Improved Tests for Trend in Time Series Data

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.

[1]  K. R. Kadiyala,et al.  A Transformation Used to Circumvent the Problem of Autocorrelation , 1968 .

[2]  James G. MacKinnon,et al.  A MAXIMUM LIKELIHOOD PROCEDURE FOR REGRESSION WITH AUTOCORRELATED ERRORS , 1978 .

[3]  Bridger M. Mitchell,et al.  Estimating the Autocorrelated Error Model with Trended Data: Further Results, , 1980 .

[4]  J. Chipman.  EFFICIENCY OF LEAST-SQUARES ESTIMATION OF LINEAR TREND WHEN RESIDUALS ARE AUTOCORRELATED , 1979 .

[5]  C. Nelson,et al.  Spurious Periodicity in Inappropriately Detrended Time Series , 1981 .

[6]  W. M. Carey,et al.  Digital spectral analysis: with applications , 1986 .

[7]  J. Hansen,et al.  Global trends of measured surface air temperature , 1987 .

[8]  D. Thornton.  A note on the efficiency of the cochrane-orcutt estimator of the ar(1) regression model , 1987 .

[9]  A. Parés-Sierra,et al.  The seasonal and interannual variability of the California Current system: A numerical model , 1989 .

[10]  J. Hansen,et al.  Global surface air temperatures: update through 1987 , 1988 .

[11]  David R. Brillinger,et al.  Consistent detection of a monotonic trend superposed on a stationary time series , 1989 .

[12]  Andrew Harvey,et al.  Forecasting, Structural Time Series Models and the Kalman Filter , 1990 .

[13]  D. Nychka,et al.  Climate spectra and detecting climate change , 1992 .

[14]  P. Bloomfield.  Trends in global temperature , 1992 .

[15]  R. Tibshirani,et al.  An introduction to the bootstrap , 1993 .

[16]  Henry L. Gray,et al.  Global warming and the problem of testing for trend in time series data , 1993 .

[17]  David R. Brillinger,et al.  Trend analysis: Time series and point process problems , 1994 .

[18]  Henry L. Gray,et al.  Selecting a Model for Detecting the Presence of a Trend , 1995 .

[19]  N. E. Savin,et al.  The Level and Power of the Bootstrap t Test in the AR(1) Model With Trend , 1996 .