Asymptotic and Bootstrap Inference for AR(Infinite) Processes with Conditional Heteroskedasticity

The main contribution of this paper is twofold. First, we derive the consistency and asymptotic normality of the estimated autoregressive sieve parameters when the data are generated by a stationary linear process with martingale difference errors that are possibly subject to conditional heteroskedasticity of unknown form. To the best of our knowledge, the asymptotic distribution of the least-squares estimator has not been derived under these conditions. Second, we show that a suitably constructed bootstrap estimator will have the same limit distribution as the OLS estimator. Our results provide theoretical justification for the use of either the conventional asymptotic approximation or the bootstrap approximation of the distribution of smooth functions of autoregressive parameters.
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