Non-linear time series regression

Abstract

In Jennrich (1969) the model is considered, wherex(n) is a sequence of i.i.d. (0,σ²) random variables andz(n;θ) is a continuous but possibly non-linear function ofθ_∈Θ, Θ being a compact set inR^p. We shall use a second subscript when referring to a particular coordinate ofθ₀so thatθ_0jis thejth coordinate. Jennrich establishes, under suitable conditions onz(n;θ) andx(n), the strong consistency and asymptotic normality of the least squares estimates ofθ.Our main purpose here is to extend these results to the case wherex(n) is generated by a stationary time series.