Asymptotic Properties of Estimator of Linear Regression Parameter in Case of Long-Range Dependent Regressors

The paper considers linear regression model with long-range/weak dependent random noise and time dependent regressors which are observed with long-range dependent errors. Parameter estimation of these models is an important problem of statistics of random processes. We choose widely used least squares estimator for the estimation. The aim of this work is to prove consistency and asymptotic normality of least squares estimator of the regression model. Theory of stationary Gaussian random processes with long-range and weak dependence, properties of slowly varying functions and Hölder-Young-Brascamp-Lieb inequality are used to derive the results. In this paper, we obtain sufficient conditions for consistency and asymptotic normality of least squares estimator of regression parameters.

Publication year: 
С. 26—33. Бібліогр.: 8 назв.

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