Non-linear time series regression

In Jennrich (1969) the model is considered, where x ( n ) is a sequence of i.i.d. (0, σ 2 ) random variables and z ( n ; θ ) is a continuous but possibly non-linear function of θ ∈ Θ, Θ being a compact set in R p . We shall use a second subscript when referring to a particular coordinate of θ 0 so that θ 0 j is the j th 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.