Identification of Volatility Proxies as Expectations of Squared Financial Return

Volatility proxies like Realised Volatility (RV) are extensively used to assess the forecasts of squared financial return produced by Autoregressive Conditional Heteroscedasticity (ARCH) models. But are volatility proxies identified as expectations of the squared return? If not, then the results of these comparisons can be misleading, even if the proxy is unbiased. Here, a tripartite distinction between strong, semi-strong and weak identification of a volatility proxy as an expectation of squared return is introduced. The definition implies that semi-strong and weak identification can be studied and corrected for via a multiplicative transformation. Well-known tests can be used to check for identification and bias, and Monte Carlo simulations show they are well-sized and powerful -- even in fairly small samples. As an illustration, twelve volatility proxies used in three seminal studies are revisited. Half of the proxies do not satisfy either semi-strong or weak identification, but their corrected transformations do. Correcting for identification does not always reduce the bias of the proxy, so there is a tradeoff between the choice of correction and the resulting bias.