Hildreth–Lu estimation

Hildreth–Lu estimation, named for Clifford Hildreth and John Y. Lu,^[1] is a method adjust a linear model to serial correlation in the error term. It is an iterative procedure related to the Cochrane–Orcutt estimation.

The idea is to repeatedly apply non-linear least squares to:

$y_t - \rho y_{t-1} = \alpha(1-\rho)+\beta(X_t - \rho X_{t-1}) + e_t. \,$

for different values of $\rho$ between −1 and 1. From all these auxiliary regressions, one selects the one that yields the smallest residual sum of squares.

References

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

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.