Least squares (LS) and maximum likelihood (ML) estimation are considered for unit root processes with GARCH (1, 1) errors. The asymptotic distributions of LS and ML estimators are derived under the condition α + β  1. The former has the usual unit root distribution and the latter is a...

The strong consistency of the least squares estimator in multiple regression models is established assuming the randomness of the regressors and errors with infinite variance. Only moderately restrictive conditions are imposed on the stochastic model matrix and the errors will be random...

This paper examines the asymptotic inference for AR(1) models with a possible structural break in the AR parameter β near the unity at an unknown time k₀. Consider the model y_{t}=β₁y_{t-1}I{t≤k₀}+β₂y_{t-1}I{tk₀}+ε_{t}, t=1,2,⋯,T, where I{⋅} denotes the indicator function. We...

Incorrect specification of the hazard rate in duration analysis can produce inconsistent estimators of the parameters of the model. We propose a new estimator for discrete duration models in which the hazard rate is comprised of an inner index function of the covariates and time variable and an...

The central limit theorems, the deviation inequality (and large deviation), and the moderate deviations for least squares estimators of parameters in the CIR type model driven byα-stable noises are established when the dispersion parameter ε→0 and the discrete observation frequency k→∞...

By using a large deviation theory of the stochastic process and the moment information of errors, some large deviation results for the least squares estimator θn in a nonlinear regression model are obtained when errors satisfy some general conditions. For some p1, examples are presented to show...

This paper deals with the improved forecasts for the values of the study variable in linear regression models utilizing the minimum risk approach. It considers the simultaneous forecasting of actual and average values of the study variable and reports the performance properties of the classical...