Theoretical properties of the “Caterpillar” method of time series analysis

The article is devoted to the mathematical theory of the “Caterpillar” method which has proved to be a very powerful tool of time series analysis. This method is based on the use of the principal component analysis technique applied to a multivariate sample which is obtained from the initial sample by the method of delays. A natural language used to analyse the method is the Hilbert-Schmidt operator theory. We give conditions when two deterministic functions are completely separated from each other for a finite period of observations. We also show that under mild conditions any deterministic function can be asymptotically separated from any ergodic random noise