Simultaneous Indirect Inference, Impulse Responses and ARMA Models

A two-stage simulation-based framework is proposed to derive Identification Robust confidence sets by applying Indirect Inference, in the context of Autoregressive Moving Average (ARMA) processes for finite samples. Resulting objective functions are treated as test statistics, which are inverted rather than optimized, via the Monte Carlo test method. Simulation studies illustrate accurate size and good power. Projected impulse-response confidence bands are simultaneous by construction and exhibit robustness to parameter identification problems. The persistence of shocks on oil prices and returns is analyzed via impulse-response confidence bands. Our findings support the usefulness of impulse-responses as an empirically relevant transformation of the confidence set.