Linear Filters and Nonlinear Forecasting

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...

Full description

Saved in:
Bibliographic Details
Published in:Proceedings of the Royal Society. B, Biological sciences Biological sciences, 1994-05, Vol.256 (1346), p.157-161
Main Authors: Lloyd, Alun L., Gravenor, Michael B.
Format: Article
Language:English
Subjects:
Autocorrelation
Biological and medical sciences
Datasets
Determinism
Fundamental and applied biological sciences. Psychology
General aspects
Information retrieval noise
Logistics
Mathematics in biology. Statistical analysis. Models. Metrology. Data processing in biology (general aspects)
Optical filters
Predictability
Time series
Time series forecasting
White noise
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0962-8452
1471-2954
DOI:10.1098/rspb.1994.0064