Nonlinear time series models: consistency and asymptotic normality of nls under new conditions

Abstract

In this paper we study the consistency and asymptotic normality properties of nonlinear least squares (NLS) under a set of assumptions that are not difficult to verify. The statistical literature on estimation of nonlinear models by NLS rely on abstract theoretical conditions. See for example the books of Tong(1990), and Granger and Terasvirta(1993). There are alternative statistical frameworks but all of them depend on high level (very technical) assumptions that are difficult and tedious to verify, see for example Gallant and White(1988) and Wooldridge(1994). In this paper we show that for a general class of nonlinear dynamic regression models, there are explicit and easy to check conditions that satisfy the general framework of Gallant and White(1988). We show the usefulness of our assumptions with some examples from the class of Smooth Transition Autoregressive (STAR) models.