Abstract
Phase space prediction is a feature selection method which triesto exploit non-linear dynamics of an underlying system. We describe and offer a critical reconsideration of this approach,discuss questions of whether non-linear methods are justified by the data, and apply them to ozone time series from single locations. Our main objectives are to obtain air quality forecasts in order to provide public health warnings and to provide an insight into the dynamics of the underlying system.Interestingly, comparable linear data sets (surrogates)have very similar structure and give similar predictionaccuracy to that of the ozone data. In this instance theredoes not appear to be any advantage to applying the phasespace approach to univariate time series.
This is a preview of subscription content, access via your institution.
References
Chen, J. L., Islam, S. and Biswas, P.: 1998, ‘Nonlinear dynamics of hourly ozone concentrations: nonparametric short term prediction’, Atmos. Environ. 32(11), 1839–1848.
Grassberger, P. and Procaccia I.: 1983, ‘Characterization of strange attractors’, Phys.Rev.Lett. 50(5),346–349.
Haase, P., Schlink, U. and Richter M.: 2001, ‘Non-Parametric Short-Term Prediction of Ozone Concentration in Berlin: Preconditions and Justification’, Proceedings of the International Conference on Air Pollution Modelling and Simulation, Paris, France.
Hegger, R., Kantz, H. and Schreiber, T.: 1999, ‘Practical implementation of nonlinear time series methods: The TISEAN package’, Chaos 9, 413.
Kantz, H. and Schreiber, T.: 2000, Nonlinear Time Series Analysis, Cambridge University Press, Cambridge, 304 pp.
Kennel, M. B., Brown R. and Abarbanel, H. D. I.: 1992, ‘Determining embedding dimension for phase-space reconstruction using a geometrical construction’, Phys.Rev. A45(6), 3403–3411.
Kocak, K., Saylan, L. and Sen, O.: 2000, ‘Nonlinear time series prediction of O3 concentration in Istanbul’, Atmos. Environ. 34, 1267–1271.
Li, I. F., Biswas, P. and Islam, S.: 1994, ‘Estimation of the dominant degrees of freedom for air pollutant concentration data: applications to ozone measurements’, Atmos. Environ. 28(9), 1707–1714.
Lorenz, E. N.: 1963, ‘Deterministic nonperiodic flow’, J. Atmos. Sci. 20, 130–141.
Raga, G. B. and Moyne, L. Le: 1996, ‘On the nature of air pollution dynamics in Mexico City – I. Nonlinear analysis’, Atmos. Environ. 30(23), 3987–3993.
Schlink, U., Herbarth, O. and Tetzlaff, G.: 1997, ‘A component time-series model for SO2 data: Forecasting, interpretation and modification’, Atmos. Environ. 31(9), 1285–1295.
Schreiber, T. and Schmitz, A.: 2000, ‘Surrogate time series’, Physica D 142, 346.
Sugihara, G. and May R. M.: 1990, ‘Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series’, Nature 344, 734–741.
Takens, F.: 1981, ‘Detecting strange attractors in turbulence’, in D. A. Rand and L. S. Young (eds), Dynamical Systems and Turbulence, Lecture Notes in Mathematics 898, Springer, Berlin, Germany, pp. 366–381.
Theiler, J., Eubank, S., Longtin, A., Galdrikian, B. and Farmer, J. D.: 1992, ‘Testing for nonlinearity in time series: The method of surrogate data’, Physica D 58, 77–94.
Author information
Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Haase, P., Schlink, U. & Richter, M. Critical Reconsideration of Phase Space Embedding and Local Non-Parametric Prediction of Ozone Time Series. Water, Air, & Soil Pollution: Focus 2, 513–524 (2002). https://doi.org/10.1023/A:1021388813370
Issue Date:
- chaos
- embedding
- local non-parametricprediction
- missing value reconstruction
- non-lineardynamics
- ozone concentrations
- surrogates