Geoscience Reference
In-Depth Information
5 Time-Series Analysis
Alternations of clayey and silty layers in the
Upper Triassic sediments near Heilbronn
in Germany, indicating cyclic changes in
environmental conditions. Time-series analysis
aims to investigate the temporal behavior of
a variable such as grainsize. Together with
age determinations, this method can be used
to determine the period of the cycles and to
speculate about the mechanism that caused
the rhythmic changes in grain size.
5.1 Introduction
Time-series analysis aims to investigate the temporal behavior of a variable
x
(
t
). Examples include the investigation of long-term records of mountain
uplit , sea-level l uctuations, orbitally-induced insolation variations and
their inl uence on the ice-age cycles, millennium-scale variations in the
atmosphere-ocean system, the ef ect of the El Niño/Southern Oscillation on
tropical rainfall and sedimentation (Fig. 5.1), and tidal inl uences on noble
gas emissions from bore holes. h e temporal pattern of a sequence of events
can be random, clustered, cyclic, or chaotic. Time-series analysis provides
various tools with which to detect these temporal patterns. Understanding
the underlying processes that produced the observed data allows us to
predict future values of the variable. We use the Signal Processing and
Wavelet Toolboxes, which contain all the necessary routines for time-series
analysis (MathWorks 2014a and b).
Section 5.2 discusses signals in general and contains a technical
description of how to generate synthetic signals for time-series analysis.
h e use of spectral analysis to detect cyclicities in a single time series (auto-
spectral analysis) and to determine the relationship between two time series
