The use of the inverse problem of spectral analysis to forecast time series. (English) Zbl 1499.35721

Summary: The paper proposes a new method to forecast time series. We assume that a time series is a sequence of eigenvalues of a discrete self-adjoint operator acting in a Hilbert space. In order to construct such an operator, we use the theory of solving inverse problems of spectral analysis. The paper gives a theoretical justification for the proposed method. An algorithm for solving the inverse problem is given. Also, we give an example of constructing a differential operator whose eigenvalues practically coincide with a given time series.


35R30 Inverse problems for PDEs
35A01 Existence problems for PDEs: global existence, local existence, non-existence
47A52 Linear operators and ill-posed problems, regularization
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