Proc Import Datafile= /Home/Smithpc0/Sasuser.V94/Lagrange.Xlsx

Proc Import Datafile= /Home/Smithpc0/Sasuser.V94/Lagrange.Xlsx

proc import datafile="/home/smithpc0/sasuser.v94/lagrange.xlsx"

out=smithpc0

dbms=xlsx

replace;

run;

ods graphics off;

DATA work.smithpc0;

SET work.smithpc0;

LAGINT=LAG(INTRATE);

PROC AUTOREG;

TITLE "Corrected estimate of simplest Fisher equation -- note it does OLS first";

MODEL INTRATE = INFLATION /NLAG=1 dwprob;

RUN;

PROC AUTOREG;

TITLE "Demonstration of Lagrange Multiplier test when lagged dependent variable present";

MODEL INTRATE = INFLATION LAGINT /NLAG=1 dwprob GODFREY=1;

RUN;
Corrected estimate of simplest Fisher equation -- note it does OLS first

The AUTOREG Procedure

Dependent Variable / INTRATE
INTRATE

Corrected estimate of simplest Fisher equation -- note it does OLS first

The AUTOREG Procedure

Ordinary Least Squares Estimates
SSE / 116.799032 / DFE / 23
MSE / 5.07822 / Root MSE / 2.25349
SBC / 115.924152 / AIC / 113.486401
MAE / 1.70071887 / AICC / 114.031855
MAPE / 52.1611231 / HQC / 114.162529
Durbin-Watson / 0.7263 / Total R-Square / 0.5168
Durbin-Watson Statistics
Order / DW / PrDW / PrDW
1 / 0.7263 / <.0001 / 0.9999

NOTE: Pr<DW is the p-value for testing positive autocorrelation, and Pr>DW is the p-value for testing negative autocorrelation.

Parameter Estimates
Variable / DF / Estimate / Standard
Error / tValue / Approx
Pr > |t| / Variable Label
Intercept / 1 / 2.5368 / 0.8352 / 3.04 / 0.0059
INFLATION / 1 / 0.9364 / 0.1888 / 4.96 / <.0001 / INFLATION
Estimates of Autocorrelations
Lag / Covariance / Correlation / -198765432101234567891
0 / 4.6720 / 1.000000 / ||********************|
1 / 2.4649 / 0.527592 / ||***********|
Preliminary MSE / 3.3715
Estimates of Autoregressive Parameters
Lag / Coefficient / Standard
Error / tValue
1 / -0.527592 / 0.181114 / -2.91

Corrected estimate of simplest Fisher equation -- note it does OLS first

The AUTOREG Procedure

Yule-Walker Estimates
SSE / 64.9687935 / DFE / 22
MSE / 2.95313 / Root MSE / 1.71847
SBC / 104.805554 / AIC / 101.148927
MAE / 1.22003669 / AICC / 102.291784
MAPE / 36.0281065 / HQC / 102.16312
Durbin-Watson / 1.1547 / Transformed Regression R-Square / 0.3235
Total R-Square / 0.7312
Durbin-Watson Statistics
Order / DW / PrDW / PrDW
1 / 1.1547 / 0.0104 / 0.9896

NOTE: Pr<DW is the p-value for testing positive autocorrelation, and Pr>DW is the p-value for testing negative autocorrelation.

Parameter Estimates
Variable / DF / Estimate / Standard
Error / tValue / Approx
Pr > |t| / Variable Label
Intercept / 1 / 3.6992 / 1.0075 / 3.67 / 0.0013
INFLATION / 1 / 0.5801 / 0.1789 / 3.24 / 0.0037 / INFLATION

Demonstration of Lagrange Multiplier test when lagged dependent variable present

The AUTOREG Procedure

Dependent Variable / INTRATE
INTRATE

Demonstration of Lagrange Multiplier test when lagged dependent variable present

The AUTOREG Procedure

Ordinary Least Squares Estimates
SSE / 25.9872817 / DFE / 21
MSE / 1.23749 / Root MSE / 1.11243
SBC / 79.5524932 / AIC / 76.0183318
MAE / 0.95000311 / AICC / 77.2183318
MAPE / 24.042034 / HQC / 76.9559458
Durbin-Watson / 1.7094 / Total R-Square / 0.8765
Durbin-Watson Statistics
Order / DW / PrDW / PrDW
1 / 1.7094 / 0.1655 / 0.8345

NOTE: Pr<DW is the p-value for testing positive autocorrelation, and Pr>DW is the p-value for testing negative autocorrelation.

Godfrey's Serial Correlation Test
Alternative / LM / PrLM
AR(1) / 0.3615 / 0.5477
Parameter Estimates
Variable / DF / Estimate / Standard
Error / tValue / Approx
Pr > |t| / Variable Label
Intercept / 1 / -0.6867 / 0.5856 / -1.17 / 0.2540
INFLATION / 1 / 0.6806 / 0.1650 / 4.12 / 0.0005 / INFLATION
LAGINT / 1 / 0.6750 / 0.0879 / 7.68 / <.0001
Estimates of Autocorrelations
Lag / Covariance / Correlation / -198765432101234567891
0 / 1.0828 / 1.000000 / ||********************|
1 / 0.1251 / 0.115513 / ||**|
Preliminary MSE / 1.0684
Estimates of Autoregressive Parameters
Lag / Coefficient / Standard
Error / tValue
1 / -0.115513 / 0.222110 / -0.52

Demonstration of Lagrange Multiplier test when lagged dependent variable present

The AUTOREG Procedure

Yule-Walker Estimates
SSE / 25.6031136 / DFE / 20
MSE / 1.28016 / Root MSE / 1.13144
SBC / 82.3865413 / AIC / 77.674326
MAE / 0.93967452 / AICC / 79.7795891
MAPE / 22.9518674 / HQC / 78.924478
Durbin-Watson / 1.9349 / Transformed Regression R-Square / 0.8571
Total R-Square / 0.8783
Durbin-Watson Statistics
Order / DW / PrDW / PrDW
1 / 1.9349 / 0.3510 / 0.6490

NOTE: Pr<DW is the p-value for testing positive autocorrelation, and Pr>DW is the p-value for testing negative autocorrelation.

Godfrey's Serial Correlation Test
Alternative / LM / PrLM
AR(1) / 0.1337 / 0.7146
Parameter Estimates
Variable / DF / Estimate / Standard
Error / tValue / Approx
Pr > |t| / Variable Label
Intercept / 1 / -0.6307 / 0.6472 / -0.97 / 0.3414
INFLATION / 1 / 0.6825 / 0.1663 / 4.10 / 0.0006 / INFLATION
LAGINT / 1 / 0.6650 / 0.0947 / 7.02 / <.0001