%0 Journal Article
%A
%A
%T Linear filters and nonlinear forecasting
%D 1994
%R 10.1098/rspb.1994.0064
%J Proceedings of the Royal Society of London. Series B: Biological Sciences
%P 157-161
%V 256
%N 1346
%X We consider the consequences of using linear filters to reduce noise before analysing short time series for low-dimensional chaotic behaviour. We discuss mathematical theory which suggests that certain filters should not affect the results of particular nonlinear analyses. We note that these results have only been proved for purely deterministic systems and need not be true when a stochastic component is present in the time series. In particular, we demonstrate that simple moving average filters can falsely suggest that a white noise data set is chaotic by using a test commonly used by biologists. This incorrect result is not obtained if the method of surrogate data is used together with this test. The results demonstrate the extreme care needed when analysing small data sets by using sophisticated mathematical techniques. The graphical technique we describe may also aid testing for linearity in time series.
%U http://rspb.royalsocietypublishing.org/content/royprsb/256/1346/157.full.pdf