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Proceeding Paper

On the Family of Covariance Functions Based on ARMA Models †

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), 37; https://doi.org/10.3390/engproc2021005037
Published: 5 July 2021
(This article belongs to the Proceedings of The 7th International conference on Time Series and Forecasting)
In time series analyses, covariance modeling is an essential part of stochastic methods such as prediction or filtering. For practical use, general families of covariance functions with large flexibilities are necessary to model complex correlations structures such as negative correlations. Thus, families of covariance functions should be as versatile as possible by including a high variety of basis functions. Another drawback of some common covariance models is that they can be parameterized in a way such that they do not allow all parameters to vary. In this work, we elaborate on the affiliation of several established covariance functions such as exponential, Matérn-type, and damped oscillating functions to the general class of covariance functions defined by autoregressive moving average (ARMA) processes. Furthermore, we present advanced limit cases that also belong to this class and enable a higher variability of the shape parameters and, consequently, the representable covariance functions. For prediction tasks in applications with spatial data, the covariance function must be positive semi-definite in the respective domain. We provide conditions for the shape parameters that need to be fulfilled for positive semi-definiteness of the covariance function in higher input dimensions. View Full-Text
Keywords: ARMA processes; covariance function; stochastic modeling; time series analysis; Matérn covariance function; positive definiteness ARMA processes; covariance function; stochastic modeling; time series analysis; Matérn covariance function; positive definiteness
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MDPI and ACS Style

Schubert, T.; Brockmann, J.M.; Korte, J.; Schuh, W.-D. On the Family of Covariance Functions Based on ARMA Models. Eng. Proc. 2021, 5, 37. https://doi.org/10.3390/engproc2021005037

AMA Style

Schubert T, Brockmann JM, Korte J, Schuh W-D. On the Family of Covariance Functions Based on ARMA Models. Engineering Proceedings. 2021; 5(1):37. https://doi.org/10.3390/engproc2021005037

Chicago/Turabian Style

Schubert, Till, Jan M. Brockmann, Johannes Korte, and Wolf-Dieter Schuh. 2021. "On the Family of Covariance Functions Based on ARMA Models" Engineering Proceedings 5, no. 1: 37. https://doi.org/10.3390/engproc2021005037

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