟(jì)背景分析隨著國(guó)際競(jìng)爭(zhēng)的日趨激烈，各國(guó)對(duì)于能源問(wèn)題的重視程度不斷加強(qiáng)，能源問(wèn)題被不斷提升至國(guó)家的討論日程。因?yàn)閺哪撤N意義上說(shuō)，能源決定了一個(gè)國(guó)家的未來(lái)發(fā)展，能否獲得有效的能源保障關(guān)系到國(guó)家的生死存亡，對(duì)各國(guó)發(fā)展意義重大。鑒于能源在國(guó)家發(fā)展中的重要地位，能源的供需情況成為世界各國(guó)矚目的焦點(diǎn)，能源消費(fèi)問(wèn)題成為研究能源供需的重要出發(fā)點(diǎn)。尤其是對(duì)于中國(guó)而言，隨著國(guó)民經(jīng)濟(jì)的高速發(fā)展，能源消費(fèi)量劇增，2001年突破14億噸標(biāo)準(zhǔn)煤成為僅次于美國(guó)的世界第二大能源消費(fèi)國(guó)，預(yù)計(jì)我國(guó)將于2010年超過(guò)美國(guó)位居能源消費(fèi)世界第一。面對(duì)數(shù)目如此巨大的能源消費(fèi)量，我國(guó)呈現(xiàn)出嚴(yán)重的能源供不應(yīng)求局

2、面，能源供求的矛盾日益突出。近期，我國(guó)相繼采取了一系列的解決未來(lái)能源問(wèn)題的行動(dòng)，例如：中國(guó)在巴西購(gòu)買(mǎi)鋁土，在智利購(gòu)買(mǎi)銅，在澳大利亞購(gòu)買(mǎi)鋅，向哈薩克斯坦購(gòu)買(mǎi)石油，與日本爭(zhēng)奪“安大線”等等都表明能源對(duì)我國(guó)的重大意義。能否保證能源的供需平衡是我國(guó)未來(lái)的一個(gè)巨大挑戰(zhàn)，而能源消費(fèi)則成為此問(wèn)題的重要因素。鑒于此選取我國(guó)能源消費(fèi)作為分析的對(duì)象，分析影響能源消費(fèi)量的因素，來(lái)探究我國(guó)能源問(wèn)題的過(guò)去、現(xiàn)在和未來(lái)。二、研究目的面對(duì)如此嚴(yán)峻的能源消費(fèi)形勢(shì)，在盡量不影響經(jīng)濟(jì)發(fā)展的前提下，尋找出巨大能耗的主要影響因素，并據(jù)此研究改變能源消費(fèi)結(jié)構(gòu)的途徑，對(duì)于解決我國(guó)能源供需矛盾、促進(jìn)能源消費(fèi)合理化具有重要意義。本文即是采用

3、我國(guó)自1975年以來(lái)33年的數(shù)據(jù)，運(yùn)用計(jì)量經(jīng)濟(jì)分析方法，對(duì)影響我國(guó)能源消費(fèi)的主要因素進(jìn)行定量分析，希望能夠?yàn)槲覈?guó)能源消費(fèi)問(wèn)題的解決有所幫助。三、變量的選取和樣本數(shù)據(jù)變量的選取由于本文是對(duì)于我國(guó)整體能源消費(fèi)的研究，通過(guò)對(duì)能源消費(fèi)理論的分析，人口越多則對(duì)能源的需求量越多，消耗也越多，而國(guó)內(nèi)生產(chǎn)總值則是經(jīng)濟(jì)規(guī)模和活躍程度的一個(gè)重要體現(xiàn)。所以本文選擇人口數(shù)量與人均國(guó)內(nèi)生產(chǎn)總值兩個(gè)宏觀因素作為解釋變量，從總體和宏觀角度來(lái)分析我國(guó)能源消費(fèi)問(wèn)題。其中：EC=能源消費(fèi)總量（被解釋變量）POP=年底人口數(shù)量（解釋變量）PGDP=人均國(guó)內(nèi)生產(chǎn)總值（解釋變量）數(shù)據(jù)的收集我國(guó)自1975年以來(lái)的能源消費(fèi)數(shù)據(jù)表年份PGD

4、PERPOPEC人均國(guó)內(nèi)生產(chǎn)總值（元）能源生產(chǎn)量（萬(wàn)噸標(biāo)準(zhǔn)煤）年底人口總數(shù)（萬(wàn)人）能源消耗量（萬(wàn)噸標(biāo)準(zhǔn)煤）2000790213856912674314696420018670147424127627155547200294501562771284531695772003106001782981292271970832004124002061071299882302812005142592290361307562613692006166022447621314482864672007203372641721321293114422008239122774191328023206112009259

5、63286092133450336126201030567312124134091360648201136018340177134735387043201239544351040135404402138201343320358783136072416913注釋?zhuān)?、以上所有數(shù)據(jù)均是根據(jù)中國(guó)1987統(tǒng)計(jì)年鑒與國(guó)家統(tǒng)計(jì)局網(wǎng)站數(shù)據(jù)進(jìn)行整合所得。 2、人均國(guó)民生產(chǎn)總值是按當(dāng)年價(jià)進(jìn)行計(jì)算所得。 3、能源消費(fèi)總量包括全國(guó)對(duì)煤炭、石油、天然氣、水電、核電及風(fēng)電的消費(fèi)量。四、模型的參數(shù)估計(jì)、檢驗(yàn)及修4.1模型的假定條件首先根據(jù)以上數(shù)據(jù)畫(huà)出散點(diǎn)圖，如下所示：從上圖可知解釋變量、與的關(guān)系都可大致看作線性關(guān)系，所以

6、我們建立以下二元回歸模型： 此模型應(yīng)滿足以下假設(shè)條件：假設(shè)1、解釋變量PGDP、POP是非隨機(jī)的或是固定的，且相互之間互不相關(guān) 假設(shè)2、隨機(jī)誤差項(xiàng)m具有零均值、同方差和無(wú)序列相關(guān)性： E(ut)=0 t=1,2, ,n Var (ut)= s 2 t=1,2, ,n Cov(ui, uj)=0 ij i,j= 1,2, ,n假設(shè)3、隨機(jī)誤差項(xiàng)m與解釋變量X之間不相關(guān)： Cov(xjt ,ut)=0 t=1,2, ,n j=1，2假設(shè)4、m服從零均值、同方差的正態(tài)分布 ut N(0, s 2) t=1,2, ,n4.2模型參數(shù)的估計(jì)運(yùn)用eviews軟件可以對(duì)數(shù)據(jù)進(jìn)行初步的回歸，回歸結(jié)果如下表所示

7、：Dependent Variable: ECMethod: Least SquaresDate: 11/04/15 Time: 20:13Sample: 1975 2007Included observations: 33VariableCoefficientStd. Errort-StatisticProb. C-60969.8827707.90-2.2004510.0356PGDP8.2722420.65213712.684820.0000POP1.2018680.2642644.5479910.0001R-squared0.971304 Mean dependent var114651

8、.1Adjusted R-squared0.969391 S.D. dependent var57468.45S.E. of regression10054.31 Akaike info criterion21.35590Sum squared resid3.03E+09 Schwarz criterion21.49194Log likelihood-349.3723 F-statistic507.7264Durbin-Watson stat0.243129 Prob(F-statistic)0.000000根據(jù)上表可得回歸結(jié)果為：結(jié)果分析：(1) 擬合優(yōu)度：根據(jù)回歸結(jié)果可得到，修正的可決系數(shù)

9、為，這說(shuō)明模型對(duì)樣本的擬合很好。(2) 檢驗(yàn)：針對(duì)給定顯著性水平，在分布表中查出自由度為和的臨界值。本模型得出的結(jié)果，因此，應(yīng)拒絕原假設(shè)，說(shuō)明回歸方程顯著。(3) 檢驗(yàn)：分別針對(duì)，給定顯著性水平，查分布表得自由度為的臨界值。模型回歸結(jié)果顯示：與，對(duì)應(yīng)的統(tǒng)計(jì)量分別為-2.200451，12.68482，4.547991，其絕對(duì)值均大于。這說(shuō)明分別都應(yīng)當(dāng)拒絕原假設(shè)，即在其他解釋變量不變的情況下，解釋變量PGDP,POP分別對(duì)被解釋變量EC都有顯著性影響。(4) 觀察得知D-W值非常小，說(shuō)明該模型有待進(jìn)一步修正，尤其是應(yīng)該進(jìn)行序列相關(guān)檢驗(yàn)。4.3 模型的檢驗(yàn)4.3.1 異方差的檢驗(yàn)1. 根據(jù)殘差圖初

10、步判定異方差是否存在圖顯示回歸方程的殘差分布有明顯增大形式，所以判定該回歸方程存在異方差。2. 用White檢驗(yàn)法檢驗(yàn)“異方差”問(wèn)題，檢驗(yàn)結(jié)果見(jiàn)下表：White Heteroskedasticity Test:F-statistic7.760637 Probability0.000243Obs*R-squared17.35027 Probability0.001652Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 11/05/15 Time: 20:26Sample: 1975 2007Included ob

11、servations: 33VariableCoefficientStd. Errort-StatisticProb. C1.42E+105.10E+092.7937680.0093PGDP-115015.457899.11-1.9864800.0568PGDP22.4035221.7228881.3950540.1740POP-281940.0100562.8-2.8036220.0091POP21.3992830.4980252.8096630.0089R-squared0.525766 Mean dependent var91899224Adjusted R-squared0.45801

12、8 S.D. dependent var1.19E+08S.E. of regression87873573 Akaike info criterion39.55942Sum squared resid2.16E+17 Schwarz criterion39.78617Log likelihood-647.7305 F-statistic7.760637Durbin-Watson stat1.063793 Prob(F-statistic)0.000243根據(jù)上表中Obs*R-squared行的值得，可以判斷出，在0.05的判斷標(biāo)準(zhǔn)下，（9.488為顯著性水平為0.05，自由度為4的情況下的卡

13、方分布的值），拒絕原假設(shè)，所以該模型存在異方差問(wèn)題。4.3.2 序列相關(guān)性檢驗(yàn)1.根據(jù)散點(diǎn)圖判別序列相關(guān)性其中Y的實(shí)際觀察值序列（Actual）、擬合值序列（Fitted）以及殘差序列（Residual），變量對(duì)其一階滯后變量的散點(diǎn)圖如下：結(jié)合上面兩幅圖，分析初步得出該模型存在正自相關(guān)的結(jié)論。2. 序列相關(guān)性檢驗(yàn)本文利用拉格朗日乘數(shù)檢驗(yàn)，檢驗(yàn)結(jié)果如下：Breusch-Godfrey Serial Correlation LM Test:F-statistic105.4246 Probability0.000000Obs*R-squared29.13145 Probability0.000000

14、Test Equation:Dependent Variable: RESIDMethod: Least SquaresDate: 11/05/15 Time: 20:31VariableCoefficientStd. Errort-StatisticProb. C-13965.9110178.61-1.3720830.1809PGDP-0.4977400.252640-1.9701520.0588POP0.1401170.0974431.4379400.1615RESID(-1)1.6030510.14714810.894140.0000RESID(-2)-0.8709770.157902-

15、5.5159300.0000R-squared0.882771 Mean dependent var1.56E-11Adjusted R-squared0.866024 S.D. dependent var9735.044S.E. of regression3563.289 Akaike info criterion19.33348Sum squared resid3.56E+08 Schwarz criterion19.56023Log likelihood-314.0025 F-statistic52.71230Durbin-Watson stat2.065478 Prob(F-stati

16、stic)0.000000根據(jù)上表中Obs*R-squared行的P值，可以判斷出，該模型拒絕原假設(shè)，存在序列相關(guān)性。樣本量，序列相關(guān)的階數(shù)，LM統(tǒng)計(jì)量, , ，所以存在序列相關(guān)性4.3.3 隨機(jī)解釋變量問(wèn)題與多重共線性問(wèn)題的檢驗(yàn)將初始回歸得到的殘差與被解釋變量EC及解釋變量PGDP,POP的相關(guān)關(guān)系顯示如下表：ECPGDPPOPRESIDEC1.0000000.9754590.9040990.169398PGDP0.9754591.0000000.851153-8.19E-15POP0.9040990.8511531.000000-4.41E-14RESID0.169398-8.19E-15

17、-4.41E-141.000000根據(jù)上表可以看出，殘差序列與解釋變量的相關(guān)系數(shù)非常小，所以可以判定，該模型基本不存在隨機(jī)解釋變量問(wèn)題。由上表同時(shí)可以看出，解釋變量POP與PGDP之間存在較為嚴(yán)重的多重共線性問(wèn)題。4.4 根據(jù)檢驗(yàn)結(jié)果進(jìn)行模型修正4.4.1修正多重共線性本模型中，解釋變量POP與PGDP之間存在較為嚴(yán)重的多重共線性問(wèn)題，針對(duì)此類(lèi)問(wèn)題一般采取取對(duì)數(shù)的方法修正。修正結(jié)果如下表：Dependent Variable: LOG(EC)Method: Least SquaresDate: 11/06/15 Time: 11:04Sample: 1975 2007Included obse

18、rvations: 33VariableCoefficientStd. Errort-StatisticProb. C1.1481339.8583350.1164630.9081LOG(PGDP)0.2945610.0761223.8695770.0005LOG(POP)0.6978150.8965510.7783330.4425R-squared0.964666 Mean dependent var11.53519Adjusted R-squared0.962311 S.D. dependent var0.484419S.E. of regression0.094044 Akaike inf

19、o criterion-1.803609Sum squared resid0.265326 Schwarz criterion-1.667562Log likelihood32.75954 F-statistic409.5262Durbin-Watson stat0.188063 Prob(F-statistic)0.000000與原表進(jìn)行對(duì)比后，可以看出取對(duì)數(shù)后，常數(shù)項(xiàng)和POP都無(wú)法通過(guò)t檢驗(yàn)而需要被舍去，回歸的結(jié)果變差。同時(shí)，由于多重共線性對(duì)回歸結(jié)果的影響程度小于序列相關(guān)以及異方差，因此，在本文中，沒(méi)有采用對(duì)數(shù)化的方程，仍然使用真值進(jìn)行計(jì)量分析。4.4.2 修正序列相關(guān)性由于本文模型是時(shí)間

20、序列模型，所以首先進(jìn)行序列相關(guān)性問(wèn)題修正。運(yùn)用廣義差分法對(duì)模型進(jìn)行修正由，可得 ，其中 ，,結(jié)果如下：Dependent Variable: EC1Method: Least SquaresDate: 11/04/15 Time: 20:29Sample(adjusted): 1976 2007Included observations: 32 after adjusting endpointsVariableCoefficientStd. Errort-StatisticProb. C3367.58513689.030.2460060.8074PGDP19.0122851.0168818.8

21、626770.0000POP10.4582640.9618400.4764450.6373R-squared0.868522 Mean dependent var20243.58Adjusted R-squared0.859454 S.D. dependent var12819.62S.E. of regression4805.999 Akaike info criterion19.88218Sum squared resid6.70E+08 Schwarz criterion20.01959Log likelihood-315.1148 F-statistic95.78456Durbin-W

22、atson stat0.804892 Prob(F-statistic)0.000000根據(jù)上表可看出運(yùn)用廣義積分法對(duì)模型進(jìn)行修正后，的檢驗(yàn)值都小于的臨界值，且D-W的值的值都很小，說(shuō)明該修正方法不合適。接下來(lái)再運(yùn)用Cochrane-Orcutt迭代法進(jìn)行自相關(guān)修正。Cochrane-Orcutt迭代法結(jié)果如下所示：Dependent Variable: ECMethod: Least SquaresDate: 11/05/15 Time: 21:18Sample(adjusted): 1977 2007Included observations: 31 after adjusting end

23、pointsConvergence achieved after 6 iterationsVariableCoefficientStd. Errort-StatisticProb. C-100000.539482.68-2.5327700.0177PGDP6.7075240.9178217.3080960.0000POP1.6000280.3752894.2634540.0002AR(1)1.6541710.14342711.533210.0000AR(2)-0.9228220.154888-5.9579830.0000R-squared0.997004 Mean dependent var1

24、19039.7Adjusted R-squared0.996543 S.D. dependent var56518.34S.E. of regression3323.162 Akaike info criterion19.20191Sum squared resid2.87E+08 Schwarz criterion19.43320Log likelihood-292.6296 F-statistic2162.887Durbin-Watson stat2.058220 Prob(F-statistic)0.000000Inverted AR Roots .83+.49i .83 -.49i模型

25、經(jīng)過(guò)Cochrane-Orcutt迭代法可變?yōu)椋涸撃Ｐ筒捎肅ochrane-Orcutt迭代法，加入和項(xiàng)后，檢驗(yàn)和檢驗(yàn)都拒絕原假設(shè)，且顯示擬合程度非常好。DW的值為2.058220，該模型的樣本量，查表得,DW的值在之間，接受原假設(shè)，認(rèn)為該模型非序列相關(guān)。4.4.3 修正后再次進(jìn)行異方差檢驗(yàn)（White檢驗(yàn)）檢驗(yàn)結(jié)果如下表所示：White Heteroskedasticity Test:F-statistic2.295311 Probability0.086165Obs*R-squared8.090064 Probability0.088334Test Equation:Dependent V

26、ariable: RESID2Method: Least SquaresDate: 11/05/15 Time: 21:41Sample: 1977 2007Included observations: 31VariableCoefficientStd. Errort-StatisticProb. C8.53E+081.13E+090.7529220.4583PGDP-731.079311466.07-0.0637600.9496PGDP2-0.0945450.333039-0.2838860.7787POP-16172.6122062.36-0.7330410.4701POP20.07662

27、70.1079390.7099110.4841R-squared0.260970 Mean dependent var9262212.Adjusted R-squared0.147273 S.D. dependent var17347550S.E. of regression16019287 Akaike info criterion36.16318Sum squared resid6.67E+15 Schwarz criterion36.39446Log likelihood-555.5292 F-statistic2.295311Durbin-Watson stat2.870678 Pro

28、b(F-statistic)0.086165該修正后的模型中加入了和兩項(xiàng)后，則，則拒絕原假設(shè)，修正后的模型具有同方差，即不存在異方差。4.4.4 修正后再次進(jìn)行序列相關(guān)性檢驗(yàn)檢驗(yàn)結(jié)果如下表所示：Breusch-Godfrey Serial Correlation LM Test:F-statistic6.954647 Probability0.004146Obs*R-squared4.37421 Probability0.003389Test Equation:Dependent Variable: RESIDMethod: Least SquaresDate: 11/06/15 Time:

29、09:00VariableCoefficientStd. Errort-StatisticProb. C-70060.6137786.80-1.8541030.0761PGDP-2.2736420.979549-2.3211110.0291POP0.6904310.3625161.9045520.0689AR(1)0.6161860.2167522.8428150.0090AR(2)-0.4799390.194665-2.4654650.0212RESID(-1)-0.5777780.250612-2.3054660.0301RESID(-2)-0.9757360.262763-3.71337

30、10.0011R-squared0.366910 Mean dependent var1.57E-07Adjusted R-squared0.208637 S.D. dependent var3093.696S.E. of regression2752.107 Akaike info criterion18.87380Sum squared resid1.82E+08 Schwarz criterion19.19760Log likelihood-285.5439 F-statistic2.318216Durbin-Watson stat2.225994 Prob(F-statistic)0.

31、065929根據(jù)上表中Obs*R-squared行的P值，可以判斷出，在0.05的判斷標(biāo)準(zhǔn)下，該模型不存在序列相關(guān)性問(wèn)題。樣本量，序列相關(guān)的階數(shù)，LM統(tǒng)計(jì)量, , ，說(shuō)明修正后的模型不存在序列相關(guān)性。五、 時(shí)間序列問(wèn)題5.1 時(shí)間序列平穩(wěn)性檢驗(yàn)首先，畫(huà)出序列EC的時(shí)間路徑圖。由圖可以看出序列EC存在一個(gè)明顯的上升趨勢(shì)，于是初步判定序列EC不平穩(wěn)。但要確定序列EC的平穩(wěn)性需要進(jìn)一步進(jìn)行單位根檢驗(yàn)：進(jìn)行ADF檢驗(yàn)有三種形式，需要從帶趨勢(shì)和截距項(xiàng)的形式開(kāi)始，逐步進(jìn)行。（1）帶趨勢(shì)和截距項(xiàng)Null HECpothesis: EC has a unit root Exogenous: Constant,

32、 Linear TrendLag Length: 1 (Fixed)t-Statistic  Prob.*Augmented DickeEC-Fuller test statistic-1.293269 0.8709Test critical values:1% level-4.2845805% level-3.56288210% level-3.215267*MacKinnon (1996) one-sided p-values.Augmented DickeEC-Fuller Test EquationDependent Variable: D(EC)Meth

33、od: Least SquaresDate: 11/28/09 Time: 13:16Sample (adjusted): 1977 2007Included observations: 31 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.  EC(-1)-0.0861380.066605-1.2932690.2069D(EC(-1)0.9112320.1786335.1011300.0000C1441.4042335.0290.6172960.5422TREND(1975)548.7014311

34、.82411.7596510.0898R-squared0.729403    Mean dependent var7024.258Adjusted R-squared0.699336    S.D. dependent var7808.841S.E. of regression4281.808    Akaike info criterion19.68205Sum squared resid4.95E+08    Schwarz cr

35、iterion19.86708Log likelihood-301.0718    Hannan-Quinn criter.19.74237F-statistic24.25974    Durbin-Watson stat1.700169Prob(F-statistic)0.000000可以看出，模型中C和T的檢驗(yàn)無(wú)法通過(guò)，因此需要排除時(shí)間趨勢(shì)，進(jìn)行下一個(gè)形式的檢驗(yàn)，即帶截距項(xiàng)的檢驗(yàn)。（2）帶截距項(xiàng)Null HECpothesis: EC has a unit root Exogenous: ConstantLag

36、 Length: 1 (Fixed)t-Statistic  Prob.*Augmented DickeEC-Fuller test statistic 1.059182 0.9962Test critical values:1% level-3.6616615% level-2.96041110% level-2.619160*MacKinnon (1996) one-sided p-values.Augmented DickeEC-Fuller Test EquationDependent Variable: D(EC)Method: Least S

37、quaresDate: 11/28/09 Time: 13:19Sample (adjusted): 1977 2007Included observations: 31 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.  EC(-1)0.0243680.0230061.0591820.2986D(EC(-1)0.7422740.1561714.7529640.0001C-514.39412129.019-0.2416110.8108R-squared0.698370  

38、0; Mean dependent var7024.258Adjusted R-squared0.676825    S.D. dependent var7808.841S.E. of regression4439.205    Akaike info criterion19.72610Sum squared resid5.52E+08    Schwarz criterion19.86488Log likelihood-302.7546  &#

39、160; Hannan-Quinn criter.19.77134F-statistic32.41453    Durbin-Watson stat1.492949Prob(F-statistic)0.000000同樣，C的檢驗(yàn)仍無(wú)法通過(guò)，此種形式是錯(cuò)誤的，需要進(jìn)行最后一個(gè)形式的檢驗(yàn)。（3）不帶截距項(xiàng)Null HECpothesis: EC has a unit root Exogenous: NoneLag Length: 1 (Fixed)t-Statistic  Prob.*Augmented DickeEC-Full

40、er test statistic 1.733905 0.9774Test critical values:1% level-2.6416725% level-1.95206610% level-1.610400*MacKinnon (1996) one-sided p-values.Augmented DickeEC-Fuller Test EquationDependent Variable: D(EC)Method: Least SquaresDate: 11/28/09 Time: 13:20Sample (adjusted): 1977 2007Included

41、observations: 31 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.  EC(-1)0.0195480.0112741.7339050.0936D(EC(-1)0.7573410.1408375.3774330.0000R-squared0.697741    Mean dependent var7024.258Adjusted R-squared0.687319    S.D. dependent var

42、7808.841S.E. of regression4366.541    Akaike info criterion19.66367Sum squared resid5.53E+08    Schwarz criterion19.75619Log likelihood-302.7869    Hannan-Quinn criter.19.69383Durbin-Watson stat1.499492在最終形式中可以容易的看出，序列EC不平穩(wěn)。接下來(lái)，需要對(duì)EC做差分，使不平

43、穩(wěn)的數(shù)據(jù)平穩(wěn)化，并確定序列的單整階數(shù)。5.2 不平穩(wěn)序列平穩(wěn)化對(duì)序列EC做一階差分后進(jìn)行單位根檢驗(yàn)：Null HECpothesis: D(EC) has a unit root Exogenous: NoneLag Length: 1 (Fixed)t-Statistic  Prob.*Augmented DickeEC-Fuller test statistic-0.960177 0.2934Test critical values:1% level-2.6443025% level-1.95247310% level-1.610211*MacKinnon (

44、1996) one-sided p-values.Augmented DickeEC-Fuller Test EquationDependent Variable: D(EC,2)Method: Least SquaresDate: 11/28/09 Time: 13:32Sample (adjusted): 1978 2007Included observations: 30 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.  D(EC(-1)-0.0867450.090343-0.9601770

45、.3452D(EC(-1),2)0.2425340.1998411.2136360.2350R-squared0.047298    Mean dependent var492.9950Adjusted R-squared0.013273    S.D. dependent var4562.332S.E. of regression4531.953    Akaike info criterion19.74003Sum squared resid5.75E+08 &

46、#160;  Schwarz criterion19.83345Log likelihood-294.1005    Hannan-Quinn criter.19.76992Durbin-Watson stat1.862451dEC序列仍然是不平穩(wěn)序列，需要進(jìn)一步進(jìn)行二階差分。二階查分后，通過(guò)ddEC的時(shí)間路徑圖可以初步判斷，ddEC序列已經(jīng)平穩(wěn)。下面對(duì)ddEC序列進(jìn)行單位根檢驗(yàn)，以確定ddEC序列是否已經(jīng)平穩(wěn)。Null HECpothesis: D(EC,2) has a unit rootExogenous: NoneLag Le

47、ngth: 1 (Fixed)t-Statistic  Prob.*Augmented DickeEC-Fuller test statistic-4.855532 0.0000Test critical values:1% level-2.6471205% level-1.95291010% level-1.610011*MacKinnon (1996) one-sided p-values.Augmented DickeEC-Fuller Test EquationDependent Variable: D(EC,3)Method: Least Squares

48、Date: 11/28/09 Time: 13:33Sample (adjusted): 1979 2007Included observations: 29 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.  D(EC(-1),2)-1.1296610.232654-4.8555320.0000D(EC(-1),3)0.3563370.1799791.9798800.0580R-squared0.488642    Mean dependent var-87

49、.66552Adjusted R-squared0.469702    S.D. dependent var6018.904S.E. of regression4383.058    Akaike info criterion19.67535Sum squared resid5.19E+08    Schwarz criterion19.76965Log likelihood-283.2926    Hannan-Quinn criter.19.70489Durbin-Watson stat1.803053由輸出結(jié)果可以看出，ddEC序列已經(jīng)平穩(wěn)，并且DW值也符合要求，說(shuō)明EC是I(2)的，其中滯后階數(shù)1。檢驗(yàn)序列PGDP、POP的平穩(wěn)性，檢驗(yàn)步驟與檢驗(yàn)EC的平穩(wěn)性相同。由時(shí)間路徑圖初步判斷PGDP、POP都是不平穩(wěn)的。PGDP序列形式為不帶截距項(xiàng)，三階差分后平穩(wěn)，即dddPGD