Fractional Integration with Drift: Estimation in Small Samples

(Empirial Economics, No 22, 1997)

Posted: 18 Feb 1997

See all articles by Anthony A. Smith

Anthony A. Smith

Yale University - Cowles Foundation

Fallaw Sowell

Carnegie Mellon University - David A. Tepper School of Business

Stanley E. Zin

Carnegie Mellon University; National Bureau of Economic Research (NBER)

Abstract

We examine the finite-sample behavior of estimators of the order of integration in a fractionally integrated time-series model. In particular, we compare exact time-domain likelihood estimation to frequency-domain approximate likelihood estimation. We show that over-differencing is of critical importance for time-domain maximum-likelihood estimation in finite samples. Over-differencing moves the differencing parameter (in the over-differenced model) away from the boundary of the parameter space, while at the same time obviating the need to estimate the drift parameter. The two estimators that we compare are asymptotically equivalent. In small samples, however, the time-domain estimator has smaller mean squared error than the frequency-domain estimator. Although the frequency-domain estimator has larger bias than the time-domain estimator for some regions of the parameter bias, it can also have smaller bias. We use a simulation procedure which exploits the approximate linearity of the bias function to reduce the bias in the time-domain estimator.

JEL Classification: C13, C15, C22, C51

Suggested Citation

Smith, Anthony A. and Sowell, Fallaw and Zin, Stanley E., Fractional Integration with Drift: Estimation in Small Samples. (Empirial Economics, No 22, 1997), Available at SSRN: https://ssrn.com/abstract=4656

Anthony A. Smith (Contact Author)

Yale University - Cowles Foundation ( email )

Box 208281
New Haven, CT 06520-8281
United States

Fallaw Sowell

Carnegie Mellon University - David A. Tepper School of Business ( email )

5000 Forbes Avenue
Pittsburgh, PA 15213-3890
United States

Stanley E. Zin

Carnegie Mellon University ( email )

Pittsburgh, PA 15213-3890
United States

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

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