自相关的操作过程

自相关操作过程分析一、自相关的检验方法1：DW检验考察模型y二a+氐+U，我们怀疑随机项存在自相关。ttt运用软件结果如下：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从表中可以看出,DW统计量为dw=0.4224,查表可得临界值为d—1.10,d—1.37，所以可以判断模型的随机项存在正的自相关。LU方法2：直接检验法(回归检验法)一阶自相关形式为：Ut=卩Ut_i+Vt即对模型e=pet_i+vt进行回归，进行t检验，判断系数是

否为0.结果如下：在EVIEW软件中常用X(-k)表示变量的X的滞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可写出模型为et=0.9818et_1，因为et-的系数的T检验的犯错概率为0.0008，远远地小于0.05，这说明系数显著地不为0。即模型存在自相关。3.GB检验考虑模型y二a+Bx+Px+…+Px+u(1)t 11t22t kktt我们怀疑假随机项存在P阶自相关：u=pu+pu+ pu+vt1t-1 2t-2 pt-p t作约束回归y=a+Px+Px+•…+Px+pu+pu+•…+pu+vt 11t 22t kkt1t-1 2t-2 pt-pt原假设：H:p二=p=001p在原假设成立的条件下，统计量LM二nR2〜咒2(P)其中R2是约束回归模型(3)的拟合优度；注意点：GB检验必须在对(1)式回归结果的界面上才能做。二阶的LM检验结果如下：Breusch-GodfreySerialCorrelationLMTest:F-statistic 17.52167Probability 0.000275Obs*R-squared(LM Probability 0.002582统计量)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从表中可以看出：LM=nR2二16x0.744916二11.91866，其犯错误的概率为0.00258,小于0.05，所以存在自相关。从RESID(-1)和RESID(-2)的系数检验可以看出,存在一阶自相关,但是不存在二阶自相关。第二部分，模型自相关的消除（方法是广义差分法）第一步，求出自相关系数-1-dw二1-于2』。・7888在小样本情况下，可以通过小样本计算公式adw(k+1)21—+p 2In丿p= ♦(k+1)21—In丿第二步，进行广义差分变换消除自相关y*=y-pyt t t—1<x*=x—pxt t t-1a*=a(1—p)这样可得到差分变化后的模型y*=a*+Px*+v （4丿t tt注意：广义差分变换会造成丢失数据，在小样本情况下，可通过普瑞斯变化弥补：Jy；=』1土人x*=Jl—p2xJ1 十 1对广义差分变换后的模型（4）进行OLS估计，得到结果如下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很遗憾，DW统计量的值为0.9907仍然小于临界值1.10，所以仍然存在正的自相关。在软件中，可以用命令语句直接进行广义差分变换消除自相关。加入模型存在一阶自相关，则菜单命令语句为YCXAR（1）结果如下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