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Financial Innovation

Table 7 Additional results based on intraday data calculations

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

 

Crude oil

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

0.0000

0.0000

0.0003

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

0.0001

0.0001

0.0003

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

0.0003

0.0002

0.0000

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

0.0000

0.0000

0.0001

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

0.0007

0.0019

0.0005

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

0.0068

0.1771

0.1184

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

0.0042

0.0729

0.1275

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

0.0101

0.0528

0.1050

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

0.0347

0.0561

0.0938

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

0.1175

0.1902

0.2544

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

0.0068

0.1771

0.1182

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

0.0041

0.0729

0.1272

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

0.0098

0.0527

0.1050

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

0.0346

0.0561

0.0938

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

0.1169

0.1887

0.2540

 

Heating oil

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

0.0027

0.0089

0.0017

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

0.0018

0.0006

0.0005

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

0.0001

0.0002

0.0003

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

0.0002

0.0000

0.0001

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

0.0092

0.0036

0.0013

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

0.1857

0.2080

0.2754

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

0.0499

0.0548

0.1373

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

0.0199

0.0544

0.1122

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

0.0749

0.0969

0.1357

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

0.2376

0.2978

0.2995

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

0.1835

0.2009

0.2742

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

0.0481

0.0543

0.1369

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

0.0198

0.0542

0.1119

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

0.0747

0.0969

0.1356

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

0.2306

0.2953

0.2986

 

Natural gas

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

0.0010

0.0015

0.0010

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

0.0069

0.0109

0.0068

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

0.0056

0.0080

0.0165

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

0.0076

0.0111

0.0312

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

0.0003

0.0301

0.0679

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

0.2017

0.1191

0.2681

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

0.0502

0.0715

0.1153

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

0.0138

0.0329

0.0904

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

0.0454

0.0959

0.1571

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

0.1419

0.2592

0.2853

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

0.2009

0.1178

0.2674

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

0.0436

0.0612

0.1093

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

0.0082

0.0251

0.0751

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

0.0381

0.0857

0.1300

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

0.1416

0.2362

0.2333

  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 realized volatility series as provided by Risk Lab (see Footnote 4 for details)
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