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shaode01

发表于 2011-7-18 20:25:27 |AI写论文

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data a;
input year x y;
cards;
1987  357.4 12925
1988  364.79 14022
1989  371.39 15196
1990  380.88 16117
1991  386.1 16664
1992  392.16 21888
1993  397.08 23599
1994  402.71 16666
1995  411.11 17788
1996  416.47 18427
1997  422.31 18815
1998  425.98 18602
1999  429.95 18592
2000  438.18 19795
2001  442.16 20019
2002  448.1 20459
2003  456.6 19834
2004  444.68 20690
2005  455.7 20713
2006  469.85 23791
2007  478.9 24681
2008  486.73 25830
2009  491.43 27713
;
proc gplot data=a;
plot x*year=1 y*year=2;
symbol1 c=black i=join v=circle;
symbol2 c=black i=join v=star;
proc arima data=a;
identify var=x stationarity=(adf);
identify var=y stationarity=(adf);

proc arima data=a;
identify var=y crosscorr=x;
estimate  input=x  plot;
forecast lead=0 id=year out=result;
proc arima data=result;
identify var=residual stationarity=(adf=2);

run;

要求如题。我想探究y和x之间的关系，做了回归，检验了残差序列，如果有不妥当的地方，敬请指出！我会追加奖赏，谢谢大家！

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pinggu2688 查看完整内容

Correlation of y and x Variance of input = 1463.115 Number of Observations 23 09:26 Sunday, July 18, 2011 5 The ARIMA Procedure Crosscorrelations ...

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关键词：stationarity crosscorr identify Residual Forecast 程序残差

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pinggu2688 发表于 2011-7-18 20:25:28

Correlation of y and x

                              Variance of input =    1463.115
                              Number of Observations       23
                                                                     09:26 Sunday, July 18, 2011 5

                                       The ARIMA Procedure

                                       Crosscorrelations

         Lag Covariance Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1

         -5    23769.269       0.17087 |          .    |*** .          |
         -4    32323.798       0.23236 |          .    |*****  .          |
         -3    49582.091       0.35642 |          .    |*******.          |
         -2    69256.129       0.49785 |          .    |**********       |
         -1    90824.964       0.65290 |          .    |*************    |
         0       116493       0.83741 |          .    |***************** |
         1    94296.098       0.67785 |          .    |**************    |
         2    71768.333       0.51591 |          .    |**********       |
         3    52968.991       0.38077 |          .    |********          |
         4    36039.380       0.25907 |          .    |*****  .          |
         5    23850.579       0.17145 |          .    |*** .          |

                                 "." marks two standard errors

                              Conditional Least Squares Estimation

                                 Standard                Approx
   Parameter    Estimate       Error t Value Pr > |t|    Lag Variable Shift

   MU          -14135.4       4836.9    -2.92    0.0081    0 y             0
   NUM1          79.62002    11.34016    7.02    <.0001    0 x             0

                                 Constant Estimate    -14135.4
                                 Variance Estimate    4327575
                                 Std Error Estimate    2080.283
                                 AIC                   418.6307
                                 SBC                   420.9017
                                 Number of Residuals       23
                        * AIC and SBC do not include log determinant.

                              Correlations of Parameter Estimates

                              Variable                y       x
                              Parameter             MU    NUM1

                              y             MU    1.000 -0.996
                              x          NUM1 -0.996    1.000

                                                                     09:26 Sunday, July 18, 2011 6

                                       The ARIMA Procedure

                              Autocorrelation Check of Residuals

   To       Chi-          Pr >
   Lag    Square    DF    ChiSq --------------------Autocorrelations--------------------

   6       9.12    6 0.1670    0.440    0.043 -0.005 -0.095 -0.208 -0.264
   12    15.47    12 0.2169 -0.115 -0.113 -0.123 -0.240 -0.163 -0.134
   18    26.68    18 0.0851 -0.050    0.065    0.123    0.293    0.165    0.016

                              Autocorrelation Plot of Residuals

Lag Covariance Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1    Std Error

   0    4327575       1.00000 |                   |********************|          0
   1    1904251       0.44003 |          .    |*********          |    0.208514
   2       186048       0.04299 |       .       |*       .       |    0.245591
   3 -21484.611       -.00496 |       .       |       .       |    0.245918
   4    -410964       -.09496 |       .    **|       .       |    0.245923
   5    -900754       -.20814 |       .    ****|       .       |    0.247512

                                 "." marks two standard errors

                                    Inverse Autocorrelations

               Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1

                  1    -0.49456 |       **********|    .          |
                  2       0.21924 |          .    |**** .          |
                  3    -0.09044 |          .    **|    .          |
                  4       0.00447 |          .    |    .          |
                  5       0.09581 |          .    |**    .          |

                                    Partial Autocorrelations

               Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1

                  1       0.44003 |          .    |*********          |
                  2    -0.18680 |          . ****|    .          |
                  3       0.07039 |          .    |*    .          |
                  4    -0.14679 |          . ***|    .          |
                  5    -0.13120 |          . ***|    .          |

                                    Model for variable y

                                 Estimated Intercept -14135.4
                                                                     09:26 Sunday, July 18, 2011 7

                                       The ARIMA Procedure

                                       Input Number 1

                              Input Variable                   x
                              Overall Regression Factor 79.62002
                                                                     09:26 Sunday, July 18, 2011 8

                                       The ARIMA Procedure

                                 Name of Variable = RESIDUAL

                              Mean of Working Series -1.04E-9
                              Standard Deviation       1987.779
                              Number of Observations       23

                                       Autocorrelations

Lag Covariance Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1    Std Error

   0    3951265       1.00000 |                   |********************|          0
   1    1738664       0.44003 |          .    |*********          |    0.208514
   2       169870       0.04299 |       .       |*       .       |    0.245591
   3 -19616.384       -.00496 |       .       |       .       |    0.245918
   4    -375228       -.09496 |       .    **|       .       |    0.245923
   5    -822428       -.20814 |       .    ****|       .       |    0.247512

                                 "." marks two standard errors

                                    Inverse Autocorrelations

               Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1

                  1    -0.49456 |       **********|    .          |
                  2       0.21924 |          .    |**** .          |
                  3    -0.09044 |          .    **|    .          |
                  4       0.00447 |          .    |    .          |
                  5       0.09581 |          .    |**    .          |

                                    Partial Autocorrelations

               Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1

                  1       0.44003 |          .    |*********          |
                  2    -0.18680 |          . ****|    .          |
                  3       0.07039 |          .    |*    .          |
                  4    -0.14679 |          . ***|    .          |
                  5    -0.13120 |          . ***|    .          |

                                                                     09:26 Sunday, July 18, 2011 9

                                       The ARIMA Procedure

                           Augmented Dickey-Fuller Unit Root Tests

   Type          Lags       Rho Pr < Rho       Tau Pr < Tau       F Pr > F

   Zero Mean       0 -11.4610    0.0111    -2.61    0.0115
                     1 -16.8960    0.0011    -2.62    0.0115
                     2 -12.4162    0.0071    -1.87    0.0600
   Single Mean    0 -11.3726    0.0582    -2.53    0.1221    3.31 0.2867
                     1 -16.6566    0.0076    -2.53    0.1235    3.29 0.2916
                     2 -12.0525    0.0428    -1.78    0.3786    1.69 0.6613
   Trend          0 -11.4295    0.2460    -2.45    0.3450    3.04 0.6006
                     1 -17.3470    0.0408    -2.45    0.3449    3.07 0.5967
                     2 -13.2258    0.1462    -1.69    0.7171    1.52 0.8660

藤椅

pinggu2688 发表于 2011-7-19 01:06:49

结果分两段:
The ARIMA Procedure

                                       Name of Variable = x

                              Mean of Working Series 424.8113
                              Standard Deviation       38.25068
                              Number of Observations       23

                                       Autocorrelations

Lag Covariance Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1    Std Error

   0    1463.115       1.00000 |                   |********************|          0
   1    1239.784       0.84736 |          .    |***************** |    0.208514
   2    1020.932       0.69778 |    .          |**************    |    0.325445
   3    817.092       0.55846 |    .             |*********** .    |    0.385037
   4    638.743       0.43656 | .             |*********    . |    0.418776
   5    495.902       0.33894 |  .                |*******       .  |    0.438117

                                 "." marks two standard errors

                                    Inverse Autocorrelations

               Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1

                  1    -0.50877 |       **********|    .          |
                  2       0.00098 |          .    |    .          |
                  3       0.00048 |          .    |    .          |
                  4       0.01726 |          .    |    .          |
                  5    -0.00141 |          .    |    .          |

                                    Partial Autocorrelations

               Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1

                  1       0.84736 |          .    |***************** |
                  2    -0.07177 |          .    *|    .          |
                  3    -0.05144 |          .    *|    .          |
                  4    -0.02675 |          .    *|    .          |
                  5       0.00256 |          .    |    .          |

                                                                     09:26 Sunday, July 18, 2011 2

                                       The ARIMA Procedure

                           Augmented Dickey-Fuller Unit Root Tests

   Type          Lags       Rho Pr < Rho       Tau Pr < Tau       F Pr > F

   Zero Mean       0    0.3138    0.7492    5.87    0.9999
                     1    0.2961    0.7437    3.84    0.9999
                     2    0.2798    0.7385    3.47    0.9995
   Single Mean    0    -0.2220    0.9348    -0.35    0.9012    17.38 0.0010
                     1    -0.1221    0.9405    -0.21    0.9235    7.43 0.0078
                     2    -0.0516    0.9440    -0.10    0.9364    6.06 0.0305
   Trend          0 -12.9501    0.1670    -2.85    0.1971    4.05 0.4240
                     1 -20.7250    0.0109    -2.86    0.1944    4.09 0.4187
                     2 -37.1711    <.0001    -2.60    0.2842    3.38 0.5414

                                       Name of Variable = y

                              Mean of Working Series 19688.09
                              Standard Deviation       3636.82
                              Number of Observations       23

                                       Autocorrelations

Lag Covariance Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1    Std Error

   0    13226457       1.00000 |                   |********************|          0
   1    8618586       0.65162 |          .    |*************    |    0.208514
   2    4926195       0.37245 |       .       |******* .       |    0.283550
   3    2965674       0.22422 |       .          |****    .       |    0.304077
   4    1018638       0.07702 |       .          |**       .       |    0.311183
   5    -174629       -.01320 |       .          |          .       |    0.312010

                                 "." marks two standard errors

                                    Inverse Autocorrelations

               Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1

                  1    -0.53349 |       ***********|    .          |
                  2       0.13627 |          .    |*** .          |
                  3    -0.11207 |          .    **|    .          |
                  4       0.05296 |          .    |*    .          |
                  5       0.01196 |          .    |    .          |
                                                                     09:26 Sunday, July 18, 2011 3

                                       The ARIMA Procedure

                                    Partial Autocorrelations

               Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1

                  1       0.65162 |          .    |*************    |
                  2    -0.09064 |          .    **|    .          |
                  3       0.03258 |          .    |*    .          |
                  4    -0.10849 |          .    **|    .          |
                  5    -0.01851 |          .    |    .          |

                           Augmented Dickey-Fuller Unit Root Tests

   Type          Lags       Rho Pr < Rho       Tau Pr < Tau       F Pr > F

   Zero Mean       0    0.6496    0.8292    1.28    0.9440
                     1    0.6087    0.8188    1.21    0.9368
                     2    0.5847    0.8126    1.59    0.9679
   Single Mean    0    -3.3609    0.5893    -1.13    0.6842    1.79 0.6369
                     1    -3.7129    0.5431    -1.04    0.7182    1.53 0.6963
                     2    -1.6532    0.8031    -0.54    0.8632    1.53 0.6979
   Trend          0 -10.4168    0.3110    -2.30    0.4170    2.67 0.6653
                     1 -16.6613    0.0519    -2.38    0.3778    2.89 0.6272
                     2 -12.9794    0.1568    -1.65    0.7370    1.45 0.8791
                                                                     09:26 Sunday, July 18, 2011 4

                                       The ARIMA Procedure

                                       Name of Variable = y

                              Mean of Working Series 19688.09
                              Standard Deviation       3636.82
                              Number of Observations       23

                                       Autocorrelations

Lag Covariance Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1    Std Error

   0    13226457       1.00000 |                   |********************|          0
   1    8618586       0.65162 |          .    |*************    |    0.208514
   2    4926195       0.37245 |       .       |******* .       |    0.283550
   3    2965674       0.22422 |       .          |****    .       |    0.304077
   4    1018638       0.07702 |       .          |**       .       |    0.311183
   5    -174629       -.01320 |       .          |          .       |    0.312010

                                 "." marks two standard errors

                                    Inverse Autocorrelations

               Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1

                  1    -0.53349 |       ***********|    .          |
                  2       0.13627 |          .    |*** .          |
                  3    -0.11207 |          .    **|    .          |
                  4       0.05296 |          .    |*    .          |
                  5       0.01196 |          .    |    .          |

                                    Partial Autocorrelations

               Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1

                  1       0.65162 |          .    |*************    |
                  2    -0.09064 |          .    **|    .          |
                  3       0.03258 |          .    |*    .          |
                  4    -0.10849 |          .    **|    .          |
                  5    -0.01851 |          .    |    .          |

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