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

The asymptotic quasi-likelihood method is considered for the model yt = ft(θ) + Mt, t = 0,1, …,T where ftθ) is a linear predictable process of the parameter of interest θ, Mt is a martingale difference, and the nature of E(Mt2 | ℱt–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.