Do U.S. economic conditions at the state level predict the realized volatility of oil-price returns? A quantile machine-learning approach

Financial Innovation

Table 3 Results for RV

Benchmark/rival model	h = 1	h = 2	h = 4
HAR-RV vs. HAR-RV-US/q = 0.95	0.0000	0.0000	0.0003
HAR-RV vs. HAR-RV-US/q = 0.75	0.0002	0.0002	0.0002
HAR-RV vs. HAR-RV-US/q = 0.5	0.0000	0.0003	0.0002
HAR-RV vs. HAR-RV-US/q = 0.25	0.0016	0.0009	0.0000
HAR-RV vs. HAR-RV-US/q = 0.05	0.0031	0.0000	0.0002
HAR-RV vs. HAR-RV-states/q = 0.95	0.0002	0.0000	0.2340
HAR-RV vs. HAR-RV-states/q = 0.75	0.0317	0.0521	0.0809
HAR-RV vs. HAR-RV-states/q = 0.5	0.0426	0.0688	0.0913
HAR-RV vs. HAR-RV-states/q = 0.25	0.0598	0.1023	0.1425
HAR-RV vs. HAR-RV-states/q = 0.05	0.0414	0.1334	0.2129
HAR-RV-US vs. HAR-RV-states/q = 0.95	0.0002	0.0000	0.2337
HAR-RV-US vs. HAR-RV-states/q = 0.75	0.0315	0.0518	0.0807
HAR-RV-US vs. HAR-RV-states/q = 0.5	0.0426	0.0686	0.0911
HAR-RV-US vs. HAR-RV-states/q = 0.25	0.0583	0.1014	0.1425
HAR-RV-US vs. HAR-RV-states/q = 0.05	0.0384	0.1334	0.2127

The relative-performance statistic, RP, statistic is computed as \(RP = 1 - \sum _{t=1}^T \rho _\alpha \left( e_{t, R} \right) / \sum _{t=1}^T \rho _\alpha \left( e_{t, B} \right)\), where \(e_t\) denotes the model prediction errors. The benchmark (B) model is the first model given in the first column of the table, and the rival (R) model is the second model given in that column. The HAR-RV-states model includes the state-level components in the vector of potential predictors. The benchmark model is estimated by the quantile-regression technique, while the HAR-RV-states model is estimated by the quantile Lasso technique. The intercept and the classic HAR-RV terms are not penalized. The penalty parameter is determined by tenfold cross-validation. A positive RP statistic shows that the rival model outperforms the benchmark model. The parameter h denotes the forecast horizon. The parameter q denotes the quantile being analyzed. The dependent variable is the realized volatility of oil-price returns