Non-linear time series regression
E. J. Hannan · Journal of Applied Probability · 1971
In Jennrich (1969) the model is considered, where x(n) is a sequence of i.i.d. (0, σ2) random variables and z(n; θ) is a continuous but possibly non-linear function of θ∈ Θ, Θ being a compact set in Rp. We shall use a second subscript when referring to a particular coordinate of θ0 so that θ0j is the jth coordinate. Jennrich establishes, under suitable conditions on z(n; θ) and x(n), the strong consistency and asymptotic normality of the least squares estimates of θ. Our main purpose here is to extend these results to the case where x(n) is generated by a stationary time series.