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

Abstract.  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.