自相关的操作过程.docx

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t t t运用软件结果如下：Dependent Variable: YMethod: Least SquaresDate: 01/03/04 Time: 08:10Sample: 1989 2004Included observations: 16VariableCoefficie ntStd. Errort-StatisticProb.C-6129.8172174.074-2.8195070.0136X0.3298620.02856411.548210.0000R-squared0.904995Mean dependent var15982.63Adjusted R-squared0.898209S.D. dependent var12908.99S.E. of regression4118.567Akaike info criterion19.60087Sum squared resid2.37E+08Schwarz criterion19.69744Log likelihood-154.8069F-statistic133.3613Durb in-Wats on stat0.422426Prob(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=p et_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VariableCoefficie ntStd. Error t-StatisticProb.E(-1)0.9818050.229645 4.2753210.0008R-squared0.565485Mean dependent var-167.2139Adjusted R-squared0.565485S.D. dependent var4059.960S.E. of regression2676.235Akaike info criterion18.68655Sum squared resid1.00E+08Schwarz criterion18.73375Log likelihood-139.1491Durb in-Wats on stat0.750574= =Dependent Variable: EMethod: Least Squares Date: 01/03/04 Time: 08:19Sample(adjusted): 1990 2004In eluded observatio ns: 15 after adjust ing en dpo ints后k阶变量。

可写出模型为et = 0.9818et_1，因为e t-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 + B x + P x + …+ P x + u (1)t 1 1t 2 2 t k kt t我们怀疑假随机项存在P阶自相关：u = p u +p u + p u + vt 1 t -1 2 t - 2 p t - p t作约束回归y = a + P x + P x + •…+ P x + p u + p u + •…+ p u + vt 1 1t 2 2t k kt 1 t-1 2 t-2 p t- p t原假设：H : p二 =p = 00 1 p在原假设成立的条件下，统计量LM 二 nR2 〜咒 2(P)其中R 2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-Godfrey Serial Correlatio n LM Test:F-statistic 17.52167 Probability 0.000275Obs*R-squared(LM Probability 0.002582统计量)Test Equation:Dependent Variable: RESID Method: Least SquaresDate: 01/03/04Time: 08:33VariableCoefficie ntStd. 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-squared0.744916Mean dependent var4.09E-12Adjusted R-squared0.681145S.D. dependent var3978.914S.E. of regression2246.783Akaike info criterion18.48470Sum squared resid60576395Schwarz criterion18.67785Log likelihood-143.8776F-statistic11.68111Durb in-Wats on stat1.985929Prob(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』・7 8 8 8在小样本情况下，可以通过小样本计算公式a dw (k +1)2 1 — +p 2 I n 丿p = ♦ ( k +1)21 —I n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 t t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：J y；=』1土人x* = Jl — p 2 xJ 1 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Dependent Variable: Y1Method: Least Squares Date: 01/01/04 Time: 00:45Sample: 1989 2004Included observations: 16VariableCoefficie ntStd. Errort-StatisticProb.C-4156.4841266.885-3.2808690.0055X10.4832380.0556518.6834070.0000R-squared0.843403Mean dependent var5749.213Adjusted R-squared0.832218S.D. dependent var5381.228S.E. of regression2204.218Akaike info criterion18.35060Sum squared resid68020055Schwarz criterion18.44718Log likelihood-144.8048F-statistic75.40156Durb in-Wats on stat0.990666Prob(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Y C X AR（1） 结果如下Dependent Variable: YMethod: Least Squares Date: 01/01/04 Time: 00:51Sample(adjusted): 1990 2004Included observations: 15 after adjusting endpointsCon verge nee achieved after 8 iterati onsVariableCoefficie ntStd. Error t-StatisticProb.C-633.51131751.326 -0.3617320.7238X0.1863110.039676 4.6957660.0005AR⑴1.5933230.172976 9.2112240.0000R-squared0.979506Mean dependent var16917.73Adjusted R-squared0.976090S.D. dependent var12788.86S.E. of regression1977.521Akaike info criterion18.19393Sum squared resid46927071Schwarz criterion18.33554Log likelihood-133.4545F-statistic286.7653Durb in-Wats on stat2.588021Prob(F-statistic)0.000000Inverted AR Roots1.59Estimated AR process is non stati on ary从表格可以看出，DW统计量的值为2.5880,而不存在自相关的区间是，可以判断出其不存在自相关。