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.
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.
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
and an appendix offering some criticism of this paragraph:
Data can be downloaded from the GISTEMP webpage.
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)
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:
This book is accompanied by a software package written partially in C? and partially in FORTRAN:
Various methods can be found here:
and here:
A collection of research papers about nonlinear times series in geosciences can be found in this volume: