Asymptotic normality of the residual correlogram in the continuous-time nonlinear regression model
Volume 8, Issue 1 (2021), pp. 93–113
Pub. online: 21 December 2020
Type: Research Article
Open Access
Open Access
Received
28 July 2020
28 July 2020
Revised
5 December 2020
5 December 2020
Accepted
5 December 2020
5 December 2020
Published
21 December 2020
21 December 2020
Abstract
In a continuous time nonlinear regression model the residual correlogram is considered as an estimator of the stationary Gaussian random noise covariance function. For this estimator the functional central limit theorem is proved in the space of continuous functions. The result obtained shows that the limiting sample continuous Gaussian random process coincides with the limiting process in the central limit theorem for standard correlogram of the random noise in the specified regression model.
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