Consistency of Least Squares Estimator of Linear Regression Parameter in Case of Discrete Tme and Long-Range or Weak Dependent Regressors

Linear regression model with discrete time, long-range/weak dependent random noise and time dependent regressors, which are observed with long L range/weak dependent errors, is considered. Parameter estimation of such models is one of the important problems of statistics of random processes. Least squares estimator is chosen for the estimation. The aim of the work is to prove consistency of least squares estimator of such regression model.

Asymptotic Unbiasedness and Consistency of Cross-Correlogram Estimators of Response Functions in Linear Continuous Systems

The estimation problem of an unknown real-valued response function of a linear continuous system is considered. We suppose that a family of zero-mean stationary Gaussian processes, which are close, in some sense, to a white noise, disturbs the system. Integral-type sample input-output cross-correlograms are taken as estimators of the response function from . The corresponding cross-correlogram estimator depends on two parameters (a parameter of a scheme of series and a length of an averaging interval) and is biased.