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Climate of the Past An interactive open-access journal of the European Geosciences Union
© Author(s) 2015. This work is distributed under
the Creative Commons Attribution 3.0 License.
Research article
06 Oct 2015
Review status
This discussion paper is a preprint. It has been under review for the journal Climate of the Past (CP). The manuscript was not accepted for further review after discussion.
On reconstruction of time series in climatology
V. Privalsky1 and A. Gluhovsky2 1Space Dynamics Laboratory (ret.), VEP Consulting, Logan, Utah, USA
2Department of Earth, Atmospheric, and Planetary Sciences and Department of Statistics, Purdue University, West Lafayette, Indiana, USA
Abstract. The approach to time series reconstruction in climatology based upon cross-correlation coefficients and regression equations is mathematically incorrect because it ignores the dependence of time series upon their past. The proper method described here for the bivariate case requires the autoregressive time- and frequency domains modeling of the time series which contains simultaneous observations of both scalar series with subsequent application of the model to restore the shorter one into the past. The method presents further development of previous efforts taken by a number of authors starting from A. Douglass who introduced some concepts of time series analysis into paleoclimatology. The method is applied to the monthly data of total solar irradiance (TSI), 1979–2014, and sunspot numbers (SSN), 1749–2014, to restore the TSI data over 1749–1978. The results of the reconstruction are in statistical agreement with observations.

Citation: Privalsky, V. and Gluhovsky, A.: On reconstruction of time series in climatology, Clim. Past Discuss.,, 2015.
V. Privalsky and A. Gluhovsky
V. Privalsky and A. Gluhovsky


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