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Proceeding Paper

A Mathematical Investigation of a Continuous Covariance Function Fitting with Discrete Covariances of an AR Process †

Institute of Geodesy and Geoinformation, University of Bonn, 53115 Bonn, Germany
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Author to whom correspondence should be addressed.
Presented at the 7th International Conference on Time Series and Forecasting, Gran Canaria, Spain, 19–21 July 2021.
Academic Editors: Ignacio Rojas, Fernando Rojas, Luis Javier Herrera and Hector Pomare
Eng. Proc. 2021, 5(1), 18; https://doi.org/10.3390/engproc2021005018
Published: 28 June 2021
(This article belongs to the Proceedings of The 7th International conference on Time Series and Forecasting)
In this paper, we want to find a continuous function fitting through the discrete covariance sequence generated by a stationary AR process. This function can be determined as soon as the Yule–Walker equations are found. The procedure consists of two steps. At first the inverse zeros of the characteristic polynomial of the AR process must be fixed. The second step is based on the fact that an AR process can also be seen as a difference equation. By solving this difference equation, it is possible to determine a class of functions from which a candidate for a continuous covariance function can be determined. To analyze if this function is applicable as a positive definite covariance function, it is analyzed mathematically in view of the power spectral density compared to the characteristics of the power spectral density for the discrete covariances. Then it is shown that this function is positive semi-definite. At the end, a simulation of a stationary AR(3) process is elaborated to illustrate the derived properties. View Full-Text
Keywords: AR process; continuous covariance function; Fourier transform; power spectral density; positive definiteness; signal prediction AR process; continuous covariance function; Fourier transform; power spectral density; positive definiteness; signal prediction
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MDPI and ACS Style

Korte, J.; Schubert, T.; Brockmann, J.M.; Schuh, W.-D. A Mathematical Investigation of a Continuous Covariance Function Fitting with Discrete Covariances of an AR Process. Eng. Proc. 2021, 5, 18. https://doi.org/10.3390/engproc2021005018

AMA Style

Korte J, Schubert T, Brockmann JM, Schuh W-D. A Mathematical Investigation of a Continuous Covariance Function Fitting with Discrete Covariances of an AR Process. Engineering Proceedings. 2021; 5(1):18. https://doi.org/10.3390/engproc2021005018

Chicago/Turabian Style

Korte, Johannes, Till Schubert, Jan M. Brockmann, and Wolf-Dieter Schuh. 2021. "A Mathematical Investigation of a Continuous Covariance Function Fitting with Discrete Covariances of an AR Process" Engineering Proceedings 5, no. 1: 18. https://doi.org/10.3390/engproc2021005018

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