The available numerical algorithms for trend removal require a direct subjective intervention in choosing critical parameters.
In this paper an algorithm is presented, which needs no initial subjective assumptions. Monotone trends are approximated by piecewise linear curves obtained by dividing into subintervals the signal values interval, not the time interval.
The slope of each linear segment of the estimated trend is proportional to the average one-step displacement of the signal values included into the corresponding subinterval. The evaluation of the trend removal is performed on statistical ensembles of artificial time series with the random component given by realizations of autoregressive of order one stochastic processes or by fractional Brownian motions.
The accuracy of the algorithm is compared with that of two well-tested methods: polynomial fitting and a nonparametric method based on moving average.
For stationary noise the results of the algorithm are slightly better, but for nonstationary noise the preliminary results indicate that the polynomial fitting has the best accuracy.
As a verification on a real time series, the time periods with monotone variation of global average temperature over the last 1800 years are established.
The removal of a nonmonotone trend is also briefly discussed.
-Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy
trend removal; monotone trends; time series;
Cite this paper as:
C. Vamoş, Automatic algorithm for monotone trend removal, Physical Review E 75 (2007) article id. 036705, DOI: 10.1103/PhysRevE.75.036705
see the expansion block below.
About this paper
Physical Review E
Google Scholar citations
 G. E. P. Box and G. M. Jenkins, Time Series Analysis: Forcasting and Control, 2nd ed. Holden-Day, San Francisco, 1976.
 D. B. Percival and A. T. Walden, Wavelet Methods for Time Series Analysis, Cambridge University Press, Cambridge, England, 2000.
 C. K. Peng, S. V. Buldyrev, S. Havlin, M. Simons, H. E. Stanley, and A. L. Goldberger, Phys. Rev. E 49, 1685 1994.
 K. Hu, P. C. Ivanov, Z. Chen, P. Carpena, and H. E. Stanley, Phys. Rev. E 64, 011114 2001.
 S. Zhao and G. W. Wei, Comput. Stat. Data Anal. 42, 219 2003.
 P. J. Brockwell and R. A. Davies, Time Series: Theory and Methods, 2nd ed. Springer-Verlag, New York, 1991.
 N.-N. Pang, Y.-K. Yu, and T. Halpin-Healy, Phys. Rev. E 52, 3224 1995.
 E. L. Andreas and G. Trevino, J. Atmos. Ocean. Technol. 14,
 P. D. Jones and M. E. Mann, Rev. Geophys. 42, 1 2004.
 P. D. Jones and M. E. Mann, Climate over Past Millenia, Data Contribution Series # 2004-085 2004, in NOAA/NGDC Paleoclimatology Program, URL http://www.ncdc.noaa.gov/ paleo/pubs/jones2004/
 M. G. Kendall, Rank Correlation Methods, 4th ed. Griffin, London, 1975.
 R. M. Hirsch and J. R. Slack, Water Resour. Res. 20, 727 1984.
 C. Vamoş, A. Georgescu, N. Suciu, and I. Turcu, Physica A 227, 81 1996.
 C. Vamoş, N. Suciu, and A. Georgescu, Phys. Rev. E 55, 6277 1997.
 C. Vamoş, N. Suciu, and W. Blaj, Physica A 287, 461 2000.