Time series analysis and forecasting

The site is devoted to 'Caterpillar' (another name is SSA - Singular Spectrum Analysis), a powerful method of time series analysis and forecasting. The 'Caterpillar'-SSA is a model-free technique of time series analysis. It combines advantages of other methods, such as Fourier and regression analyses, with simplicity of visual control aids.

The basic 'Caterpillar'-SSA algorithm for analyzing one-dimensional time series consists of:

• Transformation of the one-dimensional time series to the trajectory matrix by means of a delay procedure (this gives the name to the whole technique);
• Singular Value Decomposition of the trajectory matrix;
• Reconstruction of the original time series based on a number of selected eigenvectors.

Thus, the result of the 'Caterpillar'-SSA processing is a decomposition of the time series into several components, which can often be identified as trends, seasonalities and other oscillatory series, or noise components.

This decomposition initializes forecasting procedures for both the original time series and its components. The method can be naturally extended to multidimensional time series and to image processing.

The 'Caterpillar'-SSA ideas were independently developed in Russia (St. Petersburg, Moscow) and also in UK and USA (under the name of SSA; that is, Singular Spectrum Analysis).

The method is a powerful and useful tool of time series analysis in meteorology, hydrology, geophysics, climatology and, according to our experience, in economics, biology, physics, medicine and other sciences; that is, where short and long, one-dimensional and multidimensional, stationary and nonstationary, almost deterministic and noisy time series are to be analyzed.

Our group participates in developing the method and corresponding software from the middle of 90s. The site contains results of this development. They are: information on two books devoted to the method and the software that allows everyone to feel simplicity and efficacy of its applications.

We are sure, that in a near future 'Caterpillar'-like methods will rank among the base methods of time series analysis and will be included in standard statistical software.