Explosive Random-Coefficient AR(1) Processes and Related Asymptotics for Least-Squares Estimation

Large sample properties of the least-squares and weighted least-squares estimates of the autoregressive parameter of the explosive random-coefficient AR(1) process are discussed. It is shown that, contrary to the standard AR(1) case, the least-squares estimator is inconsistent whereas the weighted least-squares estimator is consistent and asymptotically normal even when the error process is not necessarily Gaussian. Conditional asymptotics on the event that a certain limiting random variable is non-zero is also discussed. Copyright 2005 Blackwell Publishing Ltd.