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Table 3 Comparison results of using 2018 and 2019 stock 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

MCD-1step

0.98514

0.97887

0.94412

1.00000

MCD-1step

0.95959

0.96348

0.94559

1.00000

MCD-5steps

1.02720

1.02519

0.88151

1.00000

MCD-5steps

1.00723

1.01169

0.90602

1.00000

MCD-30steps

0.62614

0.63992

0.61153

1.00000

MCD-30steps

1.05239

0.95714

0.77976

1.00000

AAPL-1step

0.92014

0.92317

0.89283

1.00000

AAPL-1step

0.84533

0.81326

0.81872

1.00000

AAPL-5steps

0.84798

0.73461*

0.71233

1.00000

AAPL-5steps

0.85401

0.79254

0.68792

1.00000

AAPL-30steps

0.38612

0.36324

0.37081

1.00000

AAPL-30steps

0.99043

0.99286

0.72892

1.00000

BAC-1step

0.94952

0.93842

0.92619

1.00000

BAC-1step

1.04272

1.04722

0.98605

1.00000

BAC-5steps

0.83395

0.79158

0.72512

1.00000

BAC-5steps

1.22761

1.20195

0.95436

1.00000

BAC-30steps

1.34367

0.90675*

0.87630

1.00000

BAC-30steps

1.45020

1.41788

1.03482

1.00000

MSFT-1step

0.91705

0.90936

0.95921

1.00000

MSFT-1step

1.03308

1.00101

0.95347

1.00000

MSFT-5steps

0.74553

0.74267

0.74237

1.00000

MSFT-5steps

1.22340

1.18205

0.95417

1.00000

MSFT-30steps

0.66990

0.64770

0.64717

1.00000

MSFT-30steps

1.23020

1.21337

0.98476

1.00000

Tesla-1step

1.00181

0.96074

0.86238

1.00000

Tesla-1step

1.00428

1.01934

0.98955

1.00000

Tesla-5steps

1.20383

1.13335

1.01560

1.00000

Tesla-5steps

1.06610

1.07506

0.96107

1.00000

Tesla-30steps

1.97328

1.84871

1.25005

1.00000

Tesla-30steps

2.00623

1.71782*

0.84366

1.00000

Bitcoin-1step

0.99636

1.01731

0.97734

1.00000

Bitcoin-1step

0.89929

0.88914

0.87256

1.00000

Bitcoin-5steps

1.02021

1.11880

0.93826

1.00000

Bitcoin-5steps

0.62312

0.63075

0.56789

1.00000

Bitcoin-30steps

0.86649

0.95506

0.91364

1.00000

Bitcoin-30steps

0.00733

0.00749

0.00631

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. The benchmark is the GARCH-direct method, so 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. Cell with \(*\) indicate 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