CURRENT WORKING DIRECTORY IS: C:\ESL\user |_* |_* Demonstration of heteroskedasticity tests |_* |_READ (DATA3-10) PROFITS SALES UNIT 88 IS NOW ASSIGNED TO: DATA3-10 ...SAMPLE RANGE IS NOW SET TO: 1 27 |_* Sort data in descending order of sales to perform compute Goldfeld-Quandt test |_SORT SALES PROFITS /DESC DATA HAS BEEN SORTED BY VARIABLE SALES |_OLS PROFITS SALES REQUIRED MEMORY IS PAR= 2 CURRENT PAR= 2000 OLS ESTIMATION 27 OBSERVATIONS DEPENDENT VARIABLE= PROFITS ...NOTE..SAMPLE RANGE SET TO: 1, 27 R-SQUARE = 0.4074 R-SQUARE ADJUSTED = 0.3837 VARIANCE OF THE ESTIMATE-SIGMA**2 = 0.13874E+06 STANDARD ERROR OF THE ESTIMATE-SIGMA = 372.48 SUM OF SQUARED ERRORS-SSE= 0.34685E+07 MEAN OF DEPENDENT VARIABLE = 472.85 LOG OF THE LIKELIHOOD FUNCTION = -197.117 VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY NAME COEFFICIENT ERROR 25 DF P-VALUE CORR. COEFFICIENT AT MEANS SALES 18.434 4.446 4.146 0.000 0.638 0.6383 0.8233 CONSTANT 83.575 118.1 0.7075 0.486 0.140 0.0000 0.1767 |_* |_* DIAGNOS will generate a 'brute-force' Goldfeld-Quandt test when a CHOWTEST as asked for. |_DIAGNOS / CHOWTEST REQUIRED MEMORY IS PAR= 5 CURRENT PAR= 2000 DEPENDENT VARIABLE = PROFITS 27 OBSERVATIONS REGRESSION COEFFICIENTS 18.4337564214 83.5752937937 HARVEY-COLLIER [1977] RECURSIVE T-TEST = -1.6667 WITH 24 D.F. HARVEY-PHILLIPS [1974] HETEROSKEDASTICITY TEST = 0.0090 WITH M = 8 BACKWARDS HARVEY-COLLIER [1977] RECURSIVE T-TEST = 0.3675 WITH 24 D.F. HARVEY-PHILLIPS [1974] HETEROSKEDASTICITY TEST = 142.0834 WITH M = 8 SEQUENTIAL CHOW AND GOLDFELD-QUANDT TESTS N1 N2 SSE1 SSE2 CHOW PVALUE G-Q DF1 DF2 PVALUE 3 24 0.49716E+06 0.22994E+07 2.7632 0.084 4.757 1 22 0.040 4 23 0.65130E+06 0.21532E+07 2.7230 0.087 3.176 2 21 0.062 5 22 0.73505E+06 0.19835E+07 3.1726 0.061 2.471 3 20 0.091 6 21 0.78267E+06 0.19683E+07 2.9994 0.070 1.889 4 19 0.154 7 20 0.10380E+07 0.12709E+07 5.7754 0.009 2.940 5 18 0.041 8 19 0.14646E+07 0.11958E+07 3.4934 0.047 3.470 6 17 0.020 9 18 0.16948E+07 0.27454E+06 8.7547 0.001 14.11 7 16 0.000 10 17 0.18290E+07 0.13326E+06 8.8274 0.001 25.73 8 15 0.000 11 16 0.21320E+07 78394. 6.5453 0.006 42.31 9 14 0.000 12 15 0.24649E+07 45969. 4.3860 0.024 69.71 10 13 0.000 13 14 0.29881E+07 28046. 1.7247 0.200 116.2 11 12 0.000 14 13 0.31251E+07 22208. 1.1737 0.327 129.0 12 11 0.000 15 12 0.32524E+07 21136. 0.68487 0.514 118.4 13 10 0.000 16 11 0.33682E+07 16647. 0.28428 0.755 130.1 14 9 0.000 17 10 0.33962E+07 15996. 0.18974 0.828 113.2 15 8 0.000 18 9 0.34221E+07 15883. 0.10212 0.903 94.26 16 7 0.000 19 8 0.34520E+07 7666.0 0.29426E-01 0.971 158.9 17 6 0.000 20 7 0.34520E+07 4888.2 0.38690E-01 0.962 196.2 18 5 0.000 21 6 0.34545E+07 2170.0 0.39361E-01 0.961 335.1 19 4 0.000 22 5 0.34571E+07 402.79 0.36451E-01 0.964 1287. 20 3 0.000 23 4 0.34584E+07 111.43 0.33220E-01 0.967 2956. 21 2 0.000 24 3 0.34586E+07 81.773 0.32722E-01 0.968 1922. 22 1 0.018 CHOW TEST - F DISTRIBUTION WITH DF1= 2 AND DF2= 23 |_* |_* If a group of central observations is to be omitted for the G-Q test, set the GQOBS= option. |_DIAG / CHOWTEST GQOBS=9 REQUIRED MEMORY IS PAR= 5 CURRENT PAR= 2000 DEPENDENT VARIABLE = PROFITS 27 OBSERVATIONS REGRESSION COEFFICIENTS 18.4337564214 83.5752937937 HARVEY-COLLIER [1977] RECURSIVE T-TEST = -1.6667 WITH 24 D.F. HARVEY-PHILLIPS [1974] HETEROSKEDASTICITY TEST = 0.0090 WITH M = 8 BACKWARDS HARVEY-COLLIER [1977] RECURSIVE T-TEST = 0.3675 WITH 24 D.F. HARVEY-PHILLIPS [1974] HETEROSKEDASTICITY TEST = 142.0834 WITH M = 8 SEQUENTIAL CHOW AND GOLDFELD-QUANDT TESTS N1 N2 SSE1 SSE2 CHOW PVALUE G-Q DF1 DF2 PVALUE 3 24 0.49716E+06 0.22994E+07 2.7632 0.084 0.000 -4 18 0.000 4 23 0.65130E+06 0.21532E+07 2.7230 0.087 0.000 -3 17 0.000 5 22 0.73505E+06 0.19835E+07 3.1726 0.061 0.000 -2 16 0.000 6 21 0.78267E+06 0.19683E+07 2.9994 0.070 0.000 -1 15 0.000 7 20 0.10380E+07 0.12709E+07 5.7754 0.009 0.000 0 14 0.000 8 19 0.14646E+07 0.11958E+07 3.4934 0.047 140.6 1 13 0.000 9 18 0.16948E+07 0.27454E+06 8.7547 0.001 139.3 2 12 0.000 10 17 0.18290E+07 0.13326E+06 8.8274 0.001 121.4 3 11 0.000 11 16 0.21320E+07 78394. 6.5453 0.006 92.58 4 10 0.000 12 15 0.24649E+07 45969. 4.3860 0.024 112.2 5 9 0.000 13 14 0.29881E+07 28046. 1.7247 0.200 122.1 6 8 0.000 14 13 0.31251E+07 22208. 1.1737 0.327 106.7 7 7 0.000 15 12 0.32524E+07 21136. 0.68487 0.514 178.9 8 6 0.000 16 11 0.33682E+07 16647. 0.28428 0.755 242.3 9 5 0.000 17 10 0.33962E+07 15996. 0.18974 0.828 454.4 10 4 0.000 18 9 0.34221E+07 15883. 0.10212 0.903 2023. 11 3 0.000 19 8 0.34520E+07 7666.0 0.29426E-01 0.971 4674. 12 2 0.000 20 7 0.34520E+07 4888.2 0.38690E-01 0.962 3060. 13 1 0.014 21 6 0.34545E+07 2170.0 0.39361E-01 0.961 0.000 14 0 0.000 22 5 0.34571E+07 402.79 0.36451E-01 0.964 0.000 15 -1 0.000 23 4 0.34584E+07 111.43 0.33220E-01 0.967 0.000 16 -2 0.000 24 3 0.34586E+07 81.773 0.32722E-01 0.968 0.000 17 -3 0.000 CHOW TEST - F DISTRIBUTION WITH DF1= 2 AND DF2= 23 |_* |_* A Goldfeld-Quandt test can also be computed manually. |_* Define three groups of 9 observations apiece. Omit the middle nine observations. |_SAMPLE 1 9 |_?OLS PROFITS SALES |_* Keep the ESS and DF using temporary variables. |_GEN1 ESS1=$SSE ..NOTE..CURRENT VALUE OF $SSE = 0.16948E+07 |_GEN1 DF1=$DF ..NOTE..CURRENT VALUE OF $DF = 7.0000 |_SAMPLE 19 27 |_?OLS PROFITS SALES |_* Keep the ESS and DF using temporary variables. |_GEN1 ESS2=$SSE ..NOTE..CURRENT VALUE OF $SSE = 15883. |_GEN1 DF2=$DF ..NOTE..CURRENT VALUE OF $DF = 7.0000 |_* Calculate F statistic |_GEN1 F = (ESS1/DF1)/(ESS2/DF2) |_PRINT F F 106.7003 |_* Retrieve p-value from DISTRIB. |_DISTRIB F / TYPE=F DF1=DF1 DF2=DF2 F DISTRIBUTION- DF1= 7.0000 DF2= 7.0000 MEAN= 1.4000 VARIANCE= 2.2400 MODE= 0.55556 DATA PDF CDF 1-CDF F ROW 1 106.70 0.45612E-07 1.0000 0.14109E-05 |_* |_* Compute LM statistics |_SAMPLE 1 27 |_?OLS PROFITS SALES |_DIAGNOS /HET REQUIRED MEMORY IS PAR= 5 CURRENT PAR= 2000 DEPENDENT VARIABLE = PROFITS 27 OBSERVATIONS REGRESSION COEFFICIENTS 18.4337564214 83.5752937937 HETEROSKEDASTICITY TESTS CHI-SQUARE D.F. P-VALUE TEST STATISTIC E**2 ON YHAT: 4.882 1 0.02713 E**2 ON YHAT**2: 4.214 1 0.04010 E**2 ON LOG(YHAT**2): 4.642 1 0.03120 E**2 ON LAG(E**2) ARCH TEST: 0.041 1 0.83950 LOG(E**2) ON X (HARVEY) TEST: 12.539 1 0.00040 ABS(E) ON X (GLEJSER) TEST: 11.025 1 0.00090 E**2 ON X TEST: KOENKER(R2): 4.882 1 0.02713 B-P-G (SSR) : 11.191 1 0.00082 E**2 ON X X**2 (WHITE) TEST: KOENKER(R2): 4.970 2 0.08331 B-P-G (SSR) : 11.393 2 0.00336 |_* |_* Add non-linear term to regession |_GENR SALES2=SALES**2 |_OLS PROFITS SALES SALES2 /RESID=U REQUIRED MEMORY IS PAR= 3 CURRENT PAR= 2000 OLS ESTIMATION 27 OBSERVATIONS DEPENDENT VARIABLE= PROFITS ...NOTE..SAMPLE RANGE SET TO: 1, 27 R-SQUARE = 0.4689 R-SQUARE ADJUSTED = 0.4246 VARIANCE OF THE ESTIMATE-SIGMA**2 = 0.12953E+06 STANDARD ERROR OF THE ESTIMATE-SIGMA = 359.90 SUM OF SQUARED ERRORS-SSE= 0.31087E+07 MEAN OF DEPENDENT VARIABLE = 472.85 LOG OF THE LIKELIHOOD FUNCTION = -195.639 VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY NAME COEFFICIENT ERROR 24 DF P-VALUE CORR. COEFFICIENT AT MEANS SALES 40.829 14.11 2.894 0.008 0.509 1.4137 1.8234 SALES2 -0.41316 0.2479 -1.667 0.109-0.322 -0.8141 -0.6168 CONSTANT -97.719 157.7 -0.6197 0.541-0.126 0.0000 -0.2067 |_DIAGNOS /HET REQUIRED MEMORY IS PAR= 7 CURRENT PAR= 2000 DEPENDENT VARIABLE = PROFITS 27 OBSERVATIONS REGRESSION COEFFICIENTS 40.8287675179 -0.413155714517 -97.7192253187 HETEROSKEDASTICITY TESTS CHI-SQUARE D.F. P-VALUE TEST STATISTIC E**2 ON YHAT: 4.887 1 0.02707 E**2 ON YHAT**2: 4.714 1 0.02992 E**2 ON LOG(YHAT**2): 3.338 1 0.06770 E**2 ON LAG(E**2) ARCH TEST: 0.001 1 0.97409 LOG(E**2) ON X (HARVEY) TEST: 5.722 2 0.05721 ABS(E) ON X (GLEJSER) TEST: 7.899 2 0.01927 E**2 ON X TEST: KOENKER(R2): 4.892 2 0.08663 B-P-G (SSR) : 6.532 2 0.03816 ...MATRIX INVERSION FAILED IN ROW 4 ...RESULTS MAY BE UNRELIABLE E**2 ON X X**2 (WHITE) TEST: KOENKER(R2): ********** 4 ********* B-P-G (SSR) : ********** 4 ********* ...MATRIX INVERSION FAILED IN ROW 4 ...RESULTS MAY BE UNRELIABLE E**2 ON X X**2 XX (WHITE) TEST: KOENKER(R2): ********** 5 ********* B-P-G (SSR) : ********** 5 ********* |_* Compute White test |_GENR U2 = U**2 |_GENR SALES3=SALES**3 |_GENR SALES4=SALES**4 |_?OLS U2 SALES SALES2-SALES4 |_* Compute nR2 (Koenker) test statistic |_GEN1 NR2 = $N*$R2 ..NOTE..CURRENT VALUE OF $N = 27.000 ..NOTE..CURRENT VALUE OF $R2 = 0.27973 |_GEN1 DF = $K-1 ..NOTE..CURRENT VALUE OF $K = 5.0000 |_PRINT NR2 NR2 7.552632 |_DISTRIB NR2 / TYPE=CHI DF=DF CHI-SQUARE PARAMETERS- DF= 4.0000 MEAN= 4.0000 VARIANCE= 8.0000 MODE= 2.0000 DATA PDF CDF 1-CDF NR2 ROW 1 7.5526 0.43252E-01 0.89059 0.10941 |_* Compute LM test without quadratic term |_?OLS U2 SALES |_* Compute nR2 (Koenker) test statistic |_GEN1 NR2 = $N*$R2 ..NOTE..CURRENT VALUE OF $N = 27.000 ..NOTE..CURRENT VALUE OF $R2 = 0.16147 |_GEN1 DF = $K-1 ..NOTE..CURRENT VALUE OF $K = 2.0000 |_PRINT NR2 NR2 4.359659 |_DISTRIB NR2 / TYPE=CHI DF=DF CHI-SQUARE PARAMETERS- DF= 1.0000 MEAN= 1.0000 VARIANCE= 2.0000 MODE= 0.0000 DATA PDF CDF 1-CDF NR2 ROW 1 4.3597 0.21602E-01 0.96320 0.36800E-01 |_STOP