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

Ігор Володимирович Орловський

Abstract


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. Theory of stationary Gaussian random sequences with long-range and weak dependence, properties of slowly varying at infinity functions are used to get the results. In particular, asymptotic behavior of slowly varying at infinity functions in the integral sums is a key point in the proof of consistency in case of long-range dependent noise or random errors in regressors. Sufficient conditions for consistency of least squares estimator of regression parameter are obtained in the paper. It makes possible further study of asymptotic properties of least squares estimator of regression parameter.


Keywords


Consistency; Linear regression model; Errors in regressors; Least square estimator; Long-range dependence; Weak dependence

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DOI: https://doi.org/10.20535/1810-0546.2014.4.27946

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