Testing model specification in approximate Bayesian computation using asymptotic properties

We present a novel procedure to diagnose model misspecification in situations where inference is performed using approximate Bayesian computation (ABC). Unlike previous procedures, our proposal is based on the asymptotic properties of ABC. We demonstrate theoretically, and empirically that our procedure can consistently detect the presence of model misspecification. The examples demonstrate that our proposal shows good finite-sample properties, outperforming existing approaches. An empirical application to modeling exchange rate log returns using a g-and-k distribution completes the article. Supplementary materials for this article are available online.