Modern Stochastics: Theory and Applications

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.