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Theory and Modern Applications

Table B1 Critical values for FI models only intercept included in fractional frequency Fourier function \(d = (0.1, 0.5)\)

From: Fractional unit-root tests allowing for a fractional frequency flexible Fourier form trend: predictability of Covid-19

T

100

250

500

1%

5%

10%

1%

5%

10%

1%

5%

10%

k = 1.1

0.1

−4.269

−3.601

−3.265

−4.140

−3.508

−3.180

−4.078

−3.481

−3.166

0.2

−3.981

−3.303

−2.982

−3.829

−3.243

−2.916

−3.876

−3.232

−2.906

0.3

−3.693

−3.043

−2.728

−3.618

−2.995

−2.641

−3.522

−2.949

−2.623

0.4

−3.523

−2.808

−2.457

−3.450

−2.768

−2.402

−3.326

−2.703

−2.355

0.5

−3.295

−2.610

−2.232

−3.166

−2.485

−2.118

−3.097

−2.449

−2.079

k = 1.2

0.1

−4.166

−3.533

−3.179

−4.066

−3.442

−3.144

−4.103

−3.444

−3.108

0.2

−3.971

−3.259

−2.922

−3.816

−3.193

−2.852

−3.762

−3.188

−2.859

0.3

−3.650

−2.991

−2.675

−3.622

−2.970

−2.618

−3.644

−2.937

−2.601

0.4

−3.468

−2.774

−2.455

−3.337

−2.728

−2.373

−3.307

−2.663

−2.324

0.5

−3.292

−2.607

−2.211

−3.171

−2.486

−2.141

−3.105

−2.461

−2.071

k = 1.3

0.1

−4.119

−3.429

−3.083

−4.024

−3.377

−3.047

−4.042

−3.377

−3.058

0.2

−3.988

−3.271

−2.935

−3.844

−3.200

−2.854

−3.744

−3.155

−2.833

0.3

−3.687

−3.021

−2.682

−3.593

−2.942

−2.625

−3.542

−2.931

−2.575

0.4

−3.516

−2.834

−2.475

−3.437

−2.705

−2.355

−3.290

−2.667

−2.315

0.5

−3.304

−2.584

−2.245

−3.188

−2.505

−2.148

−3.074

−2.472

−2.109

k = 1.4

0.1

−4.091

−3.409

−3.046

−3.925

−3.352

−3.035

−3.942

−3.353

−3.004

0.2

−3.938

−3.234

−2.861

−3.805

−3.143

−2.782

−3.737

−3.151

−2.814

0.3

−3.625

−3.001

−2.649

−3.566

−2.936

−2.595

−3.529

−2.878

−2.561

0.4

−3.495

−2.760

−2.424

−3.409

−2.682

−2.371

−3.346

−2.677

−2.321

0.5

−3.302

−2.629

−2.263

−3.125

−2.474

−2.124

−3.117

−2.453

−2.091

k = 1.5

0.1

−4.045

−3.355

−3.011

−3.939

−3.299

−2.936

−3.895

−3.288

−2.939

0.2

−3.850

−3.130

−2.782

−3.738

−3.079

−2.740

−3.714

−3.065

−2.746

0.3

−3.580

−2.941

−2.604

−3.476

−2.857

−2.516

−3.535

−2.876

−2.512

0.4

−3.420

−2.736

−2.392

−3.394

−2.715

−2.358

−3.263

−2.609

−2.276

0.5

−3.260

−2.550

−2.199

−3.126

−2.460

−2.103

−3.062

−2.422

−2.065

k = 1.6

0.1

−3.991

−3.293

−2.923

−3.938

−3.254

−2.908

−3.929

−3.275

−2.920

0.2

−3.745

−3.105

−2.752

−3.711

−3.073

−2.737

−3.668

−3.065

−2.710

0.3

−3.619

−2.948

−2.573

−3.540

−2.857

−2.522

−3.440

−2.822

−2.482

0.4

−3.458

−2.740

−2.379

−3.337

−2.643

−2.293

−3.228

−2.608

−2.254

0.5

−3.208

−2.542

−2.169

−3.063

−2.445

−2.069

−3.079

−2.370

−2.030

k = 1.7

0.1

−3.884

−3.261

−2.899

−3.922

−3.230

−2.864

−3.792

−3.208

−2.878

0.2

−3.748

−3.112

−2.733

−3.634

−3.019

−2.689

−3.644

−3.010

−2.645

0.3

−3.573

−2.886

−2.537

−3.499

−2.837

−2.491

−3.504

−2.809

−2.469

0.4

−3.448

−2.689

−2.340

−3.283

−2.635

−2.283

−3.269

−2.571

−2.213

0.5

−3.199

−2.510

−2.137

−3.102

−2.423

−2.072

−3.019

−2.397

−1.999

k = 1.8

0.1

−3.870

−3.212

−2.856

−3.876

−3.194

−2.854

−3.817

−3.161

−2.825

0.2

−3.727

−3.058

−2.693

−3.672

−3.023

−2.669

−3.592

−2.992

−2.648

0.3

−3.524

−2.846

−2.497

−3.488

−2.845

−2.493

−3.406

−2.749

−2.413

0.4

−3.319

−2.685

−2.330

−3.294

−2.624

−2.261

−3.241

−2.589

−2.236

0.5

−3.225

−2.520

−2.149

−3.015

−2.398

−2.055

−3.017

−2.361

−2.008

k = 1.9

0.1

−3.894

−3.198

−2.814

−3.805

−3.164

−2.824

−3.771

−3.156

−2.807

0.2

−3.712

−3.016

−2.650

−3.642

−3.003

−2.651

−3.623

−2.962

−2.626

0.3

−3.480

−2.830

−2.484

−3.445

−2.818

−2.448

−3.458

−2.773

−2.415

0.4

−3.347

−2.678

−2.296

−3.178

−2.567

−2.231

−3.223

−2.540

−2.185

0.5

−3.179

−2.477

−2.122

−3.057

−2.415

−2.072

−3.002

−2.372

−2.016

k = 2.0

0.1

−3.852

−3.165

−2.797

−3.837

−3.119

−2.777

−3.737

−3.111

−2.770

0.2

−3.652

−3.030

−2.655

−3.604

−2.963

−2.634

−3.537

−2.930

−2.594

0.3

−3.533

−2.856

−2.472

−3.480

−2.782

−2.409

−3.361

−2.742

−2.414

0.4

−3.265

−2.636

−2.272

−3.263

−2.590

−2.221

−3.186

−2.556

−2.212

0.5

−3.215

−2.500

−2.143

−3.053

−2.379

−2.010

−2.941

−2.312

−1.965