Second Moment Estimator for An AR(1) Model Driven by A Long Memory Gaussian Noise
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In this paper, we consider an inference problem for the first order autoregressive process driven by a long memory Gaussian process. The assumptions and results are stated in terms of the covariance function of the noise. Some examples include the fractional Gaussian noise and the fractional ARIMA model. For the second moment estimator, we prove the strong consistency and the asymptotic normality, and obtain the Berry-Esseen bound under appropriate conditions. The proof is based on the decay rate of the stationary solution's covariance associated with the Gaussian noise.
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