Coping with dating errors in causality estimation

¹ Saratov Branch of V. A. Kotel'nikov Institute of Radio- engineering and Electronics of the Russian Academy of Sciences - 38 Zelyonaya St., Saratov 410019, Russia
² Institute of Applied Physics of the Russian Academy of Sciences - 46 Ulyanova St., Nizhny Novgorod 603950, Russia
³ Potsdam Institute for Climate Impact Research - Telegraphenberg A31, Potsdam 14473, Germany
⁴ Institute for Geology, Mineralogy & Geophysics, Ruhr-Universität Bochum - Universitätsstr. 150, 44801, Bochum, Germany
⁵ Department of Earth Sciences, ETH Zurich - Sonneggstrasse 5, 8092 Zurich, Switzerland
⁶ Department of Earth Sciences, Durham University - Durham, DH1 3LE, UK

Received: 20 October 2016
Accepted: 30 January 2017

Abstract

We consider the problem of estimating causal influences between observed processes from time series possibly corrupted by errors in the time variable (dating errors) which are typical in palaeoclimatology, planetary science and astrophysics. “Causality ratio” based on the Wiener-Granger causality is proposed and studied for a paradigmatic class of model systems to reveal conditions under which it correctly indicates directionality of unidirectional coupling. It is argued that in the case of a priori known directionality, the causality ratio allows a characterization of dating errors and observational noise. Finally, we apply the developed approach to palaeoclimatic data and quantify the influence of solar activity on tropical Atlantic climate dynamics over the last two millennia. A stronger solar influence in the first millennium A.D. is inferred. The results also suggest a dating error of about 20 years in the solar proxy time series over the same period.