Table 7 Sub-sample VaR and ES Results for Long PBW Positions at 97.5% Confidence.

From: Tailoring tail risk models for clean energy investments: a dual approach to long and short position forecasting

 

GARCH

GJRGARCH

IGARCH

 

N

ST

HS

CF

N

ST

HS

CF

N

ST

HS

CF

Panel A: Sample I

          

mVaR

−6.470−

6.904

−6.974

−7.137

−6.479

−7.027

−7.040

−7.175

−6.857

−7.234

−7.200

−7.627

stdVaR

4.052

4.355

4.329

4.460

4.057

4.475

4.371

4.491

4.060

4.329

4.344

4.454

mES

−7.725

−8.731

−8.832

−9.049

−7.730

−8.863

−8.800

−9.118

−8.184

−9.210

−9.245

−9.753

stdES

4.834

5.524

5.423

5.602

4.835

5.644

5.373

5.667

4.845

5.479

5.457

5.572

AE

2.709

2.072

1.912

1.753

2.231

1.753

1.753

1.753

2.072

1.434

1.434

0.956

ADMax

1.083

0.987

1.003

0.972

1.243

1.025

1.047

0.931

0.932

0.960

1.057

1.076

Tick

0.223

0.212

0.210

0.209

0.219

0.209

0.210

0.208

0.208

0.203

0.206

0.204

FZL

2.275

2.175

2.155

2.141

2.238

2.138

2.142

2.126

2.143

2.099

2.114

2.095

Panel B: Sample II

          

mVaR

−5.902

−6.613

−6.579

−6.893

−5.730

-6.354

-6.226

−6.649

−6.120−

6.813

−6.772

−7.155

stdVaR

2.884

3.128

3.214

3.234

3.197

3.601

3.430

3.519

2.917

3.202

3.248

3.265

mES

−7.070

−9.088

−9.090

−9.264

−6.860

−8.762

-8.641

−8.988

−7.329−

9.409

−9.333

−9.608

stdES

3.427

4.048

4.191

4.169

3.795

4.691

4.492

4.552

3.467

4.130

4.235

4.198

AE

1.120

1.120

1.120

1.120

1.280

1.120

1.280

1.120

1.120

1.120

1.120

1.120

ADMax

6.918

6.335

6.980

6.451

6.682

5.982

6.677

6.213

6.466

5.857

6.631

5.900

Tick

0.269

0.267

0.280

0.271

0.257

0.250

0.264

0.258

0.267

0.264

0.278

0.269

FZL

2.459

2.368

2.431

2.393

2.457

2.339

2.421

2.384

2.418

2.335

2.404

2.363

Panel C: Sample III

          

mVaR

−5.304

−5.575

−5.360

-6.074

−5.512

−5.907

−5.446

-6.250

−5.380

−5.657−

5.365

−6.180

stdVaR

1.476

1.602

1.528

1.780

1.549

1.754

1.617

1.841

1.498

1.625

1.571

1.794

mES

−6.376

−7.669

−7.873

−8.211−

6.619

−8.136

−7.956

-8.454

−6.465

−7.846

−7.958

−8.377

stdES

1.757

2.251

2.366

2.474

1.843

2.447

2.441

2.545

1.783

2.272

2.384

2.476

AE

1.606

1.124

1.446

0.964

0.964

0.803

1.285

0.482

1.446

1.124

1.446

0.803

ADMax

1.928

1.819

1.981

1.467

1.706

1.510

1.925

1.237

1.952

1.819

2.078

1.481

Tick

0.155

0.155

0.156

0.156

0.152

0.154

0.154

0.158

0.155

0.155

0.159

0.157

FZL

1.903

1.897

1.915

1.900

1.868

1.883

1.900

1.906

1.897

1.901

1.932

1.905

  1. The table presents the mean values and standard deviations of VaR and ES forecasts at 97.5% confidence level for long positions in PBW. Additionally, it includes backtesting outcomes for three GARCH variants paired with different distributions: normal (N), skewed t (ST), historical simulation (HS), or Cornish-Fisher expansion (CF) over the sub-sample forecast horizons. The table shows the AE ratio, the absolute maximum deviation (ADMax) and mean values of the tick and FZL metrics.
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