# Automatic algorithm for monotone trend removal

## Abstract

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.

## Authors

C. Vamoș
-Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy

## Keywords

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

## PDF

##### Journal

Physical Review E

2470-0053

2470-0045

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