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Table 4 Comparison results of using 2018 and 2019 index data

From: A model-free approach to do long-term volatility forecasting and its variants

2018

GE

GA

P-GA

GARCH

2019

GE

GA

P-GA

GARCH

NASDAQ-1step

0.91309

0.92303

0.92421

1.00000

NASDAQ-1step

0.99960

0.98950

0.93843

1.00000

NASDAQ-5steps

0.76419

0.79718

0.78823

1.00000

NASDAQ-5steps

1.15282

1.09176

0.84051

1.00000

NASDAQ-30steps

0.66520

0.65489

0.67389

1.00000

NASDAQ-30steps

0.68994

0.69846

0.59218

1.00000

NYSE-1step

0.93509

0.93401

0.96619

1.00000

NYSE-1step

0.92486

0.91118

0.92193

1.00000

NYSE-5steps

0.83725

0.79330

0.75822

1.00000

NYSE-5steps

0.86249

0.82114

0.71038

1.00000

NYSE-30steps

0.75053

0.61443*

0.61830

1.00000

NYSE-30steps

0.22122

0.22173

0.18116

1.00000

Smallcap-1step

0.90546

0.91346

0.91101

1.00000

Smallcap-1step

1.02041

1.00626

0.98482

1.00000

Smallcap-5steps

0.72627

0.73955

0.73223

1.00000

Smallcap-5steps

1.15868

1.08929

0.85490

1.00000

Samllcap-30steps

0.50005

0.46482

0.46312

1.00000

Samllcap-30steps

1.30467

1.28949

0.90360

1.00000

Djones-1step

0.90932

0.90707

0.91192

1.00000

Djones-1step

0.96752

0.96433

0.96977

1.00000

Djones-5steps

0.82480

0.79965

0.76226

1.00000

Djones-5steps

0.98725

0.93315

0.91238

1.00000

Djones-30steps

0.72547

0.53021*

0.56854

1.00000

Djones-30steps

0.86333

0.85006

0.81803

1.00000

S &P500-1step

0.91860

0.91256

0.88405

1.00000

S &P500-1step

0.96978

0.96526

0.93162

1.00000

S &P500-5steps

0.85108

0.77305

0.75646

1.00000

S &P500-5steps

0.96704

0.94028

0.77434

1.00000

S &P500-30steps

0.88917

0.68156*

0.72104

1.00000

S &P500-30steps

0.34389

0.34537

0.30127

1.00000

BSE-1step

0.99942

0.88322*

0.92568

1.00000

BSE-1step

0.70667

0.70194

0.66667

1.00000

BSE-5steps

0.92061

0.78484*

0.84408

1.00000

BSE-5steps

0.25675

0.25897

0.23603

1.00000

BSE-30steps

0.52431

0.41010*

0.44092

1.00000

BSE-30steps

0.03764

0.03951

0.02888

1.00000

BIST-1step

0.93221

0.92215

0.94138

1.00000

BIST-1step

0.96807

0.97209

0.98234

1.00000

BIST-5steps

0.82149

0.79664

0.81417

1.00000

BIST-5steps

0.98944

1.03903

0.85370

1.00000

BIST-30steps

1.34581

1.42233

1.09900

1.00000

BIST-30steps

2.21996

2.10562

0.85743

1.00000

  1. Column names “GA” and “GE” represent GE-NoVaS and GA-NoVaS methods, respectively; “GARCH” means the GARCH-direct method; and “P-GA” means the P-GA-NoVaS method. As the benchmark is the GARCH-direct method, numerical values in the table corresponding to the GARCH-direct method are 1. Other numerical values are relative performance compared to the GARCH-direct method. The bold value indicates that the corresponding method is the optimal choice for this data case. A cell with \(*\) indicates that the GA-NoVaS method is at least 10\(\%\) better than the GE-NoVaS method, or inversely, the GE-NoVaS method is at least 10\(\%\) better
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