Semiparametric Sieve-Type Generalized Least Squares Inference

Abstract

This paper considers the problem of statistical inference in linear regression models with dependent errors. A sieve-type generalized least squares (GLS) procedure is proposed based on an autoregressive approximation to the generating mechanism of the errors. The asymptotic properties of the sieve-type GLS estimator are established under general conditions, including mixingaletype conditions as well as conditions which allow for long-range dependence in the stochastic regressors and/or the errors. A Monte Carlo study examines the finite-sample properties of the method for testing regression hypotheses.

Asymptotic normality of the time‐domain generalized least squares estimator for linear regression models

“…6 regarding mixing and approximation concepts). Compared with our work, the work of Kapetanios and Psaradakis (2016) can be seen as a complementary and parallel direction of generalization of the results of Amemiya (1973). Whereas we propose to relax [Amem1] and [Amem2], Kapetanios and Psaradakis (2016)…”

“…Assumptions [Hann4] and [Hann5] are similar to the mixing and stochastic assumptions considered in the proofs of Kapetanios & Psaradakis (2016). A proof of the main result under these conditions could be thus adapted from the techniques of Kapetanios & Psaradakis (2016). We believe that this is an interesting direction of research.…”

“…Also related to our article is the work of Kapetanios & Psaradakis (2016), which proposed to extend the results of Amemiya (1973) in a different direction. Here, the [Gren1]-[Gren4] are replaced by various stochastic assumptions on the sequences {x t } T t=1 and {U t } T t=1 that make use of mixing and stochastic approximation concepts, and higher moment bound (see Potscher & Prucha 1997, Ch.…”