Standard Article

Time Series

Stochastic Modeling and Environmental Change

  1. Peter Bühlmann

Published Online: 15 SEP 2006

DOI: 10.1002/9780470057339.vat010

Encyclopedia of Environmetrics

Encyclopedia of Environmetrics

How to Cite

Bühlmann, P. 2006. Time Series. Encyclopedia of Environmetrics. 6.

Author Information

  1. ETHZ Zurich, Switzerland

Publication History

  1. Published Online: 15 SEP 2006


Many data occur in the form of time series where observations are recorded at different times. The presence of the notion of time often creates dependence among observations whose structure is of particular interest in time series analysis. When viewed from a stochastic perspective, time series data xt with t = 1, 2, …, n are one finite realization of sample size n from a stochastic process {Xtt = 0, ±1, ±2, …}: xt and Xt are generally r-vectors whose components take values on the real line, or in some discrete space being categorical or having an order. The restriction to equi-spaced time recordings can be relaxed to t1 > t2 > … > tn and the data-generating process can be indexed by continuous time {Xt}, for example with t [0, 1].