engleski

Asymptotic properties of the least squares estimations in regression models with singular errors

In this work the asymptotic properties of the least square estimator are analyzed in linear regression models with long memory stationary errors. Continuous models with one dimensional and $k$-dimensional inputs are treated here. In the scope of the analysis of consistency, the asymptotic behaviour of the correlation matrix is given as well as the sufficient conditions for consistency. In the scope of the analysis of asymptotic distributions of the least square estimator, centred on the mean and norming with an appropriate matrix, the integral representation of the asymptotic distributions is proved. We can see from these results that the asymptotic distributions need not be normal at all. They depend on the errors" distributions.

asymptotic properties of least squares estimator; regression model; singular errors; asymptotic distributions

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