STEPWISE AUTOREGRESSION TO DETERMINE ORDER, 'New Mexico' ED DATA
FORECASTING MODEL: Using PRE-TRANSITION Trend-Cycle Component data points with TIME as predictor

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_PRE


STEPWISE AUTOREGRESSION TO DETERMINE ORDER, 'New Mexico' ED DATA
FORECASTING MODEL: Using PRE-TRANSITION Trend-Cycle Component data points with TIME as predictor
Backwards Stepwise Regression to Determine Order of Autocorrelation

The AUTOREG Procedure

Variable Name=H1

Ordinary Least Squares Estimates
SSE 19840.689 DFE 61
MSE 325.25720 Root MSE 18.03489
SBC 549.470914 AIC 545.184644
MAE 15.0240922 AICC 545.384644
MAPE 3.40945714 HQC 546.870455
Durbin-Watson 0.0643 Regress R-Square 0.0687
    Total R-Square 0.0687

Parameter Estimates
Variable DF Estimate Standard
Error		 t Value Approx
Pr > |t|
Intercept 1 449.2448 5.2639 85.34 <.0001
TIME 1 -0.2651 0.1250 -2.12 0.0379

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 
0 314.9 1.000000 |                    |********************|
1 291.0 0.923984 |                    |******************  |
2 253.8 0.805918 |                    |****************    |
3 204.9 0.650658 |                    |*************       |
4 148.8 0.472600 |                    |*********           |
5 91.3714 0.290131 |                    |******              |
6 34.9083 0.110844 |                    |**                  |
7 -19.0655 -0.060538 |                   *|                    |
8 -66.4748 -0.211077 |                ****|                    |
9 -105.7 -0.335515 |             *******|                    |
10 -136.3 -0.432926 |           *********|                    |
11 -156.2 -0.495862 |          **********|                    |
12 -164.3 -0.521624 |          **********|                    |
13 -161.3 -0.512230 |          **********|                    |

Backward Elimination of Autoregressive
Terms
Lag Estimate t Value Pr > |t|
12 -0.004778 -0.02 0.9819
2 0.005650 0.03 0.9783
8 0.007302 0.04 0.9717
5 -0.009676 -0.05 0.9622
13 -0.012747 -0.13 0.8943
11 0.014090 0.10 0.9185
9 -0.023541 -0.14 0.8903
6 -0.029044 -0.17 0.8646
7 0.041740 0.44 0.6624
3 0.084444 0.51 0.6110
10 0.070777 1.33 0.1871

Preliminary MSE 37.0279

Estimates of Autoregressive Parameters
Lag Coefficient Standard
Error		 t Value
1 -1.069088 0.058786 -18.19
4 0.223010 0.058786 3.79

Expected Autocorrelations
Lag Autocorr
0 1.0000
1 0.9227
2 0.8066
3 0.6565
4 0.4789

Algorithm converged.


STEPWISE AUTOREGRESSION TO DETERMINE ORDER, 'New Mexico' ED DATA
FORECASTING MODEL: Using PRE-TRANSITION Trend-Cycle Component data points with TIME as predictor
Backwards Stepwise Regression to Determine Order of Autocorrelation

The AUTOREG Procedure

Variable Name=H1

Maximum Likelihood Estimates
SSE 250.758507 DFE 59
MSE 4.25014 Root MSE 2.06159
SBC 289.117272 AIC 280.544734
MAE 1.71819298 AICC 281.234389
MAPE 0.3924855 HQC 283.916355
Log Likelihood -136.27237 Regress R-Square 0.0250
Durbin-Watson 1.4672 Total R-Square 0.9882
    Observations 63

Parameter Estimates
Variable DF Estimate Standard
Error		 t Value Approx
Pr > |t|
Intercept 1 444.3043 6.1277 72.51 <.0001
TIME 1 -0.1779 0.1459 -1.22 0.2277
AR1 1 -1.2349 0.0175 -70.45 <.0001
AR4 1 0.3396 0.0151 22.48 <.0001

Expected Autocorrelations
Lag Autocorr
0 1.0000
1 0.9714
2 0.8955
3 0.7760
4 0.6187

Autoregressive parameters assumed given
Variable DF Estimate Standard
Error		 t Value Approx
Pr > |t|
Intercept 1 444.3043 6.0423 73.53 <.0001
TIME 1 -0.1779 0.1444 -1.23 0.2229


STEPWISE AUTOREGRESSION TO DETERMINE ORDER, 'New Mexico' ED DATA
FORECASTING MODEL: Using PRE-TRANSITION Trend-Cycle Component data points with TIME as predictor
Backwards Stepwise Regression to Determine Order of Autocorrelation

The AUTOREG Procedure

Variable Name=H2

Dependent Variable TCC_PRE


STEPWISE AUTOREGRESSION TO DETERMINE ORDER, 'New Mexico' ED DATA
FORECASTING MODEL: Using PRE-TRANSITION Trend-Cycle Component data points with TIME as predictor
Backwards Stepwise Regression to Determine Order of Autocorrelation

The AUTOREG Procedure

Variable Name=H2

Ordinary Least Squares Estimates
SSE 431.702991 DFE 61
MSE 7.07710 Root MSE 2.66028
SBC 308.32252 AIC 304.036251
MAE 2.03700838 AICC 304.236251
MAPE 4.52573164 HQC 305.722061
Durbin-Watson 0.0904 Regress R-Square 0.0079
    Total R-Square 0.0079

Parameter Estimates
Variable DF Estimate Standard
Error		 t Value Approx
Pr > |t|
Intercept 1 43.7566 0.7765 56.35 <.0001
TIME 1 0.0129 0.0184 0.70 0.4879

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 6.8524 1.000000 |                    |********************|
1 5.8931 0.859995 |                    |*****************   |
2 4.7530 0.693624 |                    |**************      |
3 3.7461 0.546676 |                    |***********         |
4 2.8827 0.420682 |                    |********            |
5 2.1778 0.317812 |                    |******              |
6 1.7414 0.254122 |                    |*****               |
7 1.3417 0.195805 |                    |****                |
8 0.8005 0.116817 |                    |**                  |
9 0.2893 0.042211 |                    |*                   |
10 -0.0811 -0.011836 |                    |                    |
11 -0.3447 -0.050307 |                   *|                    |
12 -0.4875 -0.071147 |                   *|                    |
13 -0.5240 -0.076473 |                  **|                    |

Backward Elimination of Autoregressive
Terms
Lag Estimate t Value Pr > |t|
13 0.001022 0.01 0.9944
3 -0.002684 -0.01 0.9895
12 -0.006883 -0.05 0.9614
11 0.004583 0.03 0.9740
4 0.009795 0.06 0.9519
10 -0.008906 -0.07 0.9481
9 0.024580 0.18 0.8569
7 -0.066692 -0.35 0.7271
5 0.092220 0.64 0.5227
6 -0.065482 -0.67 0.5082
8 0.039040 0.57 0.5685
2 0.176517 1.38 0.1736

Preliminary MSE 1.7844

Estimates of Autoregressive Parameters
Lag Coefficient Standard
Error		 t Value
1 -0.859995 0.065880 -13.05

Algorithm converged.


STEPWISE AUTOREGRESSION TO DETERMINE ORDER, 'New Mexico' ED DATA
FORECASTING MODEL: Using PRE-TRANSITION Trend-Cycle Component data points with TIME as predictor
Backwards Stepwise Regression to Determine Order of Autocorrelation

The AUTOREG Procedure

Variable Name=H2

Maximum Likelihood Estimates
SSE 37.1728011 DFE 60
MSE 0.61955 Root MSE 0.78711
SBC 161.033914 AIC 154.60451
MAE 0.61516552 AICC 155.01129
MAPE 1.37375111 HQC 157.133226
Log Likelihood -74.302255 Regress R-Square 0.0795
Durbin-Watson 0.4864 Total R-Square 0.9146
    Observations 63

Parameter Estimates
Variable DF Estimate Standard
Error		 t Value Approx
Pr > |t|
Intercept 1 40.0111 4.2139 9.49 <.0001
TIME 1 0.1655 0.0965 1.71 0.0916
AR1 1 -0.9761 0.0309 -31.57 <.0001

Autoregressive parameters assumed given
Variable DF Estimate Standard
Error		 t Value Approx
Pr > |t|
Intercept 1 40.0111 3.8924 10.28 <.0001
TIME 1 0.1655 0.0727 2.28 0.0265


STEPWISE AUTOREGRESSION TO DETERMINE ORDER, 'New Mexico' ED DATA
FORECASTING MODEL: Using PRE-TRANSITION Trend-Cycle Component data points with TIME as predictor
Backwards Stepwise Regression to Determine Order of Autocorrelation

The AUTOREG Procedure

Variable Name=H3

Dependent Variable TCC_PRE


STEPWISE AUTOREGRESSION TO DETERMINE ORDER, 'New Mexico' ED DATA
FORECASTING MODEL: Using PRE-TRANSITION Trend-Cycle Component data points with TIME as predictor
Backwards Stepwise Regression to Determine Order of Autocorrelation

The AUTOREG Procedure

Variable Name=H3

Ordinary Least Squares Estimates
SSE 180.231122 DFE 61
MSE 2.95461 Root MSE 1.71890
SBC 253.292159 AIC 249.00589
MAE 1.41670076 AICC 249.20589
MAPE 3.63165739 HQC 250.691701
Durbin-Watson 0.1411 Regress R-Square 0.8851
    Total R-Square 0.8851

Parameter Estimates
Variable DF Estimate Standard
Error		 t Value Approx
Pr > |t|
Intercept 1 30.2054 0.5017 60.21 <.0001
TIME 1 0.2581 0.0119 21.67 <.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 2.8608 1.000000 |                    |********************|
1 2.5077 0.876585 |                    |******************  |
2 2.0081 0.701938 |                    |**************      |
3 1.5954 0.557691 |                    |***********         |
4 1.2418 0.434068 |                    |*********           |
5 0.8977 0.313807 |                    |******              |
6 0.5863 0.204931 |                    |****                |
7 0.3316 0.115914 |                    |**                  |
8 0.0992 0.034672 |                    |*                   |
9 -0.1077 -0.037645 |                   *|                    |
10 -0.3056 -0.106814 |                  **|                    |
11 -0.5245 -0.183342 |                ****|                    |
12 -0.6410 -0.224077 |                ****|                    |
13 -0.5534 -0.193444 |                ****|                    |

Backward Elimination of Autoregressive
Terms
Lag Estimate t Value Pr > |t|
9 -0.000372 -0.00 0.9987
4 -0.024638 -0.11 0.9105
5 0.028568 0.18 0.8605
8 0.048034 0.30 0.7639
7 -0.039517 -0.28 0.7793
6 0.031482 0.38 0.7045
10 -0.041774 -0.31 0.7545
3 -0.089688 -0.69 0.4956
11 0.084313 0.65 0.5174
13 -0.218086 -1.74 0.0875
12 0.050211 0.81 0.4186

Preliminary MSE 0.6080

Estimates of Autoregressive Parameters
Lag Coefficient Standard
Error		 t Value
1 -1.128141 0.124713 -9.05
2 0.286973 0.124713 2.30

Algorithm converged.


STEPWISE AUTOREGRESSION TO DETERMINE ORDER, 'New Mexico' ED DATA
FORECASTING MODEL: Using PRE-TRANSITION Trend-Cycle Component data points with TIME as predictor
Backwards Stepwise Regression to Determine Order of Autocorrelation

The AUTOREG Procedure

Variable Name=H3

Maximum Likelihood Estimates
SSE 16.0336113 DFE 59
MSE 0.27176 Root MSE 0.52130
SBC 112.2447 AIC 103.672161
MAE 0.42590949 AICC 104.361816
MAPE 1.07414648 HQC 107.043783
Log Likelihood -47.836081 Regress R-Square 0.5555
Durbin-Watson 1.4802 Total R-Square 0.9898
    Observations 63

Parameter Estimates
Variable DF Estimate Standard
Error		 t Value Approx
Pr > |t|
Intercept 1 29.1456 1.4916 19.54 <.0001
TIME 1 0.2914 0.0359 8.13 <.0001
AR1 1 -1.5102 0.1084 -13.94 <.0001
AR2 1 0.6016 0.1101 5.47 <.0001

Autoregressive parameters assumed given
Variable DF Estimate Standard
Error		 t Value Approx
Pr > |t|
Intercept 1 29.1456 1.4593 19.97 <.0001
TIME 1 0.2914 0.0339 8.59 <.0001