Abstract
This paper considers adaptive estimation of AR∞ models under time-varying variances of unknown forms. We utilize the sieve method to approximate the autoregressive model of infinite order, and then develop kernel-based estimators of the residual variances and associated adaptive least squares (ALS) estimators of the autoregressive coefficients. We prove the ALS estimator has the same efficiency as its infeasible counterpart. Simulation results show the adaptive procedure can help achieve efficiency gains in finite samples.
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