The difficult problem of testing for linear trend in the presence of correlated residuals is addressed. Because the residuals are correlated, tests for trend based on the classical least-squares regression techniques are inappropriate. Whenever the residuals are even moderately correlated, the procedures in the literature that are intended to adjust for the correlation in the residuals tend to have the problem that the observed significance levels are higher than nominal levels for small to moderate realization lengths. Although it is well known that this tendency exists, the extent of the problem is not widely appreciated. We introduce a bootstrap-based procedure to test for trend in this setting. This procedure is better adapted to controlling the significance levels and is studied via simulation results. The procedure is then applied to the problem of testing for trend in global atmospheric temperature data and in data from models for ocean acoustic travel time along a path.

Key Words
Bootstrap; Global warming; Hypothesis testing; Regression with correlated residuals.

Wayne A. Woodward is Professor of Statistics, and H. L. Gray is C. F. Frensley Professor of Mathematics and Statistics, Department of Statistical Science, Southern Methodist University, Dallas, TX 75275. Steven Bottone is Technical Staff Member, Mission Research Corporation, P.O. Drawer 719, 735 State Street, Santa Barbara, CA 93102.