Asymptotic Properties of GARCH-X Processes

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QML INFERENCE FOR VOLATILITY MODELS WITH COVARIATES (2015, background): “It is thus questionable to compare volatility forecasts with realized volatilities, a practice which is however becoming common in finance since the celebrated paper of Hansen and Lunde (2005).”
The Cross-Quantilogram: Measuring Quantile Dependence and Testing Directional Predictability between Time Series (2014, methodology): “The GARCH-X process is 20 commonly used for modeling volatility of economic or financial time series in the litera- ture, see Han (2015) and references therein.”
Two are better than one: Volatility forecasting using multiplicative component GARCH‐MIDAS models (2020, unknown): “We base our analysis on the MCS approach introduced by Hansen et al. (2011). Following the arguments in Patton (2011), we use the QLIKE loss as the evaluation criterion.”