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Hildreth–Lu estimation, named for Clifford Hildreth and John Y. Lu, is a method for adjusting a linear model in response to the presence of serial correlation in the error term. It is an iterative procedure related to the Cochrane–Orcutt estimation.

The idea is to repeatedly apply ordinary least squares to

${\displaystyle y_{t}-\rho y_{t-1}=\alpha (1-\rho )+(X_{t}-\rho X_{t-1})\beta +e_{t}\,}$

for different values of ${\displaystyle \rho }$ between −1 and 1. From all these auxiliary regressions, one selects the pair (α, β) that yields the smallest residual sum of squares.

See also

• Prais–Winsten estimation

References

1. Hildreth, C.; Lu, J. Y. (November 1960). "Demand Relations with Autocorrelated Disturbances". Technical Bulletin. 276. Michigan State University Agricultural Experiment Station.

Further reading

• Davidson, Russell; MacKinnon, James G. (1993). Estimation and Inference in Econometrics. New York: Oxford University Press. pp. 331–341. ISBN 0-19-506011-3.
• Kmenta, Jan (1986). Elements of Econometrics (Second ed.). New York: Macmillan. pp. 298–317. ISBN 0-02-365070-2.
• Maddala, G. S.; Lahiri, Kajal (2009). Introduction to Econometrics (Fourth ed.). Chichester: Wiley. pp. 246–250. ISBN 978-0-470-01512-4.
• Pindyck, Robert S.; Rubinfeld, Daniel L. (1998). Econometric Models and Economic Forecasts (Fourth ed.). Boston: McGraw-Hill. pp. 159–164. ISBN 0-07-118831-2.

• Autocorrelation
• Regression with time series structure