Valid Post‐Averaging Inference in AR‐G/GARCH Models

Data analysis derives statistical inference from the result of data‐driven model (variable) selection or averaging. One puzzle however is that inference after model selection may not be guaranteed to satisfy tests and confidence intervals provided by classical statistical theory. This paper proposes a valid post‐averaging confidence interval in an AR model driven by a general GARCH (G/GARCH) model, in which the innovations exhibit a heavy‐tailed structure with a tail index λ∈(0,4]. To achieve this, we investigate the asymptotic inference of the nested least squares averaging estimator under model uncertainty with a fixed coefficient setup. Interestingly, based on a Mallows‐type model averaging (MTMA) criterion, the weights of under‐fitted models decay to zero whereas asymptotically random weights are assigned only to just‐fitted and over‐fitted models. Utilizing the asymptotic behavior of model weights, we derive the asymptotic distributions of the MTMA estimator and show that the proposed confidence interval is valid for any λ≥2. Monte Carlo simulations show that the proposed method achieves the nominal level.