UNIVERSITY OF CALIFORNIA, LOS ANGELES
Department of Economics
Economics 143 (Cameron) - Applied Regression Analysis
Classroom Handout #18: Serially Correlated Errors and the AUTO Command
Data are from January 1984 through October 1997, on number of business failures
and manufacturing production (in constant 1987 dollars, not seasonally adjusted.
|_read(failn.dat) yrmo fail / skiplines=1
...SAMPLE RANGE IS NOW SET TO: 1 166
|_read(mfgprod.dat) yrmo mfgprod / skiplines=1
|_genr t=time(0)
Create separate YR and MO variables from the YRMO variable in CITIBASE
|_genr yr=(yrmo-mod(yrmo,100))/100
|_genr mo=mod(yrmo,100)
|_stat
NAME N MEAN ST. DEV VARIANCE MINIMUM MAXIMUM
YRMO 166 9048.6 400.25 0.16020E+06 8401.0 9710.0
FAIL 166 5772.1 1324.2 0.17536E+07 3404.0 9143.0
MFGPROD 166 100.19 11.296 127.60 78.989 128.30
T 166 83.500 48.064 2310.2 1.0000 166.00
YR 166 90.422 4.0034 16.027 84.000 97.000
MO 166 6.4398 3.4385 11.824 1.0000 12.000
Create a set of monthly dummy variables to capture seasonality
|_if(mo.eq.1) jan=1
|_if(mo.eq.2) feb=1
|_if(mo.eq.3) mar=1
|_if(mo.eq.4) apr=1
|_if(mo.eq.5) may=1
|_if(mo.eq.6) jun=1
|_if(mo.eq.7) jul=1
|_if(mo.eq.8) aug=1
|_if(mo.eq.9) sep=1
|_if(mo.eq.10) oct=1
|_if(mo.eq.11) nov=1
|_if(mo.eq.12) dec=1
Illustrate use of EXACTDW option on OLS to check for first-order serially
correlated errors (AR(1) errors); test rejects "zero serial correlation"
|_ols fail mfgprod t feb mar apr may jun jul &
| aug sep oct nov dec / exactdw
DURBIN-WATSON STATISTIC = 0.74405
DURBIN-WATSON P-VALUE = 0.000000
R-SQUARE = 0.6812 R-SQUARE ADJUSTED = 0.6539
VARIANCE OF THE ESTIMATE-SIGMA**2 = 0.60688E+06
STANDARD ERROR OF THE ESTIMATE-SIGMA = 779.02
SUM OF SQUARED ERRORS-SSE= 0.92246E+08
MEAN OF DEPENDENT VARIABLE = 5772.1
LOG OF THE LIKELIHOOD FUNCTION = -1333.47
ANALYSIS OF VARIANCE - FROM MEAN
SS DF MS F
REGRESSION 0.19710E+09 13. 0.15162E+08 24.983
ERROR 0.92246E+08 152. 0.60688E+06 P-VALUE
TOTAL 0.28935E+09 165. 0.17536E+07 0.000
VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY
NAME COEFFICIENT ERROR 152 DF P-VALUE CORR. COEFFICIENT AT MEANS
MFGPROD -233.70 20.94 -11.16 0.000-0.671 -1.9934 -4.0563
T 67.705 4.780 14.16 0.000 0.754 2.4574 0.9794
FEB 249.27 298.2 0.8359 0.405 0.068 0.0525 0.0036
MAR 1243.0 299.6 4.149 0.000 0.319 0.2616 0.0182
APR 607.56 299.2 2.031 0.044 0.163 0.1279 0.0089
MAY 937.30 300.8 3.116 0.002 0.245 0.1973 0.0137
JUN 1314.9 320.7 4.100 0.000 0.316 0.2768 0.0192
JUL -99.116 296.5 -0.3343 0.739-0.027 -0.0209 -0.0014
AUG 1277.0 320.2 3.989 0.000 0.308 0.2688 0.0187
SEP 1098.8 329.7 3.333 0.001 0.261 0.2313 0.0161
OCT 1441.2 320.7 4.494 0.000 0.342 0.3034 0.0211
NOV 219.87 305.5 0.7198 0.473 0.058 0.0447 0.0030
DEC -803.77 300.1 -2.678 0.008-0.212 -0.1636 -0.0109
CONSTANT 22898. 1659. 13.80 0.000 0.746 0.0000 3.9669
There are lots of apparently individually statistically significant coefficients
when the standard errors are calculated using the default OLS formulas (which
are not valid if there is autocorrelation in the errors).
|_auto fail mfgprod t feb mar apr may jun jul &
| aug sep oct nov dec
DEPENDENT VARIABLE = FAIL
..NOTE..R-SQUARE,ANOVA,RESIDUALS DONE ON ORIGINAL VARS
LEAST SQUARES ESTIMATION 166 OBSERVATIONS
BY COCHRANE-ORCUTT TYPE PROCEDURE WITH CONVERGENCE = 0.00100
ITERATION RHO LOG L.F. SSE
1 0.00000 -1333.47 0.92246E+08
2 0.63181 -1289.89 0.54398E+08
3 0.69439 -1289.02 0.53783E+08
4 0.72625 -1288.77 0.53591E+08
5 0.74688 -1288.66 0.53502E+08
6 0.76166 -1288.61 0.53452E+08
7 0.77279 -1288.58 0.53423E+08
8 0.78138 -1288.57 0.53405E+08
9 0.78809 -1288.57 0.53393E+08
10 0.79337 -1288.57 0.53386E+08
11 0.79754 -1288.57 0.53381E+08
12 0.80081 -1288.57 0.53379E+08
13 0.80339 -1288.58 0.53377E+08
14 0.80542 -1288.58 0.53376E+08
15 0.80700 -1288.58 0.53375E+08
16 0.80825 -1288.58 0.53374E+08
17 0.80922 -1288.59 0.53374E+08
LOG L.F. = -1288.59 AT RHO = 0.80922
ASYMPTOTIC ASYMPTOTIC ASYMPTOTIC
ESTIMATE VARIANCE ST.ERROR T-RATIO
RHO 0.80922 0.00208 0.04560 17.74625
R-SQUARE = 0.8155 R-SQUARE ADJUSTED = 0.7998
VARIANCE OF THE ESTIMATE-SIGMA**2 = 0.35115E+06
STANDARD ERROR OF THE ESTIMATE-SIGMA = 592.58
SUM OF SQUARED ERRORS-SSE= 0.53374E+08
MEAN OF DEPENDENT VARIABLE = 5772.1
LOG OF THE LIKELIHOOD FUNCTION = -1288.59
ANALYSIS OF VARIANCE - FROM MEAN
SS DF MS
REGRESSION 0.23597E+09 13. 0.18152E+08
ERROR 0.53374E+08 152. 0.35115E+06
TOTAL 0.28935E+09 165. 0.17536E+07
VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY
NAME COEFFICIENT ERROR 152 DF P-VALUE CORR. COEFFICIENT AT MEANS
MFGPROD -20.689 52.54 -0.3938 0.694-0.032 -0.1765 -0.3591
T 21.127 12.74 1.658 0.099 0.133 0.7668 0.3056
FEB -232.77 201.3 -1.156 0.249-0.093 -0.0490 -0.0034
MAR 676.51 256.4 2.638 0.009 0.209 0.1424 0.0099
APR 64.903 281.0 0.2310 0.818 0.019 0.0137 0.0009
MAY 307.31 307.9 0.9980 0.320 0.081 0.0647 0.0045
JUN 15.490 418.8 0.3699E-01 0.971 0.003 0.0033 0.0002
JUL -452.88 296.5 -1.527 0.129-0.123 -0.0953 -0.0066
AUG -10.246 415.8 -0.2464E-01 0.980-0.002 -0.0022 -0.0001
SEP -419.54 452.2 -0.9278 0.355-0.075 -0.0883 -0.0061
OCT 139.95 398.3 0.3514 0.726 0.028 0.0295 0.0020
NOV -358.41 271.0 -1.322 0.188-0.107 -0.0729 -0.0049
DEC -811.59 170.3 -4.765 0.000-0.360 -0.1652 -0.0110
CONSTANT 6169.2 4141. 1.490 0.138 0.120 0.0000 1.0688
Not much left that matters when standard errors are computed correctly
Updated: 4:24 PM 11/23/98; Prepared by: Trudy Ann Cameron; Site Index