The volatility models used in practice are unlikely to equal the Data Generating Process (DGP). Accordingly, models that are valid under misspecification is of great importance. We establish exact, general and mild conditions under which a large class of volatility prediction specifications exists. Crucially, the specifications within the class generate volatility predictions that are weakly identified for volatility under misspecification. Next, we derive a consistent and asymptotically normal estimator that is valid under dependence of unknown form. The volatility prediction specifications we consider in more detail are modifications of the log-ARCH-X model. The specifications are highly interpretable and versatile, and accommodate zero returns (in contrast to the classic log-ARCH specification), short-term and long-term persistence, asymmetry, volatility proxies and additional covariates. Since the volatility specifications are in logs, inference is standard under nullity of the parameters, and positivity of the volatility predictions are guaranteed. In our simulation experiments the predictions are both unbiased and identified for the benchmark model, whereas in our empirical illustration the volatility predictions compare well with those of the benchmark volatility model.