Strong consistency of parameter estimates for purely explosive autoregressive models with exogenous inputs

Asymptotic properties and strong consistency in the analysis of recursive estimation for stochastic regression models are important and fundamental. However, almost all of the existing results concerning the strong consistency of the least-squares estimates are established for non-explosive autoregressive models with exogenous inputs under the persistent excitation condition. In this paper, we establish the strong consistency of least-squares parameter estimates for explosive autoregressive models with persistently exciting exogenous inputs.