假設(shè)影響人民幣匯率的因素有，國內(nèi)生產(chǎn)總值，錢幣和準(zhǔn)錢幣M2，外匯儲(chǔ)備三個(gè)變量，為方便量化，用錢幣供應(yīng)量同比增加率來描述錢幣和準(zhǔn)錢幣M2，用與100美元等值的人民幣數(shù)值來近似描述人民幣的匯率水平。采集1991-2007年的數(shù)據(jù)以下：序項(xiàng)目國內(nèi)生產(chǎn)總值錢幣和準(zhǔn)錢幣M2（錢幣供應(yīng)外匯儲(chǔ)備人民幣匯率人民幣元號(hào)年份（億元）量同比增加率）(億美元)（=100美元)11991532.320250.47.6217.121992551.523134.27.6194.431993576.226364.71121241994861.929813.411516.251995835.133070.51173661996831.436380.4111050.57199782939762.75.71398.981998827.942877.45.21449.691999827.846144.62.31546.8102000827.823072.32.31655.7112001827.7107449.72.32121.7122002827.7117208.322864.1132003827.7128958.924032.5142004827.7141964.526099.3152005819.2169996.42.38188.3162006797.2204556.12.310663.4172007760.42495302.315282.5一、模型參數(shù)估計(jì)對(duì)模型進(jìn)行多次試驗(yàn)，最后優(yōu)選出模型的形式：LOG(RESERVE)01gGDP2gM2^23gLOG(RESERVE)i并對(duì)模型進(jìn)行了參數(shù)估計(jì)，結(jié)果以下：DependentVariable:LOG(EXCHANGE)Method:LeastSquaresDate:12/06/11Time:22:44Sample:19912007Includedobservations:17VariableCoefficientStd.Errort-StatisticProb.C5.0708000.20790324.390210.0000GDP-3.08E-065.55E-07-5.5482960.0001M2^20.0001496.45E-052.3084140.0381LOG(RESERVE)0.2392850.0316787.5535960.0000R-squared0.829795Meandependentvar6.642979AdjustedR-squared0.790517S.D.dependentvar0.158903S.E.ofregression0.072729Akaikeinfocriterion-2.201825Sumsquaredresid0.068764Schwarzcriterion-2.005775Loglikelihood22.71552F-statistic21.12611Durbin-Watsonstat1.226706Prob(F-statistic)0.000028經(jīng)過參數(shù)估計(jì)的模型方程二、模型的檢驗(yàn)（一）對(duì)模型進(jìn)行經(jīng)濟(jì)意義檢驗(yàn)：表示當(dāng)沒有任何經(jīng)濟(jì)變量影響的時(shí)候，人民幣匯率為5.070800，但數(shù)值自己沒有任何意義；表示每當(dāng)國內(nèi)生產(chǎn)總值增加一個(gè)單位，人民幣匯率的對(duì)數(shù)值會(huì)相應(yīng)減少3.08E-06個(gè)單位，國內(nèi)生產(chǎn)總值和人民幣匯率表現(xiàn)負(fù)相關(guān)關(guān)系；表示每當(dāng)錢幣供應(yīng)量同比增加率的平方增加一個(gè)單位，人民幣匯率的對(duì)數(shù)值會(huì)相應(yīng)增加1.49E-04個(gè)單位，錢幣供應(yīng)量和人民幣匯率表現(xiàn)正相關(guān)關(guān)系；表示每當(dāng)外匯儲(chǔ)備的對(duì)數(shù)值增加一個(gè)單位，人民幣匯率的對(duì)數(shù)值會(huì)相應(yīng)增加0.24個(gè)單位，外匯儲(chǔ)備和人民幣匯率表現(xiàn)正相關(guān)關(guān)系。吻合經(jīng)濟(jì)學(xué)知識(shí),模型經(jīng)過經(jīng)濟(jì)意義檢驗(yàn)。相關(guān)性檢驗(yàn)擬合優(yōu)度檢驗(yàn)R2=0.790517，說明人民幣匯率中79.05%可由國內(nèi)生產(chǎn)總值，錢幣和準(zhǔn)錢幣M2，外匯儲(chǔ)備講解，擬合程度比較好。2顯然性檢驗(yàn)整體線性關(guān)系檢驗(yàn)（F檢驗(yàn)）：Prob(F-statistic)=0.000028<0.05，整體線性關(guān)系顯然。回歸系數(shù)顯然性檢驗(yàn)（t檢驗(yàn)）：Prob.=0.0001<0.05，經(jīng)過t檢驗(yàn)；gdp對(duì)log(exchange)線性影響顯然。Prob.=0.0381<0.05，經(jīng)過t檢驗(yàn)；m2^2對(duì)log(exchange)線性影響顯然。Prob.=0.0000<0.05，經(jīng)過t檢驗(yàn)，log(reserve)對(duì)log(exchange)線性影響顯著。3、異方差檢驗(yàn)①圖示法檢驗(yàn)：經(jīng)過作圖解析，模型可能存在遞加的異方差。但這其實(shí)不能夠充分證明該模型存在異方差性，要想獲取異方差的形式并加以除掉，還需要更進(jìn)一步的采用其他方法。②對(duì)上面的模型進(jìn)行WHITE檢驗(yàn)WhiteHeteroskedasticityTest:F-statistic1.490830Probabili0.306152tyObs*R-squared11.17166Probabili0.264126ty尾端面積PROB.=0.26412>0.05未檢驗(yàn)出存在異方差。③進(jìn)一步進(jìn)行G-Q檢驗(yàn)采用在上述OLS結(jié)果中未能經(jīng)過T檢驗(yàn)的M2^2進(jìn)行G-Q檢驗(yàn)。把M2的數(shù)據(jù)按升序排列，并將其分成三部分，采用第一部分1991-1997的數(shù)據(jù)和第三部分2001-2007年的數(shù)據(jù)分別按原方程進(jìn)行回歸。DependentVariable:LOG(EXCHANGE)Method:LeastSquaresDate:12/17/09Time:20:35Sample:19911997Includedobservations:7R-squared0.993658Meandependentvar6.649499AdjustedR-squared0.987316S.D.dependentvar0.133113S.E.ofregression0.014991Akaikeinfocriterion-5.267110Sumsquaredresid0.000674Schwarzcriterion-5.298018Loglikelihood22.43488F-statistic156.6808Durbin-Watsonstat1.965270Prob(F-statistic)0.000856DependentVariable:LOG(EXCHANGE)Method:LeastSquaresDate:12/17/09Time:20:36Sample:20012007Includedobservations:6Excludedobservations:1R-squared0.913623Meandependent6.647565varAdjustedR-squared0.784058S.D.dependentvar0.181469S.E.ofregression0.084328Akaikeinfocriterion-1.873490Sumsquaredresid0.014222Schwarzcriterion-2.012317Loglikelihood9.620469F-statistic7.051470Durbin-Watsonstat0.689236Prob(F-statistic)0.126725SSR的比值為SSR2/SSR1=0.014222/0.000674=21.10>F0.05(3,3)=9.28，拒絕原假設(shè)，μi存在異方差。④對(duì)原方程進(jìn)行加權(quán)數(shù)1/abs(e)，除掉異方差，并進(jìn)行回歸。DependentVariable:LOG(EXCHANGE)Method:LeastSquaresDate:12/17/09Time:19:22Sample(adjusted):19912007Includedobservations:17afteradjustingendpointsWeightingseries:1/ABS(E)VariableCoefficientStd.Errort-StatisticProb.C5.1230750.19571326.176500.0000GDP-3.00E-063.62E-07-8.2976280.0000M2^20.0001561.94E-058.0619410.0000LOG(RESERVE)0.2315770.0284238.1476230.0000WeightedStatisticsR-squared1.000000Meandependentvar6.712539AdjustedR-squared1.000000S.D.dependentvar14.87848S.E.ofregression0.005674Akaikeinfocriterion-7.303547Sumsquaredresid0.000419Schwarzcriterion-7.107497Loglikelihood66.08015F-statistic24.33806Durbin-Watsonstat1.308886Prob(F-statistic)0.000013UnweightedStatisticsR-squared0.826616Meandependent6.642979varAdjustedR-squared0.786605S.D.dependentvar0.158903S.E.ofregression0.073405Sumsquaredresid0.070048Durbin-Watsonstat1.184263⑤再一次進(jìn)行WHITE檢驗(yàn):WhiteHeteroskedasticityTest:F-statistic0.372977Probability0.905799Obs*R-squared6.025270Probability0.7373870.737387>0.05，接受原假設(shè)，懷特檢驗(yàn)經(jīng)過且結(jié)果較除掉異方差前更為優(yōu)異。加權(quán)后的模型不存在異方差。序列相關(guān)檢驗(yàn)①圖示法檢驗(yàn)：經(jīng)過圖示檢驗(yàn)，從圖中表示的數(shù)據(jù)能夠看出，殘差值有逐年減小的趨勢，預(yù)示著可能表現(xiàn)序列負(fù)相關(guān)性，需要進(jìn)行更進(jìn)一步的檢驗(yàn)。②對(duì)上面的模型進(jìn)行

D-W檢驗(yàn):參數(shù)估計(jì)表獲?。篋urbin-Watsonstat

1.3