# 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

## 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:

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.