strong dependence

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 Uniqueness of the Non-Linear Regression Model Parameter with Least Squares Estimator

In the paper the nonlinear regression model with continuous time and random noise, which is a local functional of strongly dependent stationary Gaussian random process, is considered. Sufficient conditions of asymptotic uniqueness of the least squares estimator of regression function parameters are obtained. This result is applied to the least squares estimator of amplitude and angular frequencies of harmonic oscillations sum observed on the background of given random noise.