Robust estimation of multivariate and spatial autoregression

Abstract

This dissertation consists of five chapters. In Chapter 1, we collect some fundamental concepts and definitions employed in the forthcoming chapters. In Chapter 2, we consider the limiting behavior of a vector autoregressive model of order one (VAR(1)) with independent and identically distributed (i.i.d.) innovations vector with dependent components in the domain of attraction of a multivariate stable law with possibly different indices of stability. It is shown that in some cases the ordinary least squares (OLS) estimates are inconsistent. This inconsistency basically originates from the fact that each coordinate of the partial sum processes of dependent i.i.d. vectors of innovations in the domain of attraction of stable laws needs a different normalizer to converge to a limiting process. It is also revealed that certain M-estimates, with some regularity conditions, as an appropriate alternative, not only resolve inconsistency of the OLS estimates but also give higher consistency rates in all cases. In Chapter 3, we study the limiting behavior of the M-estimators of parameters for a spatial unilateral autoregressive model with i.i.d. innovations in the domain of attraction of a stable law with index alpha ∈ (0, 2]. Both stationary and unit root models and some extensions are considered. It is shown that self-normalized M-estimators are asymptotically normal. In Chapter 4, we investigate the limit theory of the M-estimators of parameters for a near unit root spatial autoregressive model considered in Chapter 3. Finally, some suggestions for future research are presented in Chapter 5.