Previsão de volatilidade a tempo discreto: Uma abordagem via regressão quantílica

I propose the Heterogeneous Quantile Autoregressive Distributed Lag Realized Volatility, with Jumps and Leverage Effect (HQADL-RV-JL). The specification incorporates the main stylized volatility facts, falling into HAR model class under the Quantile Regression framework. This approach allows for the flexibility of autoregressive coefficients across the quantiles, where each regressor may have an impact on scale, location and shape of conditional response distribution. The model was estimated on an equally spaced grid spanning 91 quantile levels between 0.05 and 0.95, using S&P500 index high-frequency returns. The results shows that the estimates of continuous volatility components are highly significant across the quantile levels, considering the daily, weekly and monthly frequencies. Furthermore, the daily and weekly coefficients for the jumps and leverage components were significant for almost all quantile levels, highlighting not only the adequacy of both asymmetric effects concerning their adjustments to this semiparametric specification, but also its importance for future volatility of returns. Regarding its performance, the results suggests that median forecast of the propose model is as good as the conditional mean prediction of Corsi e Renò (2012) specification in the medium and long term. Lastly, it was also performed the volatility density forecast for the last four days of the sample. The distributional aspects of the predicted densities exhibit asymmetries to a certain degree, taking the form of a bimodal distribution.