STEPWISE AUTOREGRESSION TO DETERMINE ORDER, 'New Mexico' ED DATA
ITS MODEL: Using ALL Trend-Cycle Component data points with PRESLOPE, INTERVENTION, & POSTSLOPE as predictors

INTERPRETING OUTPUT:
    **Stepwise autoregression method initially fits a high-order model with many autoregressive lags, then sequentially removes autoregressive parameters until all remaining parameters have significant t tests.
    **The BACKWARD ELIMINATION OF AUTOREGRESSIVE TERMS report shows which autoregressive parameters (at which lags) were insignificant and eliminated
    **Look at the Retained autoregressive parameters help determine the autoregressive 'order' for your final model- ESTIMATES OF AUROTREGRESSIVE PARAMETERS report
Variable Name=H1

Dependent Variable TCC
  Trend-Cycle Component


STEPWISE AUTOREGRESSION TO DETERMINE ORDER, 'New Mexico' ED DATA
Backwards Stepwise Regression to Determine Order of Autocorrelation

The AUTOREG Procedure

Variable Name=H1

Ordinary Least Squares Estimates
SSE 19944.0258 DFE 68
MSE 293.29450 Root MSE 17.12584
SBC 626.363167 AIC 617.256502
MAE 13.509841 AICC 617.853517
MAPE 3.07764963 HQC 620.881892
Durbin-Watson 0.0941 Regress R-Square 0.5290
    Total R-Square 0.5290

Parameter Estimates
Variable DF Estimate Standard
Error		 t Value Approx
Pr > |t|
Intercept 1 449.2448 4.9986 89.87 <.0001
PRESLOPE 1 -0.2651 0.1187 -2.23 0.0287
INTERVENTION 1 -20.9603 13.1522 -1.59 0.1156
POSTSLOPE 1 -4.2111 2.2109 -1.90 0.0611

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 
0 277.0 1.000000 |                    |********************|
1 255.7 0.923201 |                    |******************  |
2 222.3 0.802370 |                    |****************    |
3 178.0 0.642721 |                    |*************       |
4 128.1 0.462570 |                    |*********           |
5 78.3178 0.282736 |                    |******              |
6 30.1477 0.108836 |                    |**                  |
7 -15.3782 -0.055517 |                   *|                    |
8 -56.0229 -0.202249 |                ****|                    |
9 -91.8271 -0.331505 |             *******|                    |
10 -118.6 -0.428224 |           *********|                    |
11 -136.4 -0.492282 |          **********|                    |
12 -143.9 -0.519600 |          **********|                    |
13 -141.6 -0.511032 |          **********|                    |

Backward Elimination of Autoregressive
Terms
Lag Estimate t Value Pr > |t|
12 0.002056 0.01 0.9917
2 0.003407 0.02 0.9861
13 -0.003183 -0.04 0.9722
5 -0.022385 -0.12 0.9076
10 -0.026149 -0.14 0.8906
11 0.007170 0.08 0.9357
7 0.028465 0.15 0.8787
8 -0.016126 -0.10 0.9198
6 -0.037062 -0.35 0.7286
4 0.085087 0.66 0.5114
9 0.093229 1.93 0.0580

Preliminary MSE 33.4401

Estimates of Autoregressive Parameters
Lag Coefficient Standard
Error		 t Value
1 -1.144016 0.071659 -15.96
3 0.275203 0.071659 3.84

Expected Autocorrelations
Lag Autocorr
0 1.0000
1 0.9233
2 0.8021
3 0.6425

Algorithm converged.


STEPWISE AUTOREGRESSION TO DETERMINE ORDER, 'New Mexico' ED DATA
Backwards Stepwise Regression to Determine Order of Autocorrelation

The AUTOREG Procedure

Variable Name=H1

Maximum Likelihood Estimates
SSE 360.369844 DFE 66
MSE 5.46015 Root MSE 2.33670
SBC 352.08332 AIC 338.423324
MAE 1.84673078 AICC 339.715631
MAPE 0.43322392 HQC 343.861409
Log Likelihood -163.21166 Regress R-Square 0.1106
Durbin-Watson 1.6936 Total R-Square 0.9915
    Observations 72

Parameter Estimates
Variable DF Estimate Standard
Error		 t Value Approx
Pr > |t|
Intercept 1 446.5818 9.3399 47.81 <.0001
PRESLOPE 1 -0.2937 0.2196 -1.34 0.1856
INTERVENTION 1 -0.7764 2.3478 -0.33 0.7419
POSTSLOPE 1 -2.5432 2.0820 -1.22 0.2262
AR1 1 -1.3966 0.0290 -48.09 <.0001
AR3 1 0.4696 0.0281 16.73 <.0001

Expected Autocorrelations
Lag Autocorr
0 1.0000
1 0.9730
2 0.9020
3 0.7902

Autoregressive parameters assumed given
Variable DF Estimate Standard
Error		 t Value Approx
Pr > |t|
Intercept 1 446.5818 9.2813 48.12 <.0001
PRESLOPE 1 -0.2937 0.2174 -1.35 0.1813
INTERVENTION 1 -0.7764 2.3147 -0.34 0.7384
POSTSLOPE 1 -2.5432 1.8685 -1.36 0.1781


STEPWISE AUTOREGRESSION TO DETERMINE ORDER, 'New Mexico' ED DATA
Backwards Stepwise Regression to Determine Order of Autocorrelation

The AUTOREG Procedure

Variable Name=H2

Dependent Variable TCC
  Trend-Cycle Component


STEPWISE AUTOREGRESSION TO DETERMINE ORDER, 'New Mexico' ED DATA
Backwards Stepwise Regression to Determine Order of Autocorrelation

The AUTOREG Procedure

Variable Name=H2

Ordinary Least Squares Estimates
SSE 441.032389 DFE 68
MSE 6.48577 Root MSE 2.54672
SBC 351.930371 AIC 342.823707
MAE 1.90082369 AICC 343.420722
MAPE 4.15834553 HQC 346.449097
Durbin-Watson 0.3567 Regress R-Square 0.8232
    Total R-Square 0.8232

Parameter Estimates
Variable DF Estimate Standard
Error		 t Value Approx
Pr > |t|
Intercept 1 43.7566 0.7433 58.87 <.0001
PRESLOPE 1 0.0129 0.0176 0.73 0.4685
INTERVENTION 1 11.4670 1.9558 5.86 <.0001
POSTSLOPE 1 0.8222 0.3288 2.50 0.0148

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 6.1254 1.000000 |                    |********************|
1 5.0046 0.817018 |                    |****************    |
2 3.9049 0.637482 |                    |*************       |
3 3.1722 0.517864 |                    |**********          |
4 2.6020 0.424784 |                    |********            |
5 2.0816 0.339825 |                    |*******             |
6 1.8156 0.296398 |                    |******              |
7 1.4757 0.240919 |                    |*****               |
8 0.7771 0.126857 |                    |***                 |
9 0.0952 0.015537 |                    |                    |
10 -0.1927 -0.031463 |                   *|                    |
11 -0.3680 -0.060073 |                   *|                    |
12 -0.4644 -0.075809 |                  **|                    |
13 -0.4813 -0.078578 |                  **|                    |

Backward Elimination of Autoregressive
Terms
Lag Estimate t Value Pr > |t|
13 0.003064 0.02 0.9820
12 -0.016215 -0.12 0.9038
11 0.014277 0.11 0.9145
4 -0.027685 -0.16 0.8740
3 -0.064291 -0.45 0.6539
5 0.046856 0.35 0.7258
6 -0.065755 -0.51 0.6151
2 0.068182 0.54 0.5942
10 -0.074099 -0.59 0.5547
9 0.079444 0.65 0.5212
7 -0.168183 -1.36 0.1773
8 0.074290 1.02 0.3096

Preliminary MSE 2.0366

Estimates of Autoregressive Parameters
Lag Coefficient Standard
Error		 t Value
1 -0.817018 0.070444 -11.60

Algorithm converged.


STEPWISE AUTOREGRESSION TO DETERMINE ORDER, 'New Mexico' ED DATA
Backwards Stepwise Regression to Determine Order of Autocorrelation

The AUTOREG Procedure

Variable Name=H2

Maximum Likelihood Estimates
SSE 42.5173362 DFE 67
MSE 0.63459 Root MSE 0.79661
SBC 190.826285 AIC 179.442955
MAE 0.6130956 AICC 180.352045
MAPE 1.32673828 HQC 183.974692
Log Likelihood -84.721477 Regress R-Square 0.2866
Durbin-Watson 0.5739 Total R-Square 0.9830
    Observations 72

Parameter Estimates
Variable DF Estimate Standard
Error		 t Value Approx
Pr > |t|
Intercept 1 40.0167 4.2347 9.45 <.0001
PRESLOPE 1 0.1671 0.0978 1.71 0.0920
INTERVENTION 1 0.7852 0.8551 0.92 0.3618
POSTSLOPE 1 0.9367 0.3138 2.99 0.0040
AR1 1 -0.9758 0.0310 -31.43 <.0001

Autoregressive parameters assumed given
Variable DF Estimate Standard
Error		 t Value Approx
Pr > |t|
Intercept 1 40.0167 3.9153 10.22 <.0001
PRESLOPE 1 0.1671 0.0733 2.28 0.0259
INTERVENTION 1 0.7852 0.8547 0.92 0.3615
POSTSLOPE 1 0.9367 0.2712 3.45 0.0010


STEPWISE AUTOREGRESSION TO DETERMINE ORDER, 'New Mexico' ED DATA
Backwards Stepwise Regression to Determine Order of Autocorrelation

The AUTOREG Procedure

Variable Name=H3

Dependent Variable TCC
  Trend-Cycle Component


STEPWISE AUTOREGRESSION TO DETERMINE ORDER, 'New Mexico' ED DATA
Backwards Stepwise Regression to Determine Order of Autocorrelation

The AUTOREG Procedure

Variable Name=H3

Ordinary Least Squares Estimates
SSE 187.946525 DFE 68
MSE 2.76392 Root MSE 1.66250
SBC 290.517191 AIC 281.410527
MAE 1.33571013 AICC 282.007542
MAPE 3.36027311 HQC 285.035917
Durbin-Watson 0.2414 Regress R-Square 0.9335
    Total R-Square 0.9335

Parameter Estimates
Variable DF Estimate Standard
Error		 t Value Approx
Pr > |t|
Intercept 1 30.2054 0.4852 62.25 <.0001
PRESLOPE 1 0.2581 0.0115 22.41 <.0001
INTERVENTION 1 5.3305 1.2768 4.18 <.0001
POSTSLOPE 1 -0.1479 0.2146 -0.69 0.4931

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 2.6104 1.000000 |                    |********************|
1 2.2378 0.857268 |                    |*****************   |
2 1.7899 0.685686 |                    |**************      |
3 1.4201 0.544022 |                    |***********         |
4 1.0609 0.406431 |                    |********            |
5 0.7229 0.276930 |                    |******              |
6 0.4649 0.178104 |                    |****                |
7 0.2436 0.093310 |                    |**                  |
8 0.0372 0.014269 |                    |                    |
9 -0.0447 -0.017119 |                    |                    |
10 -0.2536 -0.097139 |                  **|                    |
11 -0.4962 -0.190095 |                ****|                    |
12 -0.6159 -0.235961 |               *****|                    |
13 -0.5239 -0.200700 |                ****|                    |

Backward Elimination of Autoregressive
Terms
Lag Estimate t Value Pr > |t|
6 -0.015410 -0.09 0.9325
5 0.033545 0.23 0.8174
11 0.049685 0.27 0.7919
7 -0.049070 -0.37 0.7124
4 0.113231 0.87 0.3889
3 -0.047190 -0.38 0.7031
2 0.170311 1.39 0.1708
8 0.190831 1.58 0.1199
9 -0.171569 -1.43 0.1576
10 0.043411 0.50 0.6162

Preliminary MSE 0.6375

Estimates of Autoregressive Parameters
Lag Coefficient Standard
Error		 t Value
1 -0.861286 0.063096 -13.65
12 0.280674 0.119087 2.36
13 -0.243142 0.120313 -2.02

Expected Autocorrelations
Lag Autocorr
0 1.0000
1 0.8465
2 0.7119
3 0.5934
4 0.4883
5 0.3941
6 0.3088
7 0.2304
8 0.1572
9 0.0876
10 0.0199
11 -0.0473
12 -0.1156
13 -0.0940

Algorithm converged.


STEPWISE AUTOREGRESSION TO DETERMINE ORDER, 'New Mexico' ED DATA
Backwards Stepwise Regression to Determine Order of Autocorrelation

The AUTOREG Procedure

Variable Name=H3

Maximum Likelihood Estimates
SSE 18.5862619 DFE 65
MSE 0.28594 Root MSE 0.53474
SBC 145.255963 AIC 129.319301
MAE 0.40652047 AICC 131.069301
MAPE 0.98533103 HQC 135.663733
Log Likelihood -57.65965 Regress R-Square 0.7025
Durbin-Watson 0.8103 Total R-Square 0.9934
    Observations 72

Parameter Estimates
Variable DF Estimate Standard
Error		 t Value Approx
Pr > |t|
Intercept 1 29.5467 1.2797 23.09 <.0001
PRESLOPE 1 0.2802 0.0308 9.09 <.0001
INTERVENTION 1 1.0906 0.5870 1.86 0.0677
POSTSLOPE 1 0.3121 0.2145 1.46 0.1504
AR1 1 -0.9749 0.0440 -22.15 <.0001
AR12 1 0.6685 0.1162 5.75 <.0001
AR13 1 -0.5956 0.1208 -4.93 <.0001

Expected Autocorrelations
Lag Autocorr
0 1.0000
1 0.9180
2 0.8285
3 0.7323
4 0.6301
5 0.5228
6 0.4112
7 0.2963
8 0.1790
9 0.0602
10 -0.0590
11 -0.1778
12 -0.2951
13 -0.3058

Autoregressive parameters assumed given
Variable DF Estimate Standard
Error		 t Value Approx
Pr > |t|
Intercept 1 29.5467 1.2413 23.80 <.0001
PRESLOPE 1 0.2802 0.0283 9.91 <.0001
INTERVENTION 1 1.0906 0.5739 1.90 0.0618
POSTSLOPE 1 0.3121 0.1992 1.57 0.1221