We thank the authors (hereafter referred to as CCC) for providing us an opportunity to clarify some points of our original paper. CCC list in their abstract three "key points"that we respond to in this Reply. The first comment is the central one and the most developed. It deals mainly with discussion of features of methods of spectral analysis, mainly SSA. We have quoted the sub parts of that comment as items 1a to 1k. The replies to comments/key points 2 and 3 are shorter. We disagree with most of the comments by CCC and explain why. We conclude that we have successfully countered CCC's criticism and shown many of their points to be unsubstantiated. The main problem seems to reside in differences concerning the literature on Singular Spectral Analysis and our use of it. Much of our response to the comments can be found in textbooks and review papers on SSA and time series analysis; we quote extensively, both in our original paper and in this response to CCC, Golyandina and Zhigljavsky (2013).