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Table 6 Results for the weakness index

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

Benchmark/rival model

h = 1

h = 2

h = 4

HAR-RV vs. HAR-RV-weak/q = 0.95

0.0012

0.0020

0.0027

HAR-RV vs. HAR-RV-weak/q = 0.75

0.0002

0.0000

0.0000

HAR-RV vs. HAR-RV-weak/q = 0.5

0.0001

0.0001

0.0000

HAR-RV vs. HAR-RV-weak/q = 0.25

0.0000

0.0005

0.0010

HAR-RV vs. HAR-RV-weak/q = 0.05

0.0054

0.0017

0.0020

HAR-RV vs. HAR-RV-states/q = 0.95

0.0052

0.1146

0.1841

HAR-RV vs. HAR-RV-states/q = 0.75

0.0093

0.0706

0.1131

HAR-RV vs. HAR-RV-states/q = 0.5

0.0234

0.0554

0.0956

HAR-RV vs. HAR-RV-states/q = 0.25

0.0105

0.0527

0.0954

HAR-RV vs. HAR-RV-states/q = 0.05

0.0311

0.0463

0.1014

HAR-RV-weak vs. HAR-RV-states/q = 0.95

0.0040

0.1129

0.1819

HAR-RV-weak vs. HAR-RV-states/q = 0.75

0.0091

0.0706

0.1131

HAR-RV-weak vs. HAR-RV-states/q = 0.5

0.0233

0.0553

0.0955

HAR-RV-weak vs. HAR-RV-states/q = 0.25

0.0105

0.0523

0.0945

HAR-RV-weak vs. HAR-RV-states/q = 0.05

0.0259

0.0447

0.0996

  1. 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 natural log of the realized volatility of oil-price returns