Asymptotic optimal inference for a class of nonlinear time series models (Q1802320)

The authors investigate first-order nonlinear time series \(\{Y_ t,\;t\geq 0\}\) generated from \(Y_ t=H_ \theta(Y_{t-1},z_ t)+\varepsilon_ t\), \(t=1,2,\dots,\) where \(\{\varepsilon_ t\}\) and \(\{z_ t\}\) are zero mean independent white noises. This class includes random coefficient RCAR(1), threshold TAR(1), exponential EAR(1), random coefficient exponential RCEAR(1), and random coefficient threshold RCTAR(1) models. Under some technical conditions, the local asymptotic normality (LAN) of the log-likelihood ratio is established. Using the LAN property, asymptotically optimal estimators of the parameters are derived. The results are used for construction of asymptotically efficient tests of linearity. An extension to higher order models is also briefly described.