A Flexible Family of Compactly Supported Covariance Functions Based on Cutoff Polynomials

Abstract In time series analysis, signal covariance modeling is an essential part of stochastic methods like prediction or filtering. geodetic applications, functions are rarely treated as true compactly supported although large amounts data would approve such. Covariance models for complex correlation shapes also rare. Ideally, general families with a flexibility desirable to model correlations structures negative correlations. this paper, we derive isotropic finite that parametrized in way positive definiteness guaranteed. These based on cutoff polynomials which derived from operations such autoconvolution and autocorrelation. Next the compact support, resulting autocovariance share advantages (a) by design, (b) extensibility arbitrary orders (c) extensive employing multiple tunable shape parameters. All these realize various (the so-called hole effect) several oscillations. The methodological concepts homogeneous random fields $$\mathbb {R}^d$$ ℝ d . family then one-dimensional applications. A example demonstrates approach using stationary time-series data.