Convergence to Normality of the Asymptotic Quasi‐Score Function on a Linear Model

The asymptotic quasi‐likelihood method is considered for the model y_t = f_t(θ) + M_t, t = 0,1, …,T where f_tθ) is a linear predictable process of the parameter of interest θ, M_t is a martingale difference, and the nature of E(M_t² | ℱ_t–1) is unknown. This paper is concerned with the limiting distribution of the asymptotic quasi‐score function of such a model. Confidence intervals and hypothesis testing of θ is derived from the limiting distribution. Comparison is made between the estimates obtained through this method and those obtained through the least squares method.