Singular Spectrum Analysis
periodical components extraction
identification of time series components
Nosovskiy A.M., Savina N.V., Osipov Yu.Yu., Filipenkov S.N.
This method was independently developed in Russia, Great Britain, and the USA under different names. "Caterpillar" and SSA (Singular Spectrum Analysis) are these names. The description of a method, its applications and can be found references to the literature in books [1, 2, 3]. The analysis of time numbers is very wide area. Therefore we shall comment, in what specificity of a considered method consists.
Let's describe briefly as the method works. For the analysis time of some gets out the whole parameter L; we shall name it «length of a window». Parameter L can get out any way enough. Then on the basis of some the matrix which columns are sliding pieces of some length L. Following a step is under construction track (“traektornaya”) is singular decomposition of tracking (“traektornaya”) matrixes in the sum of elementary matrixes. Each elementary matrix it is set a set from own number and two singulars vectors — own and factorial.
Summarizing elementary matrixes inside of each set and then, passing from result matrixes to a number, we receive decomposition of some on additive composed, for example, for the sum of a trend, the periodical press and noise or for the sum low-frequency and high-frequency components. A possibility to break set of elementary matrixes into the groups appropriating interpreted additive components of some, it is closely connected with concept of divisibility of numbers.
Thus, objective of a method is decomposition time of some on interpreted additive components. Thus the method does not require stationary of some, knowledge of pattern of a trend, as well as the information on availability in a number of periodic components and their periods. At such slight assumptions the method "Caterpillar"-SSA can solve various problems, such as, for example, trend, a tracking down of the periodical presses, smoothing of some, construction of full decomposition of some in the sum of a trend, the periodical presses and noise.
Let's note also, that the considered nonparametric method allows to receive results, is frequent only slightly less precise, than many parametrical methods at the analysis of some with known pattern.