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The paper concerns the problem of applying singular spectrum analysis to time series with missing data. A method of filling in the missing data is proposed and is applied to time series of finite rank. Conditions of exact reconstruction of missing data are developed and versions of the algorithm applicable to real-life time series are presented. The proposed algorithms result in the extraction of additive components of time series such as trends and periodic components, with simultaneous filling in of the missing data. An example is presented. [Copyright &y& Elsevier]

In the present study, we have reconstructed glacier dynamics based on the high (1–0.5 mm) resolution X-ray fluorescence spectrometry scanning, the Fourier-transform infrared technique and 14C-dating used in the analyses of the lake bottom sediments, fluvioglacial deposits and a peat bog situated on East Siberian Mountains (East Sayan, Baikal, Barguzin and Kodar Ridges) between 51.723°N, 100.601°E and 56.885°N, 117.580°E. We have found what the largest glacier deposits on the Baikal shoreline, so-called Tompuda end moraine, formed in two stages. The first stage occurred until ca. 12 cal ka BP; then, there was a short pause. The second stage ended by 9.5 cal ka BP. Azarova glacier (Kodar Ridge) retreated upwards the Kodar Ridge by ca. 11 cal ka BP. It may indicate that the Bølling-Allerød warming was very evident, and it was a trigger for these deglacial events in East Siberia. It is most likely that "remains" of the Late Pleistocene glaciers were cardinally shrunk or fully disappeared during the Holocene Thermal Optimum in the southern part of East Siberia. Climate conditions were suitable for glacier formation after 3 cal ka BP. However, if there were new glaciers in the Middle Holocene, their sizes were likely to be less than 1 km2. For this reason, these glaciers should have completely melted during the Roman and Medieval Warm Periods. It is most likely, small glaciers observed at present in the south of East Siberia were mainly formed during the Little Ice Age. [ABSTRACT FROM AUTHOR]