Theoretical Relationship between SSA and MESA

It is theoretically demonstrated that singular spectrum analysis (SSA£©is an equivalent form of Maximum Entropy Spectrum Analysis (MESA£©which is essential1y a nonlinear estimation of the classical power spectrum. Both methods have respectively some different features in application as a result of the difference of descriptive of manners. The chief merits of SSA are as follows: (i) to recognize obvious period on the time domain in such a manner that it can also identify the feeble signal under vigorous noise; (ii)not to intensively depend on m (which is equals to the best order of MESA), thus leading to steadily identify the same period on a large domain of varying m and MESA not; (iii) not just to recognize periods on time domain and to investigate their time-changed character. For the particular merits are given above ,SSA can replace MESA under a certain length of time series, making successful climatic forecast in recent years, which is beyond the scope of MESA.