A new framework named Realized Conditional Autoregressive Expectile (Realized-udCARE) is proposed, through incorporating a measurement equation into the conventionaludCARE model, in a framework analogous to Realized-GARCH. The Rangeudand realized measures (Realized Variance and Realized Range) are employed asudthe dependent variables of the measurement equation, since they have proven moreudefficient than return for volatility estimation. The dependence between Range &udrealized measures and expectile can be modelled with this measurement equation.udThe grid search accuracy of the expectile level will be potentially improved with introducingudthis measurement equation. In addition, through employing a quadraticudfitting target search, the speed of grid search is significantly improved. Bayesianudadaptive Markov Chain Monte Carlo is used for estimation, and demonstrates its superiorityudcompared to maximum likelihood in a simulation study. Furthermore, weudpropose an innovative sub-sampled Realized Range and also adopt an existing scalingudscheme, in order to deal with the micro-structure noise of the high frequencyudvolatility measures. Compared to the CARE, the parametric GARCH and theudRealized-GARCH models, Value-at-Risk and Expected Shortfall forecasting resultsudof 6 indices and 3 assets series favor the proposed Realized-CARE model,udespecially the Realized-CARE model with Realized Range and sub-sampledudRealized Range.
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