V. Privalsky1 and A. Gluhovsky21Space 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
Received: 28 Jul 2015 – Accepted for review: 01 Sep 2015 – Discussion started: 06 Oct 2015
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.
Privalsky, V. and Gluhovsky, A.: On reconstruction of time series in climatology, Clim. Past Discuss., 11, 4701-4728, doi:10.5194/cpd-11-4701-2015, 2015.