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Biometrika 1977 64(2):385-399; doi:10.1093/biomet/64.2.385
© 1977 by Biometrika Trust
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Estimation of parameters of a continuous time Gaussian stationary process with rational spectral density

PHAM-DINH-TUAN

Dipartement de. Mathimatiques Appliquies, UniversiU de Grenoble France

The estimation of parameters in a continuous time Gaussian stationary process with zero mean and rational spectral density is achieved by an adaptation of the maximum likelihood method. It consists of minimizing something analogous to the sum of the squares of the residuals in the discrete case. The estimate is shown to be asymptotically normal and efficient. A simple computational procedure is also given to construct the estimate.

Key Words: Asymptotic efficiency • Asymptotic normality • Consistency • Likelihood funotion • Spectral representation • Stochastic integral


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