PREDICTION OF MULTIDIMENSIONAL TIME SERIES BY METHOD OF INVERSE SPECTRAL PROBLEM

A. I. Sedov

Abstract


The paper develops a new method for predicting time series by the inverse spectral problem. We show that it is possible to construct  a differential operator such that its eigenvalues coincide with a given numerical sequence. The paper gives a theoretical justification of the proposed method. The algorithm for finding a solution and an example of constructing a differential operator with partial derivatives are given. In this paper, we present a generalization in the case of multidimensional time series.

Keywords


Laplace operator; inverse spectral problem; eigenvalues; time series

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References


Sedov A.I. The Use of the Inverse Problem of Spectral Analysis to Forecast Time Series. Journal of Computational and Engineering Mathematics, 2019, vol. 6, no. 1, pp. 74-78. DOI:~10.14529/jcem190108

Sedov A.I., Dubrovskii V.V. Inverse Problem of Spectral Analysis for the some Partial Differential Operator with the Resolvent of Non-trace Class. Electromagnetic waves and electronic systems, 2005, vol. 10, no.1-2. pp. 4-9. (in Russian)

Sedov A.I. Inverse problem of spectral analysis. Trace method. Magnitogorsk, Magnitogorsk State University, 2012, 104 p. (in Russian)


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