5.1 Introduction

Time-series analysis aims to understand the temporal behavior of one of several variables y( t). Examples are the investigation of long-term records of mountain uplift, sea-level fluctuations, orbitally-induced insolation variations and their influence on the ice-age cycles, millenium-scale variations of the atmosphere-ocean system, the impact of the El Ni o/Southern Oscillation on tropical rainfall and sedimentation (Fig 5.1) and tidal influences on nobel gas emissions of bore holes. The temporal structure of a sequence of events can be random, clustered, cyclic or chaotic. Time-series analysis provide various tools to detect these temporal structures. The understanding of the underlying process that produced the observed data allows us to predict future values of the variable. We use the Signal Processing Toolbox, which contains all necessary routines for time-series analysis.

Figure 5.1: a Photograph of ca. 30 kyr-old varved sediments from a landslide-dammed lake in the Northwest Argentine Andes. The mixed clastic-biogenic varves consist of reddish-brown and green to buff-colored clays sourced from Cretaceous redbeds (red-brown) and Precambrianearly Paleozoic greenshists (green-buff colored). The clastic varves are topped by thin white diatomite layers documenting the bloom of silica algae after the austral-summer rainy season. The distribution of the two source rocks and the interannual precipitation pattern in the area suggests that the reddish-brown layers reflect cyclic recurrence of enhanced precipitation, erosion and sediment input in the landslide-dammed lake. b The powerspectrum of a redcolor intensity transect across 70 varves is dominated by significant peaks at frequencies of ca. 0.076, 0.313,...