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EOS, TRANSACTIONS AMERICAN GEOPHYSICAL UNION, VOL. 86, NO. 24, doi:10.1029/2005EO240003, 2005

New Tools for Analyzing Time Series Relationships and Trends

J.C. Moore

Arctic Centre, University of Lapland, Rovaniemi, Finland


A. Grinsted

Arctic Centre, University of Lapland, Rovaniemi, Finland


S. Jevrejeva

Proudman Oceanographic Laboratory, Liverpool, UK


Abstract

Geophysical studies are plagued by short and noisy time series. These time series are typically nonstationary, contain various long-period quasi-periodic components, and have rather low signal-to-noise ratios and/or poor spatial sampling. Classic examples of these time series are tide gauge records, which are influenced by ocean and atmospheric circulation patterns, twentieth-century warming, and other long-term variability. Remarkable progress recently has been made in the statistical analysis of time series. Ghil et al. [2002] presented a general review of several advanced statistical methods with a solid theoretical foundation. This present article highlights several new approaches that are easy to use and that may be of general interest. Extracting trends from data is a key element of many geophysical studies; however, when the best fit is clearly not linear, it can be difficult to evaluate appropriate errors for the trend. Here, a method is suggested of finding a data-adaptive nonlinear trend and its error at any point along the trend. The method has significant advantages over, e.g., low-pass filtering or fitting by polynomial functions in that as the fit is data adaptive, no preconceived functions are forced on the data; the errors associated with the trend are then usually much smaller than individual measurement errors.

Published 14 June 2005.

Index Terms: 3270 Mathematical Geophysics: Time series analysis (1872, 4277, 4475); 1620 Global Change: Climate dynamics (0429, 3309); 1641 Global Change: Sea level change (1222, 1225, 4556).

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Citation: Moore, J.C., A. Grinsted, and S. Jevrejeva (2005), New Tools for Analyzing Time Series Relationships and Trends, Eos Trans. AGU, 86(24), doi:10.1029/2005EO240003.