下面是对某时间序列建立残差自回归模型时某软件输出结果:
Ordinary Least Squares Estimates
SSE 15464.5248 DFE 40
MSE 386.61312 Root MSE 19.66248
SBC 374.828818 AIC 371.353479
Regress R-Square 0.8300 Total R-Square 0.8300
Durbin-Watson 0.7628 Pr < DW <.0001
Pr > DW 1.0000
NOTE: Pr<DW is the p-value for testing positive autocorrelation, and Pr>DW is the p-value for testing negative autocorrelation.
Standard Approx
Variable DF Estimate Error t Value Pr > |t|
Intercept 1 -20.9102 6.1780 -3.38 0.0016
t 1 3.4977 0.2503 13.97 <.0001
Estimates of 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
0 368.2 1.000000 | |********************|
1 221.9 0.602573 | |************ |
2 116.1 0.315203 | |****** |
3 57.6301 0.156517 | |*** |
4 21.8145 0.059246 | |* | 5 74.8644 0.203324 | |**** |
Backward Elimination of
Autoregressive Terms
Lag Estimate t Value Pr > |t|
3 -0.035768 -0.19 0.8537
2 0.061250 0.37 0.7132
4 0.216740 1.37 0.1801
5 -0.168214 -1.33 0.1925
Preliminary MSE 234.5
The SAS System 19:39 Thursday, May 16, 2012 6
The AUTOREG Procedure
Estimates of Autoregressive Parameters
Standard
Lag Coefficient Error t Value
1 -0.602573 0.127793 -4.72
Maximum Likelihood Estimates
SSE 9642.40686 DFE 39
MSE 247.24120 Root MSE 15.72391
SBC 359.191925 AIC 353.978916
Regress R-Square 0.5767 Total R-Square 0.8940
Durbin-Watson 1.6564
Standard Approx
Variable DF Estimate Error t Value Pr > |t|
Intercept 1 -17.5396 11.5883 -1.51 0.1382
t 1 3.3597 0.4613 7.28 <.0001
AR1 1 -0.6100 0.1255 -4.86 <.0001
Autoregressive parameters assumed given.
Standard Approx
Variable DF Estimate Error t Value Pr > |t|
Intercept 1 -17.5396 11.5857 -1.51 0.1381
t 1 3.3597 0.4609 7.29 <.0001
Maximum Likelihood Estimates
SSE 10037.807 DFE 40
MSE 250.94518 Root MSE 15.84125
SBC 357.318944 AIC 353.843605
Regress R-Square 0.6876 Total R-Square 0.9533
Durbin-Watson 1.6975
NOTE: No intercept term is used. R-squares are redefined.
Standard Approx
Variable DF Estimate Error t Value Pr > |t|
t 1 2.7638 0.2948 9.38 <.0001
AR1 1 -0.6883 0.1124 -6.12 <.0001
Autoregressive parameters assumed given.
Standard Approx
Variable DF Estimate Error t Value Pr > |t|
t 1 2.7638 0.2946 9.38 <.0001
(1)写出因变量关于时间的回归模型并说明拟合效果;
(2)写出关于残差的自回归模型并说明理由;
(3)写出最终模型的口径.