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

In this paper, we want to find a continuous function fitting through the discrete covariance sequence generated by stationary AR process. This can be determined as soon Yule–Walker equations are found. The procedure consists of two steps. At first inverse zeros characteristic polynomial process must fixed. second step is based on fact that an also seen difference equation. By solving equation, it possible determine class functions from which candidate for determined. To analyze if applicable positive definite function, analyzed mathematically in view power spectral density compared characteristics covariances. Then shown semi-definite. end, simulation AR(3) elaborated illustrate derived properties.