自相關操作過程分析一、自相關的檢驗方法1：DW檢驗考察模型y二a+氐+U，我們懷疑隨機項存在自相關。ttt運用軟件結果如下：DependentVariable:YMethod:LeastSquaresDate:01/03/04Time:08:10Sample:19892004Includedobservations:16VariableCoefficientStd.Errort-StatisticProb.C-6129.8172174.074-2.8195070.0136X0.3298620.02856411.548210.0000R-squared0.904995Meandependentvar15982.63AdjustedR-squared0.898209S.D.dependentvar12908.99S.E.ofregression4118.567Akaikeinfocriterion19.60087Sumsquaredresid2.37E+08Schwarzcriterion19.69744Loglikelihood-154.8069F-statistic133.3613Durbin-Watsonstat0.422426Prob(F-statistic)0.000000從表中可以看出,DW統計量為dw=0.4224,查表可得臨界值為d—1.10,d—1.37，所以可以判斷模型的隨機項存在正的自相關。LU方法2：直接檢驗法(回歸檢驗法)一階自相關形式為：Ut=卩Ut_i+Vt即對模型e=pet_i+vt進行回歸，進行t檢驗，判斷系數是

否為0.結果如下：在EVIEW軟件中常用X(-k)表示變量的X的滯VariableCoefficientStd.Errort-StatisticProb.E(-1)VariableCoefficientStd.Errort-StatisticProb.E(-1)0.9818050.229645 4.2753210.0008R-squared0.565485Meandependentvar-167.2139AdjustedR-squared0.565485S.D.dependentvar4059.960S.E.ofregression2676.235Akaikeinfocriterion18.68655Sumsquaredresid1.00E+08Schwarzcriterion18.73375Loglikelihood-139.1491Durbin-Watsonstat0.750574==DependentVariable:EMethod:LeastSquaresDate:01/03/04Time:08:19Sample(adjusted):19902004Ineludedobservations:15afteradjustingendpoints可寫出模型為et=0.9818et_1，因為et-的系數的T檢驗的犯錯概率為0.0008，遠遠地小于0.05，這說明系數顯著地不為0。即模型存在自相關。3.GB檢驗考慮模型y二a+Bx+Px+…+Px+u(1)t 11t22t kktt我們懷疑假隨機項存在P階自相關：u=pu+pu+ pu+vt1t-1 2t-2 pt-p t作約束回歸y=a+Px+Px+?…+Px+pu+pu+?…+pu+vt 11t 22t kkt1t-1 2t-2 pt-pt原假設：H:p二=p=001p在原假設成立的條件下，統計量LM二nR2?咒2(P)其中R2是約束回歸模型(3)的擬合優度；注意點：GB檢驗必須在對(1)式回歸結果的界面上才能做。二階的LM檢驗結果如下：Breusch-GodfreySerialCorrelationLMTest:F-statistic 17.52167Probability 0.000275Obs*R-squared(LM Probability 0.002582統計量)TestEquation:DependentVariable:RESIDMethod:LeastSquaresDate:01/03/04Time:08:33VariableCoefficientStd.Errort-StatisticProb.C-1543.7871500.693-1.0287160.3239X0.0319530.0237281.3466560.2030RESID(-1)1.4715120.2953624.9820680.0003RESID(-2)-0.3821670.425863-0.8973960.3872R-squared0.744916Meandependentvar4.09E-12AdjustedR-squared0.681145S.D.dependentvar3978.914S.E.ofregression2246.783Akaikeinfocriterion18.48470Sumsquaredresid60576395Schwarzcriterion18.67785Loglikelihood-143.8776F-statistic11.68111Durbin-Watsonstat1.985929Prob(F-statistic)0.000714從表中可以看出：LM=nR2二16x0.744916二11.91866，其犯錯誤的概率為0.00258,小于0.05，所以存在自相關。從RESID(-1)和RESID(-2)的系數檢驗可以看出,存在一階自相關,但是不存在二階自相關。第二部分，模型自相關的消除（方法是廣義差分法）第一步，求出自相關系數-1-dw二1-于2』。?7888在小樣本情況下，可以通過小樣本計算公式adw(k+1)21—+p 2In丿p= ?(k+1)21—In丿第二步，進行廣義差分變換消除自相關y*=y-pyt t t—1<x*=x—pxt t t-1a*=a(1—p)這樣可得到差分變化后的模型y*=a*+Px*+v （4丿t tt注意：廣義差分變換會造成丟失數據，在小樣本情況下，可通過普瑞斯變化彌補：Jy；=』1土人x*=Jl—p2xJ1 十 1對廣義差分變換后的模型（4）進行OLS估計，得到結果如下DependentVariable:Y1Method:LeastSquaresDate:01/01/04Time:00:45Sample:19892004Includedobservations:16VariableCoefficientStd.Errort-StatisticProb.C-4156.4841266.885-3.2808690.0055X10.4832380.0556518.6834070.0000R-squared0.843403Meandependentvar5749.213AdjustedR-squared0.832218S.D.dependentvar5381.228S.E.ofregression2204.218Akaikeinfocriterion18.35060Sumsquaredresid68020055Schwarzcriterion18.44718Loglikelihood-144.8048F-statistic75.40156Durbin-Watsonstat0.990666Prob(F-statistic)0.000001很遺憾，DW統計量的值為0.9907仍然小于臨界值1.10，所以仍然存在正的自相關。在軟件中，可以用命令語句直接進行廣義差分變換消除自相關。加入模型存在一階自相關，則菜單命令語句為YCXAR（1）結果如下DependentVariable:YMethod:LeastSquaresDate:01/01/04Time:00:51Sample(adjusted):19902004Includedobservations:15afteradjustingendpointsConvergeneeachievedafter8iterationsVariableCoefficientStd.Errort-StatisticProb.C-633.51131751.326 -0.3617320.7238X0.1863110.039676 4.6957660.0005AR⑴1.5933230.172976 9.2112240.0000R-squared0.979506Meandependentvar16917.73AdjustedR-squared0.976090S.D.dependentvar12788.86S.E.ofregression1977.521Akaikeinfocriterion18.19393Sumsquaredresid46927071Schwarzcriterion