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Contents

Introduction

This page is about time series analysis as a mathematical tool to derive information from a series of measurements. Time series analysis is a branch of mathematical statistics.

Wavelets

An important tool for time series analysis are wavelets, or, to be more specific, discrete wavelet transforms (DWT). The DWT represents a time series in terms of coefficients that refer to certain time scales, therefore the DWT is able to decorrelate wide variety of time series that occur in physical applications.

Examples

Global Temperature in the 19th and 20th Century

The temporally and spatially averaged temperatures of oceans and atmospheres as well as a “average global” temperature are mentioned in the IPCC report from 2007, see

• 3.2.2 Temperature in the Instrumental Record for Land and Oceans, online here

and an appendix offering some criticism of this paragraph:

• Appendix 3.A: Low-Pass Filters and Linear Trends, online here

Data can be downloaded from the GISTEMP webpage.

References

• Manfred Mudelsee: Climate Time Series Analysis: Classical Statistical and Bootstrap Methods (amazon)

• Donald B. Percival and Andrew T.Walden: Wavelet Methods for Time Series Analysis (ZMATH)

Nonlinear Time Series Analysis

One of the most general models of nonlinear time series is of course the discrete approximation to a stochastic differential equation. For further information about this, see parametric estimation for stochastic differential equations.

Based on deterministic chaotic models:

• Holger Kantz and Thomas Schreiber: Nonlinear time series analysis, Cambridge University Press, 2nd edition 2004, ZMATH

This book is accompanied by a software package written partially in C? and partially in FORTRAN:

• TISEAN

Various methods can be found here:

• Jianqing Fan and Qiwei Yao: Nonlinear time series. Nonparametric and parametric methods., Springer Series in Statistics, New York, 2003, ZMATH

and here:

• Jiti Gao: Nonlinear times series: semiparametric and nonparametric methods., Monographs on Statistics and Applied Probability 108. Boca Raton, Chapman & Hall, 2007, ZMATH

A collection of research papers about nonlinear times series in geosciences can be found in this volume:

• Reik V. Donner, Susana M. Barbosa (Eds.): Nonlinear Time Series Analysis in the Geosciences, Applications in Climatology, Geodynamics and Solar-Terrestrial Physics, Springer, Berlin, 2008.

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