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and making the transformed regression sketched above feasible. (Note that one data point, the first, is lost in this regression.) This procedure of autoregressing estimated residuals can be done once and the resulting value of
375:
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regression, or the residuals of the residuals autoregression can themselves be autoregressed in consecutive steps until no substantial change in the estimated value of
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951:
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402:
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In this specification the error terms are white noise, so statistical inference is valid. Then the sum of squared residuals (the sum of squared estimates of
414:
293:
1160:
Dufour, J. M.; Gaudry, M. J. I.; Hafer, R. W. (1983). "A warning on the use of the
Cochrane-Orcutt procedure based on a money demand equation".
990:
1106:
Dufour, J. M.; Gaudry, M. J. I.; Liem, T. C. (1980). "The
Cochrane-Orcutt procedure numerical examples of multiple admissible minima".
949:
Cochrane, D.; Orcutt, G. H. (1949). "Application of Least
Squares Regression to Relationships Containing Auto-Correlated Error Terms".
930:
1339:
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60:
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that can be substantial in small samples. A superior transformation, which retains the first observation with a weight of
925:
903:
685:
637:
The transformation suggested by
Cochrane and Orcutt disregards the first observation of a time series, causing a loss of
259:
39:
915:
1010:(1969). "Small-Sample Properties of Several Two-Stage Regression Methods in the Context of Auto-Correlated Errors".
1361:
1195:
Doran, Howard; Kmenta, Jan (1992). "Multiple Minima in the
Estimation of Models With Autoregressive Disturbances".
791:
282:. To avoid this problem, the residuals must be modeled. If the process generating the residuals is found to be a
920:
1381:
755:
719:
644:
1133:
Oxley, Leslie T.; Roberts, Colin J. (1982). "Pitfalls in the
Application of the Cochrane‐Orcutt Technique".
716:
is not known, then it is estimated by first regressing the untransformed model and obtaining the residuals {
638:
898:
It has to be noted, though, that the iterative
Cochrane–Orcutt procedure might converge to a local but not
1386:
271:
267:
1048:
1069:
Kadiyala, Koteswara Rao (1968). "A Transformation Used to
Circumvent the Problem of Autocorrelation".
580:
408:, then the Cochrane–Orcutt procedure can be used to transform the model by taking a quasi-difference:
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535:{\displaystyle y_{t}-\rho y_{t-1}=\alpha (1-\rho )+(X_{t}-\rho X_{t-1})\beta +e_{t}.\,}
275:
1375:
1181:
1119:
1007:
1071:
1025:
964:
36:
24:
20:
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Fomby, Thomas B.; Hill, R. Carter; Johnson, Stanley R. (1984). "Autocorrelation".
405:
1365:
1319:
248:
43:
32:
370:{\displaystyle \varepsilon _{t}=\rho \varepsilon _{t-1}+e_{t},\ |\rho |<1}
985:(Fifth international ed.). Mason, OH: South-Western. pp. 409–415.
1217:
1226:
1173:
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1033:
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of the residual sum of squares. This problem disappears when using the
1208:
1084:
116:{\displaystyle y_{t}=\alpha +X_{t}\beta +\varepsilon _{t},\,}
1314:(Second ed.). New York: McGraw-Hill. pp. 259–265.
1292:. Princeton: Princeton University Press. pp. 220–225.
1357:
Econometrics lecture (topic: Cochrane–Orcutt procedure)
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1330:(Second ed.). New York: Macmillan. pp.
1013:Journal of the American Statistical Association
952:Journal of the American Statistical Association
906:instead, which keeps the initial observation.
1251:. Oxford University Press. pp. 327–373.
8:
983:Introductory Econometrics: A Modern Approach
35:. Developed in the 1940s, it is named after
1135:Oxford Bulletin of Economics and Statistics
823:{\displaystyle {\hat {\varepsilon }}_{t-1}}
1056:Cowles Commission Discussion Paper No. 383
1216:
1049:"Trend Estimators and Serial Correlation"
880:
856:
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781:{\displaystyle {\hat {\varepsilon }}_{t}}
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1270:. New York: Springer. pp. 205–236.
1249:Estimation and Inference in Econometrics
941:
692:Estimating the autoregressive parameter
688:, and later independently by Kadilaya.
677:{\displaystyle {\sqrt {(1-\rho ^{2})}}}
1392:Regression with time series structure
1147:10.1111/j.1468-0084.1982.mp44003003.x
1047:Prais, S. J.; Winsten, C. B. (1954).
258:If it is found, for instance via the
7:
1197:Review of Economics and Statistics
931:Feasible generalized least squares
14:
185:of coefficients to be estimated,
602:{\displaystyle (\alpha ,\beta )}
240:{\displaystyle \varepsilon _{t}}
871:can be used in the transformed
577:) is minimized with respect to
1026:10.1080/01621459.1969.10500968
965:10.1080/01621459.1949.10483290
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1:
1268:Advanced Econometric Methods
1120:10.1016/0165-1765(80)90055-5
904:Prais–Winsten transformation
830:, leading to an estimate of
262:, that if the error term is
1408:
17:Cochrane–Orcutt estimation
570:{\displaystyle e_{t}^{2}}
266:over time, then standard
1326:Elements of Econometrics
926:Prais–Winsten estimation
288:autoregressive structure
684:was first suggested by
270:as normally applied to
260:Durbin–Watson statistic
979:Wooldridge, Jeffrey M.
916:Hildreth–Lu estimation
889:
865:
844:
824:
782:
746:
710:
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623:
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174:{\displaystyle \beta }
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888:{\displaystyle \rho }
866:
864:{\displaystyle \rho }
845:
843:{\displaystyle \rho }
825:
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747:
711:
709:{\displaystyle \rho }
679:
624:
622:{\displaystyle \rho }
604:
572:
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399:
397:{\displaystyle e_{t}}
372:
268:statistical inference
242:
214:explanatory variables
207:
205:{\displaystyle X_{t}}
176:
148:
146:{\displaystyle y_{t}}
118:
1290:Time Series Analysis
921:Newey–West estimator
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157:of interest at time
153:is the value of the
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61:
1312:Econometric Methods
1245:MacKinnon, James G.
1243:Davidson, Russell;
1162:Empirical Economics
566:
377:, with the errors {
278:are estimated with
274:is invalid because
264:serially correlated
212:is a row vector of
54:Consider the model
1286:Hamilton, James D.
1174:10.1007/BF01973194
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155:dependent variable
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29:serial correlation
23:, which adjusts a
19:is a procedure in
1108:Economics Letters
992:978-1-111-53439-4
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686:Prais and Winsten
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1350:External links
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1308:Johnston, John
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1141:(3): 227–240.
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1008:Griliches, Zvi
1006:Rao, Potluri;
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959:(245): 32–61.
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37:statisticians
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1114:(1): 43–48.
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1079:(1): 93–96.
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1072:Econometrica
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633:Inefficiency
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286:first-order
257:
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217:
181:is a column
158:
125:
53:
25:linear model
21:econometrics
16:
15:
1320:Kmenta, Jan
406:white noise
272:regressions
1376:Categories
1366:Mark Thoma
1058:. Chicago.
937:References
639:efficiency
284:stationary
249:error term
44:Guy Orcutt
33:error term
1182:152953205
883:ρ
859:ρ
838:ρ
813:−
803:^
800:ε
767:^
764:ε
731:^
728:ε
704:ρ
661:ρ
657:−
617:ρ
594:β
588:α
513:β
502:−
491:ρ
488:−
466:ρ
463:−
454:α
443:−
432:ρ
429:−
354:ρ
322:−
315:ε
311:ρ
299:ε
229:ε
169:β
101:ε
94:β
78:α
1322:(1986).
1310:(1972).
1288:(1994).
1247:(1993).
981:(2013).
910:See also
404:} being
251:at time
216:at time
1362:YouTube
1332:302–317
1227:2109671
1093:1909605
1034:2283733
247:is the
31:in the
1338:
1296:
1274:
1255:
1225:
1180:
1091:
1032:
989:
346:
220:, and
183:vector
126:where
50:Theory
1223:JSTOR
1178:S2CID
1089:JSTOR
1052:(PDF)
1030:JSTOR
1336:ISBN
1294:ISBN
1272:ISBN
1253:ISBN
987:ISBN
362:<
280:bias
42:and
27:for
1364:by
1360:on
1213:hdl
1205:doi
1170:doi
1143:doi
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1081:doi
1022:doi
961:doi
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696:If
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